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@@ -1,3804 +0,0 @@
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-/********************************************************************************//**
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-\file OVR_Math.h
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-\brief Implementation of 3D primitives such as vectors, matrices.
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-\copyright Copyright 2014-2016 Oculus VR, LLC All Rights reserved.
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-*************************************************************************************/
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-
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-#ifndef OVR_Math_h
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-#define OVR_Math_h
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-
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-
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-// This file is intended to be independent of the rest of LibOVR and LibOVRKernel and thus
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-// has no #include dependencies on either.
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-
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-#include <math.h>
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-#include <stdint.h>
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-#include <stdlib.h>
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-#include <stdio.h>
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-#include <string.h>
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-#include <float.h>
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-#include "../OVR_CAPI.h" // Currently required due to a dependence on the ovrFovPort_ declaration.
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-
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-#if defined(_MSC_VER)
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- #pragma warning(push)
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- #pragma warning(disable: 4127) // conditional expression is constant
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-#endif
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-
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-
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-#if defined(_MSC_VER)
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- #define OVRMath_sprintf sprintf_s
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-#else
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- #define OVRMath_sprintf snprintf
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-#endif
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-
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-
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-//-------------------------------------------------------------------------------------
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-// ***** OVR_MATH_ASSERT
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-//
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-// Independent debug break implementation for OVR_Math.h.
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-
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-#if !defined(OVR_MATH_DEBUG_BREAK)
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- #if defined(_DEBUG)
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- #if defined(_MSC_VER)
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- #define OVR_MATH_DEBUG_BREAK __debugbreak()
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- #else
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- #define OVR_MATH_DEBUG_BREAK __builtin_trap()
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- #endif
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- #else
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- #define OVR_MATH_DEBUG_BREAK ((void)0)
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- #endif
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-#endif
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-
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-
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-//-------------------------------------------------------------------------------------
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-// ***** OVR_MATH_ASSERT
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-//
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-// Independent OVR_MATH_ASSERT implementation for OVR_Math.h.
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-
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-#if !defined(OVR_MATH_ASSERT)
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- #if defined(_DEBUG)
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- #define OVR_MATH_ASSERT(p) if (!(p)) { OVR_MATH_DEBUG_BREAK; }
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- #else
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- #define OVR_MATH_ASSERT(p) ((void)0)
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- #endif
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-#endif
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-
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-
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-//-------------------------------------------------------------------------------------
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-// ***** OVR_MATH_STATIC_ASSERT
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-//
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-// Independent OVR_MATH_ASSERT implementation for OVR_Math.h.
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-
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-#if !defined(OVR_MATH_STATIC_ASSERT)
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- #if defined(__cplusplus) && ((defined(_MSC_VER) && (defined(_MSC_VER) >= 1600)) || defined(__GXX_EXPERIMENTAL_CXX0X__) || (__cplusplus >= 201103L))
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- #define OVR_MATH_STATIC_ASSERT static_assert
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- #else
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- #if !defined(OVR_SA_UNUSED)
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- #if defined(__GNUC__) || defined(__clang__)
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- #define OVR_SA_UNUSED __attribute__((unused))
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- #else
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- #define OVR_SA_UNUSED
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- #endif
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- #define OVR_SA_PASTE(a,b) a##b
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- #define OVR_SA_HELP(a,b) OVR_SA_PASTE(a,b)
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- #endif
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-
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- #define OVR_MATH_STATIC_ASSERT(expression, msg) typedef char OVR_SA_HELP(compileTimeAssert, __LINE__) [((expression) != 0) ? 1 : -1] OVR_SA_UNUSED
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- #endif
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-#endif
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-
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-
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-
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-namespace OVR {
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-
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-template<class T>
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-const T OVRMath_Min(const T a, const T b)
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-{ return (a < b) ? a : b; }
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-
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-template<class T>
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-const T OVRMath_Max(const T a, const T b)
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-{ return (b < a) ? a : b; }
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-
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-template<class T>
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-void OVRMath_Swap(T& a, T& b)
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-{ T temp(a); a = b; b = temp; }
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-
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-
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-//-------------------------------------------------------------------------------------
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-// ***** Constants for 3D world/axis definitions.
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-
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-// Definitions of axes for coordinate and rotation conversions.
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-enum Axis
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-{
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- Axis_X = 0, Axis_Y = 1, Axis_Z = 2
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-};
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-
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-// RotateDirection describes the rotation direction around an axis, interpreted as follows:
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-// CW - Clockwise while looking "down" from positive axis towards the origin.
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-// CCW - Counter-clockwise while looking from the positive axis towards the origin,
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-// which is in the negative axis direction.
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-// CCW is the default for the RHS coordinate system. Oculus standard RHS coordinate
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-// system defines Y up, X right, and Z back (pointing out from the screen). In this
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-// system Rotate_CCW around Z will specifies counter-clockwise rotation in XY plane.
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-enum RotateDirection
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-{
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- Rotate_CCW = 1,
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- Rotate_CW = -1
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-};
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-
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-// Constants for right handed and left handed coordinate systems
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-enum HandedSystem
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-{
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- Handed_R = 1, Handed_L = -1
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-};
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-
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-// AxisDirection describes which way the coordinate axis points. Used by WorldAxes.
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-enum AxisDirection
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-{
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- Axis_Up = 2,
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- Axis_Down = -2,
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- Axis_Right = 1,
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- Axis_Left = -1,
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- Axis_In = 3,
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- Axis_Out = -3
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-};
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-
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-struct WorldAxes
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-{
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- AxisDirection XAxis, YAxis, ZAxis;
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-
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- WorldAxes(AxisDirection x, AxisDirection y, AxisDirection z)
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- : XAxis(x), YAxis(y), ZAxis(z)
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- { OVR_MATH_ASSERT(abs(x) != abs(y) && abs(y) != abs(z) && abs(z) != abs(x));}
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-};
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-
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-} // namespace OVR
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-
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-
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-//------------------------------------------------------------------------------------//
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-// ***** C Compatibility Types
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-
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-// These declarations are used to support conversion between C types used in
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-// LibOVR C interfaces and their C++ versions. As an example, they allow passing
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-// Vector3f into a function that expects ovrVector3f.
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-
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-typedef struct ovrQuatf_ ovrQuatf;
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-typedef struct ovrQuatd_ ovrQuatd;
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-typedef struct ovrSizei_ ovrSizei;
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-typedef struct ovrSizef_ ovrSizef;
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-typedef struct ovrSized_ ovrSized;
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-typedef struct ovrRecti_ ovrRecti;
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-typedef struct ovrVector2i_ ovrVector2i;
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-typedef struct ovrVector2f_ ovrVector2f;
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-typedef struct ovrVector2d_ ovrVector2d;
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-typedef struct ovrVector3f_ ovrVector3f;
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-typedef struct ovrVector3d_ ovrVector3d;
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-typedef struct ovrVector4f_ ovrVector4f;
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-typedef struct ovrVector4d_ ovrVector4d;
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-typedef struct ovrMatrix2f_ ovrMatrix2f;
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-typedef struct ovrMatrix2d_ ovrMatrix2d;
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-typedef struct ovrMatrix3f_ ovrMatrix3f;
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-typedef struct ovrMatrix3d_ ovrMatrix3d;
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-typedef struct ovrMatrix4f_ ovrMatrix4f;
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-typedef struct ovrMatrix4d_ ovrMatrix4d;
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-typedef struct ovrPosef_ ovrPosef;
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-typedef struct ovrPosed_ ovrPosed;
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-typedef struct ovrPoseStatef_ ovrPoseStatef;
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-typedef struct ovrPoseStated_ ovrPoseStated;
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-
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-namespace OVR {
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-
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-// Forward-declare our templates.
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-template<class T> class Quat;
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-template<class T> class Size;
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-template<class T> class Rect;
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-template<class T> class Vector2;
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-template<class T> class Vector3;
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-template<class T> class Vector4;
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-template<class T> class Matrix2;
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-template<class T> class Matrix3;
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-template<class T> class Matrix4;
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-template<class T> class Pose;
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-template<class T> class PoseState;
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-
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-// CompatibleTypes::Type is used to lookup a compatible C-version of a C++ class.
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-template<class C>
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-struct CompatibleTypes
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-{
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- // Declaration here seems necessary for MSVC; specializations are
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- // used instead.
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- typedef struct {} Type;
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-};
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-
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-// Specializations providing CompatibleTypes::Type value.
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-template<> struct CompatibleTypes<Quat<float> > { typedef ovrQuatf Type; };
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-template<> struct CompatibleTypes<Quat<double> > { typedef ovrQuatd Type; };
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-template<> struct CompatibleTypes<Matrix2<float> > { typedef ovrMatrix2f Type; };
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-template<> struct CompatibleTypes<Matrix2<double> > { typedef ovrMatrix2d Type; };
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-template<> struct CompatibleTypes<Matrix3<float> > { typedef ovrMatrix3f Type; };
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-template<> struct CompatibleTypes<Matrix3<double> > { typedef ovrMatrix3d Type; };
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-template<> struct CompatibleTypes<Matrix4<float> > { typedef ovrMatrix4f Type; };
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-template<> struct CompatibleTypes<Matrix4<double> > { typedef ovrMatrix4d Type; };
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-template<> struct CompatibleTypes<Size<int> > { typedef ovrSizei Type; };
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-template<> struct CompatibleTypes<Size<float> > { typedef ovrSizef Type; };
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-template<> struct CompatibleTypes<Size<double> > { typedef ovrSized Type; };
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-template<> struct CompatibleTypes<Rect<int> > { typedef ovrRecti Type; };
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-template<> struct CompatibleTypes<Vector2<int> > { typedef ovrVector2i Type; };
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-template<> struct CompatibleTypes<Vector2<float> > { typedef ovrVector2f Type; };
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-template<> struct CompatibleTypes<Vector2<double> > { typedef ovrVector2d Type; };
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-template<> struct CompatibleTypes<Vector3<float> > { typedef ovrVector3f Type; };
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-template<> struct CompatibleTypes<Vector3<double> > { typedef ovrVector3d Type; };
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-template<> struct CompatibleTypes<Vector4<float> > { typedef ovrVector4f Type; };
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-template<> struct CompatibleTypes<Vector4<double> > { typedef ovrVector4d Type; };
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-template<> struct CompatibleTypes<Pose<float> > { typedef ovrPosef Type; };
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-template<> struct CompatibleTypes<Pose<double> > { typedef ovrPosed Type; };
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-
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-//------------------------------------------------------------------------------------//
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-// ***** Math
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-//
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-// Math class contains constants and functions. This class is a template specialized
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-// per type, with Math<float> and Math<double> being distinct.
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-template<class T>
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-class Math
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-{
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-public:
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- // By default, support explicit conversion to float. This allows Vector2<int> to
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- // compile, for example.
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- typedef float OtherFloatType;
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-
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- static int Tolerance() { return 0; } // Default value so integer types compile
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-};
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-
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-
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-//------------------------------------------------------------------------------------//
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-// ***** double constants
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-#define MATH_DOUBLE_PI 3.14159265358979323846
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-#define MATH_DOUBLE_TWOPI (2*MATH_DOUBLE_PI)
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-#define MATH_DOUBLE_PIOVER2 (0.5*MATH_DOUBLE_PI)
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-#define MATH_DOUBLE_PIOVER4 (0.25*MATH_DOUBLE_PI)
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-#define MATH_FLOAT_MAXVALUE (FLT_MAX)
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-
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-#define MATH_DOUBLE_RADTODEGREEFACTOR (360.0 / MATH_DOUBLE_TWOPI)
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-#define MATH_DOUBLE_DEGREETORADFACTOR (MATH_DOUBLE_TWOPI / 360.0)
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-
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-#define MATH_DOUBLE_E 2.71828182845904523536
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-#define MATH_DOUBLE_LOG2E 1.44269504088896340736
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-#define MATH_DOUBLE_LOG10E 0.434294481903251827651
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-#define MATH_DOUBLE_LN2 0.693147180559945309417
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-#define MATH_DOUBLE_LN10 2.30258509299404568402
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-
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-#define MATH_DOUBLE_SQRT2 1.41421356237309504880
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-#define MATH_DOUBLE_SQRT1_2 0.707106781186547524401
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-
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-#define MATH_DOUBLE_TOLERANCE 1e-12 // a default number for value equality tolerance: about 4500*Epsilon;
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-#define MATH_DOUBLE_SINGULARITYRADIUS 1e-12 // about 1-cos(.0001 degree), for gimbal lock numerical problems
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-
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-//------------------------------------------------------------------------------------//
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-// ***** float constants
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-#define MATH_FLOAT_PI float(MATH_DOUBLE_PI)
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-#define MATH_FLOAT_TWOPI float(MATH_DOUBLE_TWOPI)
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-#define MATH_FLOAT_PIOVER2 float(MATH_DOUBLE_PIOVER2)
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-#define MATH_FLOAT_PIOVER4 float(MATH_DOUBLE_PIOVER4)
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-
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-#define MATH_FLOAT_RADTODEGREEFACTOR float(MATH_DOUBLE_RADTODEGREEFACTOR)
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-#define MATH_FLOAT_DEGREETORADFACTOR float(MATH_DOUBLE_DEGREETORADFACTOR)
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-
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-#define MATH_FLOAT_E float(MATH_DOUBLE_E)
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-#define MATH_FLOAT_LOG2E float(MATH_DOUBLE_LOG2E)
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-#define MATH_FLOAT_LOG10E float(MATH_DOUBLE_LOG10E)
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-#define MATH_FLOAT_LN2 float(MATH_DOUBLE_LN2)
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-#define MATH_FLOAT_LN10 float(MATH_DOUBLE_LN10)
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-
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-#define MATH_FLOAT_SQRT2 float(MATH_DOUBLE_SQRT2)
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-#define MATH_FLOAT_SQRT1_2 float(MATH_DOUBLE_SQRT1_2)
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-
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-#define MATH_FLOAT_TOLERANCE 1e-5f // a default number for value equality tolerance: 1e-5, about 84*EPSILON;
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-#define MATH_FLOAT_SINGULARITYRADIUS 1e-7f // about 1-cos(.025 degree), for gimbal lock numerical problems
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-
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-
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-
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-// Single-precision Math constants class.
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-template<>
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-class Math<float>
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-{
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-public:
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- typedef double OtherFloatType;
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-
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- static inline float Tolerance() { return MATH_FLOAT_TOLERANCE; }; // a default number for value equality tolerance
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- static inline float SingularityRadius() { return MATH_FLOAT_SINGULARITYRADIUS; }; // for gimbal lock numerical problems
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-};
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-
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-// Double-precision Math constants class
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-template<>
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-class Math<double>
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-{
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-public:
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- typedef float OtherFloatType;
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-
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- static inline double Tolerance() { return MATH_DOUBLE_TOLERANCE; }; // a default number for value equality tolerance
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- static inline double SingularityRadius() { return MATH_DOUBLE_SINGULARITYRADIUS; }; // for gimbal lock numerical problems
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-};
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-
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-typedef Math<float> Mathf;
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-typedef Math<double> Mathd;
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-
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-// Conversion functions between degrees and radians
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-// (non-templated to ensure passing int arguments causes warning)
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-inline float RadToDegree(float rad) { return rad * MATH_FLOAT_RADTODEGREEFACTOR; }
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-inline double RadToDegree(double rad) { return rad * MATH_DOUBLE_RADTODEGREEFACTOR; }
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-
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-inline float DegreeToRad(float deg) { return deg * MATH_FLOAT_DEGREETORADFACTOR; }
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-inline double DegreeToRad(double deg) { return deg * MATH_DOUBLE_DEGREETORADFACTOR; }
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-
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-// Square function
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-template<class T>
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-inline T Sqr(T x) { return x*x; }
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-
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-// Sign: returns 0 if x == 0, -1 if x < 0, and 1 if x > 0
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-template<class T>
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-inline T Sign(T x) { return (x != T(0)) ? (x < T(0) ? T(-1) : T(1)) : T(0); }
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-
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-// Numerically stable acos function
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-inline float Acos(float x) { return (x > 1.0f) ? 0.0f : (x < -1.0f) ? MATH_FLOAT_PI : acosf(x); }
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-inline double Acos(double x) { return (x > 1.0) ? 0.0 : (x < -1.0) ? MATH_DOUBLE_PI : acos(x); }
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-
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-// Numerically stable asin function
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-inline float Asin(float x) { return (x > 1.0f) ? MATH_FLOAT_PIOVER2 : (x < -1.0f) ? -MATH_FLOAT_PIOVER2 : asinf(x); }
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-inline double Asin(double x) { return (x > 1.0) ? MATH_DOUBLE_PIOVER2 : (x < -1.0) ? -MATH_DOUBLE_PIOVER2 : asin(x); }
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-
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-#if defined(_MSC_VER)
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- inline int isnan(double x) { return ::_isnan(x); }
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-#elif !defined(isnan) // Some libraries #define isnan.
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- inline int isnan(double x) { return ::isnan(x); }
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-#endif
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-
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-template<class T>
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-class Quat;
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-
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-
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-//-------------------------------------------------------------------------------------
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-// ***** Vector2<>
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-
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-// Vector2f (Vector2d) represents a 2-dimensional vector or point in space,
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-// consisting of coordinates x and y
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-
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-template<class T>
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-class Vector2
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-{
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-public:
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- typedef T ElementType;
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- static const size_t ElementCount = 2;
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-
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- T x, y;
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-
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- Vector2() : x(0), y(0) { }
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- Vector2(T x_, T y_) : x(x_), y(y_) { }
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- explicit Vector2(T s) : x(s), y(s) { }
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- explicit Vector2(const Vector2<typename Math<T>::OtherFloatType> &src)
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- : x((T)src.x), y((T)src.y) { }
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-
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- static Vector2 Zero() { return Vector2(0, 0); }
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-
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- // C-interop support.
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- typedef typename CompatibleTypes<Vector2<T> >::Type CompatibleType;
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-
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- Vector2(const CompatibleType& s) : x(s.x), y(s.y) { }
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-
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- operator const CompatibleType& () const
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- {
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- OVR_MATH_STATIC_ASSERT(sizeof(Vector2<T>) == sizeof(CompatibleType), "sizeof(Vector2<T>) failure");
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- return reinterpret_cast<const CompatibleType&>(*this);
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- }
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-
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-
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- bool operator== (const Vector2& b) const { return x == b.x && y == b.y; }
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- bool operator!= (const Vector2& b) const { return x != b.x || y != b.y; }
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-
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- Vector2 operator+ (const Vector2& b) const { return Vector2(x + b.x, y + b.y); }
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- Vector2& operator+= (const Vector2& b) { x += b.x; y += b.y; return *this; }
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- Vector2 operator- (const Vector2& b) const { return Vector2(x - b.x, y - b.y); }
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- Vector2& operator-= (const Vector2& b) { x -= b.x; y -= b.y; return *this; }
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- Vector2 operator- () const { return Vector2(-x, -y); }
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-
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- // Scalar multiplication/division scales vector.
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- Vector2 operator* (T s) const { return Vector2(x*s, y*s); }
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- Vector2& operator*= (T s) { x *= s; y *= s; return *this; }
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-
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- Vector2 operator/ (T s) const { T rcp = T(1)/s;
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- return Vector2(x*rcp, y*rcp); }
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- Vector2& operator/= (T s) { T rcp = T(1)/s;
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- x *= rcp; y *= rcp;
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- return *this; }
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-
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- static Vector2 Min(const Vector2& a, const Vector2& b) { return Vector2((a.x < b.x) ? a.x : b.x,
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- (a.y < b.y) ? a.y : b.y); }
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- static Vector2 Max(const Vector2& a, const Vector2& b) { return Vector2((a.x > b.x) ? a.x : b.x,
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- (a.y > b.y) ? a.y : b.y); }
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-
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- Vector2 Clamped(T maxMag) const
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- {
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- T magSquared = LengthSq();
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- if (magSquared <= Sqr(maxMag))
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- return *this;
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- else
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- return *this * (maxMag / sqrt(magSquared));
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- }
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-
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- // Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
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- bool IsEqual(const Vector2& b, T tolerance =Math<T>::Tolerance()) const
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- {
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- return (fabs(b.x-x) <= tolerance) &&
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- (fabs(b.y-y) <= tolerance);
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- }
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- bool Compare(const Vector2& b, T tolerance = Math<T>::Tolerance()) const
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- {
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- return IsEqual(b, tolerance);
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- }
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-
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- // Access element by index
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- T& operator[] (int idx)
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- {
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- OVR_MATH_ASSERT(0 <= idx && idx < 2);
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- return *(&x + idx);
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- }
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- const T& operator[] (int idx) const
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- {
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- OVR_MATH_ASSERT(0 <= idx && idx < 2);
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- return *(&x + idx);
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- }
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-
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- // Entry-wise product of two vectors
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- Vector2 EntrywiseMultiply(const Vector2& b) const { return Vector2(x * b.x, y * b.y);}
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-
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-
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- // Multiply and divide operators do entry-wise math. Used Dot() for dot product.
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- Vector2 operator* (const Vector2& b) const { return Vector2(x * b.x, y * b.y); }
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- Vector2 operator/ (const Vector2& b) const { return Vector2(x / b.x, y / b.y); }
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-
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- // Dot product
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- // Used to calculate angle q between two vectors among other things,
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- // as (A dot B) = |a||b|cos(q).
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- T Dot(const Vector2& b) const { return x*b.x + y*b.y; }
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-
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- // Returns the angle from this vector to b, in radians.
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- T Angle(const Vector2& b) const
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- {
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- T div = LengthSq()*b.LengthSq();
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- OVR_MATH_ASSERT(div != T(0));
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- T result = Acos((this->Dot(b))/sqrt(div));
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- return result;
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- }
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-
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- // Return Length of the vector squared.
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- T LengthSq() const { return (x * x + y * y); }
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-
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- // Return vector length.
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- T Length() const { return sqrt(LengthSq()); }
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-
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- // Returns squared distance between two points represented by vectors.
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- T DistanceSq(const Vector2& b) const { return (*this - b).LengthSq(); }
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-
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- // Returns distance between two points represented by vectors.
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- T Distance(const Vector2& b) const { return (*this - b).Length(); }
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-
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- // Determine if this a unit vector.
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- bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
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-
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- // Normalize, convention vector length to 1.
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- void Normalize()
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- {
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- T s = Length();
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- if (s != T(0))
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- s = T(1) / s;
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- *this *= s;
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- }
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-
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- // Returns normalized (unit) version of the vector without modifying itself.
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- Vector2 Normalized() const
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- {
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- T s = Length();
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- if (s != T(0))
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- s = T(1) / s;
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- return *this * s;
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- }
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-
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- // Linearly interpolates from this vector to another.
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- // Factor should be between 0.0 and 1.0, with 0 giving full value to this.
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- Vector2 Lerp(const Vector2& b, T f) const { return *this*(T(1) - f) + b*f; }
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-
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- // Projects this vector onto the argument; in other words,
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- // A.Project(B) returns projection of vector A onto B.
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- Vector2 ProjectTo(const Vector2& b) const
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- {
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- T l2 = b.LengthSq();
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- OVR_MATH_ASSERT(l2 != T(0));
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- return b * ( Dot(b) / l2 );
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- }
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-
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- // returns true if vector b is clockwise from this vector
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- bool IsClockwise(const Vector2& b) const
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- {
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- return (x * b.y - y * b.x) < 0;
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- }
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-};
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-
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-
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-typedef Vector2<float> Vector2f;
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-typedef Vector2<double> Vector2d;
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-typedef Vector2<int> Vector2i;
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-
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-typedef Vector2<float> Point2f;
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-typedef Vector2<double> Point2d;
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-typedef Vector2<int> Point2i;
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-
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-//-------------------------------------------------------------------------------------
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-// ***** Vector3<> - 3D vector of {x, y, z}
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-
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-//
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-// Vector3f (Vector3d) represents a 3-dimensional vector or point in space,
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-// consisting of coordinates x, y and z.
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-
|
|
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-template<class T>
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-class Vector3
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-{
|
|
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-public:
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|
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- typedef T ElementType;
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|
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- static const size_t ElementCount = 3;
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-
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- T x, y, z;
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-
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|
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- // FIXME: default initialization of a vector class can be very expensive in a full-blown
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- // application. A few hundred thousand vector constructions is not unlikely and can add
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- // up to milliseconds of time on processors like the PS3 PPU.
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- Vector3() : x(0), y(0), z(0) { }
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- Vector3(T x_, T y_, T z_ = 0) : x(x_), y(y_), z(z_) { }
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- explicit Vector3(T s) : x(s), y(s), z(s) { }
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- explicit Vector3(const Vector3<typename Math<T>::OtherFloatType> &src)
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- : x((T)src.x), y((T)src.y), z((T)src.z) { }
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-
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- static Vector3 Zero() { return Vector3(0, 0, 0); }
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-
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- // C-interop support.
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- typedef typename CompatibleTypes<Vector3<T> >::Type CompatibleType;
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-
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- Vector3(const CompatibleType& s) : x(s.x), y(s.y), z(s.z) { }
|
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-
|
|
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- operator const CompatibleType& () const
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- {
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- OVR_MATH_STATIC_ASSERT(sizeof(Vector3<T>) == sizeof(CompatibleType), "sizeof(Vector3<T>) failure");
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- return reinterpret_cast<const CompatibleType&>(*this);
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- }
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-
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- bool operator== (const Vector3& b) const { return x == b.x && y == b.y && z == b.z; }
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- bool operator!= (const Vector3& b) const { return x != b.x || y != b.y || z != b.z; }
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-
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- Vector3 operator+ (const Vector3& b) const { return Vector3(x + b.x, y + b.y, z + b.z); }
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- Vector3& operator+= (const Vector3& b) { x += b.x; y += b.y; z += b.z; return *this; }
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- Vector3 operator- (const Vector3& b) const { return Vector3(x - b.x, y - b.y, z - b.z); }
|
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- Vector3& operator-= (const Vector3& b) { x -= b.x; y -= b.y; z -= b.z; return *this; }
|
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- Vector3 operator- () const { return Vector3(-x, -y, -z); }
|
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-
|
|
|
- // Scalar multiplication/division scales vector.
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- Vector3 operator* (T s) const { return Vector3(x*s, y*s, z*s); }
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- Vector3& operator*= (T s) { x *= s; y *= s; z *= s; return *this; }
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-
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- Vector3 operator/ (T s) const { T rcp = T(1)/s;
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- return Vector3(x*rcp, y*rcp, z*rcp); }
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- Vector3& operator/= (T s) { T rcp = T(1)/s;
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- x *= rcp; y *= rcp; z *= rcp;
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- return *this; }
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-
|
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- static Vector3 Min(const Vector3& a, const Vector3& b)
|
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- {
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- return Vector3((a.x < b.x) ? a.x : b.x,
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- (a.y < b.y) ? a.y : b.y,
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- (a.z < b.z) ? a.z : b.z);
|
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- }
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- static Vector3 Max(const Vector3& a, const Vector3& b)
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- {
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- return Vector3((a.x > b.x) ? a.x : b.x,
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- (a.y > b.y) ? a.y : b.y,
|
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- (a.z > b.z) ? a.z : b.z);
|
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- }
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-
|
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- Vector3 Clamped(T maxMag) const
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- {
|
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|
- T magSquared = LengthSq();
|
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- if (magSquared <= Sqr(maxMag))
|
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- return *this;
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- else
|
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|
- return *this * (maxMag / sqrt(magSquared));
|
|
|
- }
|
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|
-
|
|
|
- // Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
|
|
|
- bool IsEqual(const Vector3& b, T tolerance = Math<T>::Tolerance()) const
|
|
|
- {
|
|
|
- return (fabs(b.x-x) <= tolerance) &&
|
|
|
- (fabs(b.y-y) <= tolerance) &&
|
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- (fabs(b.z-z) <= tolerance);
|
|
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- }
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- bool Compare(const Vector3& b, T tolerance = Math<T>::Tolerance()) const
|
|
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- {
|
|
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- return IsEqual(b, tolerance);
|
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- }
|
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-
|
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- T& operator[] (int idx)
|
|
|
- {
|
|
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- OVR_MATH_ASSERT(0 <= idx && idx < 3);
|
|
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- return *(&x + idx);
|
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- }
|
|
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-
|
|
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- const T& operator[] (int idx) const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(0 <= idx && idx < 3);
|
|
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- return *(&x + idx);
|
|
|
- }
|
|
|
-
|
|
|
- // Entrywise product of two vectors
|
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- Vector3 EntrywiseMultiply(const Vector3& b) const { return Vector3(x * b.x,
|
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- y * b.y,
|
|
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- z * b.z);}
|
|
|
-
|
|
|
- // Multiply and divide operators do entry-wise math
|
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- Vector3 operator* (const Vector3& b) const { return Vector3(x * b.x,
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- y * b.y,
|
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- z * b.z); }
|
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|
-
|
|
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- Vector3 operator/ (const Vector3& b) const { return Vector3(x / b.x,
|
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- y / b.y,
|
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- z / b.z); }
|
|
|
-
|
|
|
-
|
|
|
- // Dot product
|
|
|
- // Used to calculate angle q between two vectors among other things,
|
|
|
- // as (A dot B) = |a||b|cos(q).
|
|
|
- T Dot(const Vector3& b) const { return x*b.x + y*b.y + z*b.z; }
|
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-
|
|
|
- // Compute cross product, which generates a normal vector.
|
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|
- // Direction vector can be determined by right-hand rule: Pointing index finder in
|
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- // direction a and middle finger in direction b, thumb will point in a.Cross(b).
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- Vector3 Cross(const Vector3& b) const { return Vector3(y*b.z - z*b.y,
|
|
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- z*b.x - x*b.z,
|
|
|
- x*b.y - y*b.x); }
|
|
|
-
|
|
|
- // Returns the angle from this vector to b, in radians.
|
|
|
- T Angle(const Vector3& b) const
|
|
|
- {
|
|
|
- T div = LengthSq()*b.LengthSq();
|
|
|
- OVR_MATH_ASSERT(div != T(0));
|
|
|
- T result = Acos((this->Dot(b))/sqrt(div));
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- // Return Length of the vector squared.
|
|
|
- T LengthSq() const { return (x * x + y * y + z * z); }
|
|
|
-
|
|
|
- // Return vector length.
|
|
|
- T Length() const { return (T)sqrt(LengthSq()); }
|
|
|
-
|
|
|
- // Returns squared distance between two points represented by vectors.
|
|
|
- T DistanceSq(Vector3 const& b) const { return (*this - b).LengthSq(); }
|
|
|
-
|
|
|
- // Returns distance between two points represented by vectors.
|
|
|
- T Distance(Vector3 const& b) const { return (*this - b).Length(); }
|
|
|
-
|
|
|
- bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
|
|
|
-
|
|
|
- // Normalize, convention vector length to 1.
|
|
|
- void Normalize()
|
|
|
- {
|
|
|
- T s = Length();
|
|
|
- if (s != T(0))
|
|
|
- s = T(1) / s;
|
|
|
- *this *= s;
|
|
|
- }
|
|
|
-
|
|
|
- // Returns normalized (unit) version of the vector without modifying itself.
|
|
|
- Vector3 Normalized() const
|
|
|
- {
|
|
|
- T s = Length();
|
|
|
- if (s != T(0))
|
|
|
- s = T(1) / s;
|
|
|
- return *this * s;
|
|
|
- }
|
|
|
-
|
|
|
- // Linearly interpolates from this vector to another.
|
|
|
- // Factor should be between 0.0 and 1.0, with 0 giving full value to this.
|
|
|
- Vector3 Lerp(const Vector3& b, T f) const { return *this*(T(1) - f) + b*f; }
|
|
|
-
|
|
|
- // Projects this vector onto the argument; in other words,
|
|
|
- // A.Project(B) returns projection of vector A onto B.
|
|
|
- Vector3 ProjectTo(const Vector3& b) const
|
|
|
- {
|
|
|
- T l2 = b.LengthSq();
|
|
|
- OVR_MATH_ASSERT(l2 != T(0));
|
|
|
- return b * ( Dot(b) / l2 );
|
|
|
- }
|
|
|
-
|
|
|
- // Projects this vector onto a plane defined by a normal vector
|
|
|
- Vector3 ProjectToPlane(const Vector3& normal) const { return *this - this->ProjectTo(normal); }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Vector3<float> Vector3f;
|
|
|
-typedef Vector3<double> Vector3d;
|
|
|
-typedef Vector3<int32_t> Vector3i;
|
|
|
-
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Vector3f) == 3*sizeof(float)), "sizeof(Vector3f) failure");
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Vector3d) == 3*sizeof(double)), "sizeof(Vector3d) failure");
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Vector3i) == 3*sizeof(int32_t)), "sizeof(Vector3i) failure");
|
|
|
-
|
|
|
-typedef Vector3<float> Point3f;
|
|
|
-typedef Vector3<double> Point3d;
|
|
|
-typedef Vector3<int32_t> Point3i;
|
|
|
-
|
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-
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-//-------------------------------------------------------------------------------------
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|
|
-// ***** Vector4<> - 4D vector of {x, y, z, w}
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-
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-//
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-// Vector4f (Vector4d) represents a 3-dimensional vector or point in space,
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-// consisting of coordinates x, y, z and w.
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-
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-template<class T>
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-class Vector4
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-{
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-public:
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- typedef T ElementType;
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- static const size_t ElementCount = 4;
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-
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- T x, y, z, w;
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-
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- // FIXME: default initialization of a vector class can be very expensive in a full-blown
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- // application. A few hundred thousand vector constructions is not unlikely and can add
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- // up to milliseconds of time on processors like the PS3 PPU.
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- Vector4() : x(0), y(0), z(0), w(0) { }
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- Vector4(T x_, T y_, T z_, T w_) : x(x_), y(y_), z(z_), w(w_) { }
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- explicit Vector4(T s) : x(s), y(s), z(s), w(s) { }
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- explicit Vector4(const Vector3<T>& v, const T w_=T(1)) : x(v.x), y(v.y), z(v.z), w(w_) { }
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- explicit Vector4(const Vector4<typename Math<T>::OtherFloatType> &src)
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- : x((T)src.x), y((T)src.y), z((T)src.z), w((T)src.w) { }
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-
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- static Vector4 Zero() { return Vector4(0, 0, 0, 0); }
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-
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- // C-interop support.
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- typedef typename CompatibleTypes< Vector4<T> >::Type CompatibleType;
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-
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- Vector4(const CompatibleType& s) : x(s.x), y(s.y), z(s.z), w(s.w) { }
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-
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- operator const CompatibleType& () const
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- {
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- OVR_MATH_STATIC_ASSERT(sizeof(Vector4<T>) == sizeof(CompatibleType), "sizeof(Vector4<T>) failure");
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- return reinterpret_cast<const CompatibleType&>(*this);
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- }
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-
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- Vector4& operator= (const Vector3<T>& other) { x=other.x; y=other.y; z=other.z; w=1; return *this; }
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- bool operator== (const Vector4& b) const { return x == b.x && y == b.y && z == b.z && w == b.w; }
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- bool operator!= (const Vector4& b) const { return x != b.x || y != b.y || z != b.z || w != b.w; }
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-
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- Vector4 operator+ (const Vector4& b) const { return Vector4(x + b.x, y + b.y, z + b.z, w + b.w); }
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- Vector4& operator+= (const Vector4& b) { x += b.x; y += b.y; z += b.z; w += b.w; return *this; }
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- Vector4 operator- (const Vector4& b) const { return Vector4(x - b.x, y - b.y, z - b.z, w - b.w); }
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- Vector4& operator-= (const Vector4& b) { x -= b.x; y -= b.y; z -= b.z; w -= b.w; return *this; }
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- Vector4 operator- () const { return Vector4(-x, -y, -z, -w); }
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-
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- // Scalar multiplication/division scales vector.
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- Vector4 operator* (T s) const { return Vector4(x*s, y*s, z*s, w*s); }
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- Vector4& operator*= (T s) { x *= s; y *= s; z *= s; w *= s;return *this; }
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-
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- Vector4 operator/ (T s) const { T rcp = T(1)/s;
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- return Vector4(x*rcp, y*rcp, z*rcp, w*rcp); }
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- Vector4& operator/= (T s) { T rcp = T(1)/s;
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- x *= rcp; y *= rcp; z *= rcp; w *= rcp;
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- return *this; }
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-
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- static Vector4 Min(const Vector4& a, const Vector4& b)
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- {
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- return Vector4((a.x < b.x) ? a.x : b.x,
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- (a.y < b.y) ? a.y : b.y,
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- (a.z < b.z) ? a.z : b.z,
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- (a.w < b.w) ? a.w : b.w);
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- }
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- static Vector4 Max(const Vector4& a, const Vector4& b)
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- {
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- return Vector4((a.x > b.x) ? a.x : b.x,
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- (a.y > b.y) ? a.y : b.y,
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- (a.z > b.z) ? a.z : b.z,
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- (a.w > b.w) ? a.w : b.w);
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- }
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-
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- Vector4 Clamped(T maxMag) const
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- {
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- T magSquared = LengthSq();
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- if (magSquared <= Sqr(maxMag))
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- return *this;
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- else
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- return *this * (maxMag / sqrt(magSquared));
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- }
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-
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- // Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
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- bool IsEqual(const Vector4& b, T tolerance = Math<T>::Tolerance()) const
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- {
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- return (fabs(b.x-x) <= tolerance) &&
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- (fabs(b.y-y) <= tolerance) &&
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- (fabs(b.z-z) <= tolerance) &&
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- (fabs(b.w-w) <= tolerance);
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- }
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- bool Compare(const Vector4& b, T tolerance = Math<T>::Tolerance()) const
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- {
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- return IsEqual(b, tolerance);
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- }
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-
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- T& operator[] (int idx)
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- {
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- OVR_MATH_ASSERT(0 <= idx && idx < 4);
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- return *(&x + idx);
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- }
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-
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- const T& operator[] (int idx) const
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- {
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- OVR_MATH_ASSERT(0 <= idx && idx < 4);
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- return *(&x + idx);
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- }
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-
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- // Entry wise product of two vectors
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- Vector4 EntrywiseMultiply(const Vector4& b) const { return Vector4(x * b.x,
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- y * b.y,
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- z * b.z,
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- w * b.w);}
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-
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|
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- // Multiply and divide operators do entry-wise math
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- Vector4 operator* (const Vector4& b) const { return Vector4(x * b.x,
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- y * b.y,
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- z * b.z,
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- w * b.w); }
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-
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- Vector4 operator/ (const Vector4& b) const { return Vector4(x / b.x,
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- y / b.y,
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- z / b.z,
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- w / b.w); }
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-
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-
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- // Dot product
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- T Dot(const Vector4& b) const { return x*b.x + y*b.y + z*b.z + w*b.w; }
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-
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- // Return Length of the vector squared.
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- T LengthSq() const { return (x * x + y * y + z * z + w * w); }
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-
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|
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- // Return vector length.
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- T Length() const { return sqrt(LengthSq()); }
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-
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- bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
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-
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|
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- // Normalize, convention vector length to 1.
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- void Normalize()
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|
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- {
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- T s = Length();
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|
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- if (s != T(0))
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- s = T(1) / s;
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- *this *= s;
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- }
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-
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|
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- // Returns normalized (unit) version of the vector without modifying itself.
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- Vector4 Normalized() const
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|
|
- {
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- T s = Length();
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- if (s != T(0))
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- s = T(1) / s;
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- return *this * s;
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- }
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-
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|
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- // Linearly interpolates from this vector to another.
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- // Factor should be between 0.0 and 1.0, with 0 giving full value to this.
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- Vector4 Lerp(const Vector4& b, T f) const { return *this*(T(1) - f) + b*f; }
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-};
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-
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-typedef Vector4<float> Vector4f;
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-typedef Vector4<double> Vector4d;
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-typedef Vector4<int> Vector4i;
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-
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-
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-//-------------------------------------------------------------------------------------
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-// ***** Bounds3
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-
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-// Bounds class used to describe a 3D axis aligned bounding box.
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-
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|
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-template<class T>
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-class Bounds3
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-{
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-public:
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- Vector3<T> b[2];
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-
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- Bounds3()
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- {
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- }
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-
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- Bounds3( const Vector3<T> & mins, const Vector3<T> & maxs )
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-{
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- b[0] = mins;
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- b[1] = maxs;
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- }
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-
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- void Clear()
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- {
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- b[0].x = b[0].y = b[0].z = Math<T>::MaxValue;
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- b[1].x = b[1].y = b[1].z = -Math<T>::MaxValue;
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- }
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-
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- void AddPoint( const Vector3<T> & v )
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- {
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- b[0].x = (b[0].x < v.x ? b[0].x : v.x);
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- b[0].y = (b[0].y < v.y ? b[0].y : v.y);
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- b[0].z = (b[0].z < v.z ? b[0].z : v.z);
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- b[1].x = (v.x < b[1].x ? b[1].x : v.x);
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- b[1].y = (v.y < b[1].y ? b[1].y : v.y);
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- b[1].z = (v.z < b[1].z ? b[1].z : v.z);
|
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- }
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-
|
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- const Vector3<T> & GetMins() const { return b[0]; }
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- const Vector3<T> & GetMaxs() const { return b[1]; }
|
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-
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- Vector3<T> & GetMins() { return b[0]; }
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- Vector3<T> & GetMaxs() { return b[1]; }
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-};
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-
|
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-typedef Bounds3<float> Bounds3f;
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-typedef Bounds3<double> Bounds3d;
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-
|
|
|
-
|
|
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-//-------------------------------------------------------------------------------------
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|
|
-// ***** Size
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|
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-
|
|
|
-// Size class represents 2D size with Width, Height components.
|
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-// Used to describe distentions of render targets, etc.
|
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-
|
|
|
-template<class T>
|
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|
-class Size
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-{
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|
-public:
|
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- T w, h;
|
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-
|
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- Size() : w(0), h(0) { }
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- Size(T w_, T h_) : w(w_), h(h_) { }
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- explicit Size(T s) : w(s), h(s) { }
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- explicit Size(const Size<typename Math<T>::OtherFloatType> &src)
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- : w((T)src.w), h((T)src.h) { }
|
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-
|
|
|
- // C-interop support.
|
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|
- typedef typename CompatibleTypes<Size<T> >::Type CompatibleType;
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-
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- Size(const CompatibleType& s) : w(s.w), h(s.h) { }
|
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-
|
|
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- operator const CompatibleType& () const
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(Size<T>) == sizeof(CompatibleType), "sizeof(Size<T>) failure");
|
|
|
- return reinterpret_cast<const CompatibleType&>(*this);
|
|
|
- }
|
|
|
-
|
|
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- bool operator== (const Size& b) const { return w == b.w && h == b.h; }
|
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- bool operator!= (const Size& b) const { return w != b.w || h != b.h; }
|
|
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-
|
|
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- Size operator+ (const Size& b) const { return Size(w + b.w, h + b.h); }
|
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- Size& operator+= (const Size& b) { w += b.w; h += b.h; return *this; }
|
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- Size operator- (const Size& b) const { return Size(w - b.w, h - b.h); }
|
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- Size& operator-= (const Size& b) { w -= b.w; h -= b.h; return *this; }
|
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- Size operator- () const { return Size(-w, -h); }
|
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- Size operator* (const Size& b) const { return Size(w * b.w, h * b.h); }
|
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- Size& operator*= (const Size& b) { w *= b.w; h *= b.h; return *this; }
|
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- Size operator/ (const Size& b) const { return Size(w / b.w, h / b.h); }
|
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- Size& operator/= (const Size& b) { w /= b.w; h /= b.h; return *this; }
|
|
|
-
|
|
|
- // Scalar multiplication/division scales both components.
|
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|
- Size operator* (T s) const { return Size(w*s, h*s); }
|
|
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- Size& operator*= (T s) { w *= s; h *= s; return *this; }
|
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- Size operator/ (T s) const { return Size(w/s, h/s); }
|
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- Size& operator/= (T s) { w /= s; h /= s; return *this; }
|
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|
-
|
|
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- static Size Min(const Size& a, const Size& b) { return Size((a.w < b.w) ? a.w : b.w,
|
|
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- (a.h < b.h) ? a.h : b.h); }
|
|
|
- static Size Max(const Size& a, const Size& b) { return Size((a.w > b.w) ? a.w : b.w,
|
|
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- (a.h > b.h) ? a.h : b.h); }
|
|
|
-
|
|
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- T Area() const { return w * h; }
|
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|
-
|
|
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- inline Vector2<T> ToVector() const { return Vector2<T>(w, h); }
|
|
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-};
|
|
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-
|
|
|
-
|
|
|
-typedef Size<int> Sizei;
|
|
|
-typedef Size<unsigned> Sizeu;
|
|
|
-typedef Size<float> Sizef;
|
|
|
-typedef Size<double> Sized;
|
|
|
-
|
|
|
-
|
|
|
-
|
|
|
-//-----------------------------------------------------------------------------------
|
|
|
-// ***** Rect
|
|
|
-
|
|
|
-// Rect describes a rectangular area for rendering, that includes position and size.
|
|
|
-template<class T>
|
|
|
-class Rect
|
|
|
-{
|
|
|
-public:
|
|
|
- T x, y;
|
|
|
- T w, h;
|
|
|
-
|
|
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- Rect() { }
|
|
|
- Rect(T x1, T y1, T w1, T h1) : x(x1), y(y1), w(w1), h(h1) { }
|
|
|
- Rect(const Vector2<T>& pos, const Size<T>& sz) : x(pos.x), y(pos.y), w(sz.w), h(sz.h) { }
|
|
|
- Rect(const Size<T>& sz) : x(0), y(0), w(sz.w), h(sz.h) { }
|
|
|
-
|
|
|
- // C-interop support.
|
|
|
- typedef typename CompatibleTypes<Rect<T> >::Type CompatibleType;
|
|
|
-
|
|
|
- Rect(const CompatibleType& s) : x(s.Pos.x), y(s.Pos.y), w(s.Size.w), h(s.Size.h) { }
|
|
|
-
|
|
|
- operator const CompatibleType& () const
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(Rect<T>) == sizeof(CompatibleType), "sizeof(Rect<T>) failure");
|
|
|
- return reinterpret_cast<const CompatibleType&>(*this);
|
|
|
- }
|
|
|
-
|
|
|
- Vector2<T> GetPos() const { return Vector2<T>(x, y); }
|
|
|
- Size<T> GetSize() const { return Size<T>(w, h); }
|
|
|
- void SetPos(const Vector2<T>& pos) { x = pos.x; y = pos.y; }
|
|
|
- void SetSize(const Size<T>& sz) { w = sz.w; h = sz.h; }
|
|
|
-
|
|
|
- bool operator == (const Rect& vp) const
|
|
|
- { return (x == vp.x) && (y == vp.y) && (w == vp.w) && (h == vp.h); }
|
|
|
- bool operator != (const Rect& vp) const
|
|
|
- { return !operator == (vp); }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Rect<int> Recti;
|
|
|
-
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------//
|
|
|
-// ***** Quat
|
|
|
-//
|
|
|
-// Quatf represents a quaternion class used for rotations.
|
|
|
-//
|
|
|
-// Quaternion multiplications are done in right-to-left order, to match the
|
|
|
-// behavior of matrices.
|
|
|
-
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class Quat
|
|
|
-{
|
|
|
-public:
|
|
|
- typedef T ElementType;
|
|
|
- static const size_t ElementCount = 4;
|
|
|
-
|
|
|
- // x,y,z = axis*sin(angle), w = cos(angle)
|
|
|
- T x, y, z, w;
|
|
|
-
|
|
|
- Quat() : x(0), y(0), z(0), w(1) { }
|
|
|
- Quat(T x_, T y_, T z_, T w_) : x(x_), y(y_), z(z_), w(w_) { }
|
|
|
- explicit Quat(const Quat<typename Math<T>::OtherFloatType> &src)
|
|
|
- : x((T)src.x), y((T)src.y), z((T)src.z), w((T)src.w)
|
|
|
- {
|
|
|
- // NOTE: Converting a normalized Quat<float> to Quat<double>
|
|
|
- // will generally result in an un-normalized quaternion.
|
|
|
- // But we don't normalize here in case the quaternion
|
|
|
- // being converted is not a normalized rotation quaternion.
|
|
|
- }
|
|
|
-
|
|
|
- typedef typename CompatibleTypes<Quat<T> >::Type CompatibleType;
|
|
|
-
|
|
|
- // C-interop support.
|
|
|
- Quat(const CompatibleType& s) : x(s.x), y(s.y), z(s.z), w(s.w) { }
|
|
|
-
|
|
|
- operator CompatibleType () const
|
|
|
- {
|
|
|
- CompatibleType result;
|
|
|
- result.x = x;
|
|
|
- result.y = y;
|
|
|
- result.z = z;
|
|
|
- result.w = w;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- // Constructs quaternion for rotation around the axis by an angle.
|
|
|
- Quat(const Vector3<T>& axis, T angle)
|
|
|
- {
|
|
|
- // Make sure we don't divide by zero.
|
|
|
- if (axis.LengthSq() == T(0))
|
|
|
- {
|
|
|
- // Assert if the axis is zero, but the angle isn't
|
|
|
- OVR_MATH_ASSERT(angle == T(0));
|
|
|
- x = y = z = T(0); w = T(1);
|
|
|
- return;
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> unitAxis = axis.Normalized();
|
|
|
- T sinHalfAngle = sin(angle * T(0.5));
|
|
|
-
|
|
|
- w = cos(angle * T(0.5));
|
|
|
- x = unitAxis.x * sinHalfAngle;
|
|
|
- y = unitAxis.y * sinHalfAngle;
|
|
|
- z = unitAxis.z * sinHalfAngle;
|
|
|
- }
|
|
|
-
|
|
|
- // Constructs quaternion for rotation around one of the coordinate axis by an angle.
|
|
|
- Quat(Axis A, T angle, RotateDirection d = Rotate_CCW, HandedSystem s = Handed_R)
|
|
|
- {
|
|
|
- T sinHalfAngle = s * d *sin(angle * T(0.5));
|
|
|
- T v[3];
|
|
|
- v[0] = v[1] = v[2] = T(0);
|
|
|
- v[A] = sinHalfAngle;
|
|
|
-
|
|
|
- w = cos(angle * T(0.5));
|
|
|
- x = v[0];
|
|
|
- y = v[1];
|
|
|
- z = v[2];
|
|
|
- }
|
|
|
-
|
|
|
- Quat operator-() { return Quat(-x, -y, -z, -w); } // unary minus
|
|
|
-
|
|
|
- static Quat Identity() { return Quat(0, 0, 0, 1); }
|
|
|
-
|
|
|
- // Compute axis and angle from quaternion
|
|
|
- void GetAxisAngle(Vector3<T>* axis, T* angle) const
|
|
|
- {
|
|
|
- if ( x*x + y*y + z*z > Math<T>::Tolerance() * Math<T>::Tolerance() ) {
|
|
|
- *axis = Vector3<T>(x, y, z).Normalized();
|
|
|
- *angle = 2 * Acos(w);
|
|
|
- if (*angle > ((T)MATH_DOUBLE_PI)) // Reduce the magnitude of the angle, if necessary
|
|
|
- {
|
|
|
- *angle = ((T)MATH_DOUBLE_TWOPI) - *angle;
|
|
|
- *axis = *axis * (-1);
|
|
|
- }
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- *axis = Vector3<T>(1, 0, 0);
|
|
|
- *angle= T(0);
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- // Convert a quaternion to a rotation vector, also known as
|
|
|
- // Rodrigues vector, AxisAngle vector, SORA vector, exponential map.
|
|
|
- // A rotation vector describes a rotation about an axis:
|
|
|
- // the axis of rotation is the vector normalized,
|
|
|
- // the angle of rotation is the magnitude of the vector.
|
|
|
- Vector3<T> ToRotationVector() const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(IsNormalized() || LengthSq() == 0);
|
|
|
- T s = T(0);
|
|
|
- T sinHalfAngle = sqrt(x*x + y*y + z*z);
|
|
|
- if (sinHalfAngle > T(0))
|
|
|
- {
|
|
|
- T cosHalfAngle = w;
|
|
|
- T halfAngle = atan2(sinHalfAngle, cosHalfAngle);
|
|
|
-
|
|
|
- // Ensure minimum rotation magnitude
|
|
|
- if (cosHalfAngle < 0)
|
|
|
- halfAngle -= T(MATH_DOUBLE_PI);
|
|
|
-
|
|
|
- s = T(2) * halfAngle / sinHalfAngle;
|
|
|
- }
|
|
|
- return Vector3<T>(x*s, y*s, z*s);
|
|
|
- }
|
|
|
-
|
|
|
- // Faster version of the above, optimized for use with small rotations, where rotation angle ~= sin(angle)
|
|
|
- inline OVR::Vector3<T> FastToRotationVector() const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(IsNormalized());
|
|
|
- T s;
|
|
|
- T sinHalfSquared = x*x + y*y + z*z;
|
|
|
- if (sinHalfSquared < T(.0037)) // =~ sin(7/2 degrees)^2
|
|
|
- {
|
|
|
- // Max rotation magnitude error is about .062% at 7 degrees rotation, or about .0043 degrees
|
|
|
- s = T(2) * Sign(w);
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- T sinHalfAngle = sqrt(sinHalfSquared);
|
|
|
- T cosHalfAngle = w;
|
|
|
- T halfAngle = atan2(sinHalfAngle, cosHalfAngle);
|
|
|
-
|
|
|
- // Ensure minimum rotation magnitude
|
|
|
- if (cosHalfAngle < 0)
|
|
|
- halfAngle -= T(MATH_DOUBLE_PI);
|
|
|
-
|
|
|
- s = T(2) * halfAngle / sinHalfAngle;
|
|
|
- }
|
|
|
- return Vector3<T>(x*s, y*s, z*s);
|
|
|
- }
|
|
|
-
|
|
|
- // Given a rotation vector of form unitRotationAxis * angle,
|
|
|
- // returns the equivalent quaternion (unitRotationAxis * sin(angle), cos(Angle)).
|
|
|
- static Quat FromRotationVector(const Vector3<T>& v)
|
|
|
- {
|
|
|
- T angleSquared = v.LengthSq();
|
|
|
- T s = T(0);
|
|
|
- T c = T(1);
|
|
|
- if (angleSquared > T(0))
|
|
|
- {
|
|
|
- T angle = sqrt(angleSquared);
|
|
|
- s = sin(angle * T(0.5)) / angle; // normalize
|
|
|
- c = cos(angle * T(0.5));
|
|
|
- }
|
|
|
- return Quat(s*v.x, s*v.y, s*v.z, c);
|
|
|
- }
|
|
|
-
|
|
|
- // Faster version of above, optimized for use with small rotation magnitudes, where rotation angle =~ sin(angle).
|
|
|
- // If normalize is false, small-angle quaternions are returned un-normalized.
|
|
|
- inline static Quat FastFromRotationVector(const OVR::Vector3<T>& v, bool normalize = true)
|
|
|
- {
|
|
|
- T s, c;
|
|
|
- T angleSquared = v.LengthSq();
|
|
|
- if (angleSquared < T(0.0076)) // =~ (5 degrees*pi/180)^2
|
|
|
- {
|
|
|
- s = T(0.5);
|
|
|
- c = T(1.0);
|
|
|
- // Max rotation magnitude error (after normalization) is about .064% at 5 degrees rotation, or .0032 degrees
|
|
|
- if (normalize && angleSquared > 0)
|
|
|
- {
|
|
|
- // sin(angle/2)^2 ~= (angle/2)^2 and cos(angle/2)^2 ~= 1
|
|
|
- T invLen = T(1) / sqrt(angleSquared * T(0.25) + T(1)); // normalize
|
|
|
- s = s * invLen;
|
|
|
- c = c * invLen;
|
|
|
- }
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- T angle = sqrt(angleSquared);
|
|
|
- s = sin(angle * T(0.5)) / angle;
|
|
|
- c = cos(angle * T(0.5));
|
|
|
- }
|
|
|
- return Quat(s*v.x, s*v.y, s*v.z, c);
|
|
|
- }
|
|
|
-
|
|
|
- // Constructs the quaternion from a rotation matrix
|
|
|
- explicit Quat(const Matrix4<T>& m)
|
|
|
- {
|
|
|
- T trace = m.M[0][0] + m.M[1][1] + m.M[2][2];
|
|
|
-
|
|
|
- // In almost all cases, the first part is executed.
|
|
|
- // However, if the trace is not positive, the other
|
|
|
- // cases arise.
|
|
|
- if (trace > T(0))
|
|
|
- {
|
|
|
- T s = sqrt(trace + T(1)) * T(2); // s=4*qw
|
|
|
- w = T(0.25) * s;
|
|
|
- x = (m.M[2][1] - m.M[1][2]) / s;
|
|
|
- y = (m.M[0][2] - m.M[2][0]) / s;
|
|
|
- z = (m.M[1][0] - m.M[0][1]) / s;
|
|
|
- }
|
|
|
- else if ((m.M[0][0] > m.M[1][1])&&(m.M[0][0] > m.M[2][2]))
|
|
|
- {
|
|
|
- T s = sqrt(T(1) + m.M[0][0] - m.M[1][1] - m.M[2][2]) * T(2);
|
|
|
- w = (m.M[2][1] - m.M[1][2]) / s;
|
|
|
- x = T(0.25) * s;
|
|
|
- y = (m.M[0][1] + m.M[1][0]) / s;
|
|
|
- z = (m.M[2][0] + m.M[0][2]) / s;
|
|
|
- }
|
|
|
- else if (m.M[1][1] > m.M[2][2])
|
|
|
- {
|
|
|
- T s = sqrt(T(1) + m.M[1][1] - m.M[0][0] - m.M[2][2]) * T(2); // S=4*qy
|
|
|
- w = (m.M[0][2] - m.M[2][0]) / s;
|
|
|
- x = (m.M[0][1] + m.M[1][0]) / s;
|
|
|
- y = T(0.25) * s;
|
|
|
- z = (m.M[1][2] + m.M[2][1]) / s;
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- T s = sqrt(T(1) + m.M[2][2] - m.M[0][0] - m.M[1][1]) * T(2); // S=4*qz
|
|
|
- w = (m.M[1][0] - m.M[0][1]) / s;
|
|
|
- x = (m.M[0][2] + m.M[2][0]) / s;
|
|
|
- y = (m.M[1][2] + m.M[2][1]) / s;
|
|
|
- z = T(0.25) * s;
|
|
|
- }
|
|
|
- OVR_MATH_ASSERT(IsNormalized()); // Ensure input matrix is orthogonal
|
|
|
- }
|
|
|
-
|
|
|
- // Constructs the quaternion from a rotation matrix
|
|
|
- explicit Quat(const Matrix3<T>& m)
|
|
|
- {
|
|
|
- T trace = m.M[0][0] + m.M[1][1] + m.M[2][2];
|
|
|
-
|
|
|
- // In almost all cases, the first part is executed.
|
|
|
- // However, if the trace is not positive, the other
|
|
|
- // cases arise.
|
|
|
- if (trace > T(0))
|
|
|
- {
|
|
|
- T s = sqrt(trace + T(1)) * T(2); // s=4*qw
|
|
|
- w = T(0.25) * s;
|
|
|
- x = (m.M[2][1] - m.M[1][2]) / s;
|
|
|
- y = (m.M[0][2] - m.M[2][0]) / s;
|
|
|
- z = (m.M[1][0] - m.M[0][1]) / s;
|
|
|
- }
|
|
|
- else if ((m.M[0][0] > m.M[1][1])&&(m.M[0][0] > m.M[2][2]))
|
|
|
- {
|
|
|
- T s = sqrt(T(1) + m.M[0][0] - m.M[1][1] - m.M[2][2]) * T(2);
|
|
|
- w = (m.M[2][1] - m.M[1][2]) / s;
|
|
|
- x = T(0.25) * s;
|
|
|
- y = (m.M[0][1] + m.M[1][0]) / s;
|
|
|
- z = (m.M[2][0] + m.M[0][2]) / s;
|
|
|
- }
|
|
|
- else if (m.M[1][1] > m.M[2][2])
|
|
|
- {
|
|
|
- T s = sqrt(T(1) + m.M[1][1] - m.M[0][0] - m.M[2][2]) * T(2); // S=4*qy
|
|
|
- w = (m.M[0][2] - m.M[2][0]) / s;
|
|
|
- x = (m.M[0][1] + m.M[1][0]) / s;
|
|
|
- y = T(0.25) * s;
|
|
|
- z = (m.M[1][2] + m.M[2][1]) / s;
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- T s = sqrt(T(1) + m.M[2][2] - m.M[0][0] - m.M[1][1]) * T(2); // S=4*qz
|
|
|
- w = (m.M[1][0] - m.M[0][1]) / s;
|
|
|
- x = (m.M[0][2] + m.M[2][0]) / s;
|
|
|
- y = (m.M[1][2] + m.M[2][1]) / s;
|
|
|
- z = T(0.25) * s;
|
|
|
- }
|
|
|
- OVR_MATH_ASSERT(IsNormalized()); // Ensure input matrix is orthogonal
|
|
|
- }
|
|
|
-
|
|
|
- bool operator== (const Quat& b) const { return x == b.x && y == b.y && z == b.z && w == b.w; }
|
|
|
- bool operator!= (const Quat& b) const { return x != b.x || y != b.y || z != b.z || w != b.w; }
|
|
|
-
|
|
|
- Quat operator+ (const Quat& b) const { return Quat(x + b.x, y + b.y, z + b.z, w + b.w); }
|
|
|
- Quat& operator+= (const Quat& b) { w += b.w; x += b.x; y += b.y; z += b.z; return *this; }
|
|
|
- Quat operator- (const Quat& b) const { return Quat(x - b.x, y - b.y, z - b.z, w - b.w); }
|
|
|
- Quat& operator-= (const Quat& b) { w -= b.w; x -= b.x; y -= b.y; z -= b.z; return *this; }
|
|
|
-
|
|
|
- Quat operator* (T s) const { return Quat(x * s, y * s, z * s, w * s); }
|
|
|
- Quat& operator*= (T s) { w *= s; x *= s; y *= s; z *= s; return *this; }
|
|
|
- Quat operator/ (T s) const { T rcp = T(1)/s; return Quat(x * rcp, y * rcp, z * rcp, w *rcp); }
|
|
|
- Quat& operator/= (T s) { T rcp = T(1)/s; w *= rcp; x *= rcp; y *= rcp; z *= rcp; return *this; }
|
|
|
-
|
|
|
- // Compare two quats for equality within tolerance. Returns true if quats match withing tolerance.
|
|
|
- bool IsEqual(const Quat& b, T tolerance = Math<T>::Tolerance()) const
|
|
|
- {
|
|
|
- return Abs(Dot(b)) >= T(1) - tolerance;
|
|
|
- }
|
|
|
-
|
|
|
- static T Abs(const T v) { return (v >= 0) ? v : -v; }
|
|
|
-
|
|
|
- // Get Imaginary part vector
|
|
|
- Vector3<T> Imag() const { return Vector3<T>(x,y,z); }
|
|
|
-
|
|
|
- // Get quaternion length.
|
|
|
- T Length() const { return sqrt(LengthSq()); }
|
|
|
-
|
|
|
- // Get quaternion length squared.
|
|
|
- T LengthSq() const { return (x * x + y * y + z * z + w * w); }
|
|
|
-
|
|
|
- // Simple Euclidean distance in R^4 (not SLERP distance, but at least respects Haar measure)
|
|
|
- T Distance(const Quat& q) const
|
|
|
- {
|
|
|
- T d1 = (*this - q).Length();
|
|
|
- T d2 = (*this + q).Length(); // Antipodal point check
|
|
|
- return (d1 < d2) ? d1 : d2;
|
|
|
- }
|
|
|
-
|
|
|
- T DistanceSq(const Quat& q) const
|
|
|
- {
|
|
|
- T d1 = (*this - q).LengthSq();
|
|
|
- T d2 = (*this + q).LengthSq(); // Antipodal point check
|
|
|
- return (d1 < d2) ? d1 : d2;
|
|
|
- }
|
|
|
-
|
|
|
- T Dot(const Quat& q) const
|
|
|
- {
|
|
|
- return x * q.x + y * q.y + z * q.z + w * q.w;
|
|
|
- }
|
|
|
-
|
|
|
- // Angle between two quaternions in radians
|
|
|
- T Angle(const Quat& q) const
|
|
|
- {
|
|
|
- return T(2) * Acos(Abs(Dot(q)));
|
|
|
- }
|
|
|
-
|
|
|
- // Angle of quaternion
|
|
|
- T Angle() const
|
|
|
- {
|
|
|
- return T(2) * Acos(Abs(w));
|
|
|
- }
|
|
|
-
|
|
|
- // Normalize
|
|
|
- bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
|
|
|
-
|
|
|
- void Normalize()
|
|
|
- {
|
|
|
- T s = Length();
|
|
|
- if (s != T(0))
|
|
|
- s = T(1) / s;
|
|
|
- *this *= s;
|
|
|
- }
|
|
|
-
|
|
|
- Quat Normalized() const
|
|
|
- {
|
|
|
- T s = Length();
|
|
|
- if (s != T(0))
|
|
|
- s = T(1) / s;
|
|
|
- return *this * s;
|
|
|
- }
|
|
|
-
|
|
|
- inline void EnsureSameHemisphere(const Quat& o)
|
|
|
- {
|
|
|
- if (Dot(o) < T(0))
|
|
|
- {
|
|
|
- x = -x;
|
|
|
- y = -y;
|
|
|
- z = -z;
|
|
|
- w = -w;
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- // Returns conjugate of the quaternion. Produces inverse rotation if quaternion is normalized.
|
|
|
- Quat Conj() const { return Quat(-x, -y, -z, w); }
|
|
|
-
|
|
|
- // Quaternion multiplication. Combines quaternion rotations, performing the one on the
|
|
|
- // right hand side first.
|
|
|
- Quat operator* (const Quat& b) const { return Quat(w * b.x + x * b.w + y * b.z - z * b.y,
|
|
|
- w * b.y - x * b.z + y * b.w + z * b.x,
|
|
|
- w * b.z + x * b.y - y * b.x + z * b.w,
|
|
|
- w * b.w - x * b.x - y * b.y - z * b.z); }
|
|
|
- const Quat& operator*= (const Quat& b) { *this = *this * b; return *this; }
|
|
|
-
|
|
|
- //
|
|
|
- // this^p normalized; same as rotating by this p times.
|
|
|
- Quat PowNormalized(T p) const
|
|
|
- {
|
|
|
- Vector3<T> v;
|
|
|
- T a;
|
|
|
- GetAxisAngle(&v, &a);
|
|
|
- return Quat(v, a * p);
|
|
|
- }
|
|
|
-
|
|
|
- // Compute quaternion that rotates v into alignTo: alignTo = Quat::Align(alignTo, v).Rotate(v).
|
|
|
- // NOTE: alignTo and v must be normalized.
|
|
|
- static Quat Align(const Vector3<T>& alignTo, const Vector3<T>& v)
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(alignTo.IsNormalized() && v.IsNormalized());
|
|
|
- Vector3<T> bisector = (v + alignTo);
|
|
|
- bisector.Normalize();
|
|
|
- T cosHalfAngle = v.Dot(bisector); // 0..1
|
|
|
- if (cosHalfAngle > T(0))
|
|
|
- {
|
|
|
- Vector3<T> imag = v.Cross(bisector);
|
|
|
- return Quat(imag.x, imag.y, imag.z, cosHalfAngle);
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- // cosHalfAngle == 0: a 180 degree rotation.
|
|
|
- // sinHalfAngle == 1, rotation axis is any axis perpendicular
|
|
|
- // to alignTo. Choose axis to include largest magnitude components
|
|
|
- if (fabs(v.x) > fabs(v.y))
|
|
|
- {
|
|
|
- // x or z is max magnitude component
|
|
|
- // = Cross(v, (0,1,0)).Normalized();
|
|
|
- T invLen = sqrt(v.x*v.x + v.z*v.z);
|
|
|
- if (invLen > T(0))
|
|
|
- invLen = T(1) / invLen;
|
|
|
- return Quat(-v.z*invLen, 0, v.x*invLen, 0);
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- // y or z is max magnitude component
|
|
|
- // = Cross(v, (1,0,0)).Normalized();
|
|
|
- T invLen = sqrt(v.y*v.y + v.z*v.z);
|
|
|
- if (invLen > T(0))
|
|
|
- invLen = T(1) / invLen;
|
|
|
- return Quat(0, v.z*invLen, -v.y*invLen, 0);
|
|
|
- }
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- // Decompose a quat into quat = swing * twist, where twist is a rotation about axis,
|
|
|
- // and swing is a rotation perpendicular to axis.
|
|
|
- Quat GetSwingTwist(const Vector3<T>& axis, Quat* twist) const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(twist);
|
|
|
- OVR_MATH_ASSERT(axis.IsNormalized());
|
|
|
-
|
|
|
- // Create a normalized quaternion from projection of (x,y,z) onto axis
|
|
|
- T d = axis.Dot(Vector3<T>(x, y, z));
|
|
|
- *twist = Quat(axis.x*d, axis.y*d, axis.z*d, w);
|
|
|
- T len = twist->Length();
|
|
|
- if (len == 0)
|
|
|
- twist->w = T(1); // identity
|
|
|
- else
|
|
|
- *twist /= len; // normalize
|
|
|
-
|
|
|
- return *this * twist->Inverted();
|
|
|
- }
|
|
|
-
|
|
|
- // Normalized linear interpolation of quaternions
|
|
|
- // NOTE: This function is a bad approximation of Slerp()
|
|
|
- // when the angle between the *this and b is large.
|
|
|
- // Use FastSlerp() or Slerp() instead.
|
|
|
- Quat Lerp(const Quat& b, T s) const
|
|
|
- {
|
|
|
- return (*this * (T(1) - s) + b * (Dot(b) < 0 ? -s : s)).Normalized();
|
|
|
- }
|
|
|
-
|
|
|
- // Spherical linear interpolation between rotations
|
|
|
- Quat Slerp(const Quat& b, T s) const
|
|
|
- {
|
|
|
- Vector3<T> delta = (b * this->Inverted()).ToRotationVector();
|
|
|
- return (FromRotationVector(delta * s) * *this).Normalized(); // normalize so errors don't accumulate
|
|
|
- }
|
|
|
-
|
|
|
- // Spherical linear interpolation: much faster for small rotations, accurate for large rotations. See FastTo/FromRotationVector
|
|
|
- Quat FastSlerp(const Quat& b, T s) const
|
|
|
- {
|
|
|
- Vector3<T> delta = (b * this->Inverted()).FastToRotationVector();
|
|
|
- return (FastFromRotationVector(delta * s, false) * *this).Normalized();
|
|
|
- }
|
|
|
-
|
|
|
- // Rotate transforms vector in a manner that matches Matrix rotations (counter-clockwise,
|
|
|
- // assuming negative direction of the axis). Standard formula: q(t) * V * q(t)^-1.
|
|
|
- Vector3<T> Rotate(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(isnan(w) || IsNormalized());
|
|
|
-
|
|
|
- // rv = q * (v,0) * q'
|
|
|
- // Same as rv = v + real * cross(imag,v)*2 + cross(imag, cross(imag,v)*2);
|
|
|
-
|
|
|
- // uv = 2 * Imag().Cross(v);
|
|
|
- T uvx = T(2) * (y*v.z - z*v.y);
|
|
|
- T uvy = T(2) * (z*v.x - x*v.z);
|
|
|
- T uvz = T(2) * (x*v.y - y*v.x);
|
|
|
-
|
|
|
- // return v + Real()*uv + Imag().Cross(uv);
|
|
|
- return Vector3<T>(v.x + w*uvx + y*uvz - z*uvy,
|
|
|
- v.y + w*uvy + z*uvx - x*uvz,
|
|
|
- v.z + w*uvz + x*uvy - y*uvx);
|
|
|
- }
|
|
|
-
|
|
|
- // Rotation by inverse of *this
|
|
|
- Vector3<T> InverseRotate(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(IsNormalized());
|
|
|
-
|
|
|
- // rv = q' * (v,0) * q
|
|
|
- // Same as rv = v + real * cross(-imag,v)*2 + cross(-imag, cross(-imag,v)*2);
|
|
|
- // or rv = v - real * cross(imag,v)*2 + cross(imag, cross(imag,v)*2);
|
|
|
-
|
|
|
- // uv = 2 * Imag().Cross(v);
|
|
|
- T uvx = T(2) * (y*v.z - z*v.y);
|
|
|
- T uvy = T(2) * (z*v.x - x*v.z);
|
|
|
- T uvz = T(2) * (x*v.y - y*v.x);
|
|
|
-
|
|
|
- // return v - Real()*uv + Imag().Cross(uv);
|
|
|
- return Vector3<T>(v.x - w*uvx + y*uvz - z*uvy,
|
|
|
- v.y - w*uvy + z*uvx - x*uvz,
|
|
|
- v.z - w*uvz + x*uvy - y*uvx);
|
|
|
- }
|
|
|
-
|
|
|
- // Inversed quaternion rotates in the opposite direction.
|
|
|
- Quat Inverted() const
|
|
|
- {
|
|
|
- return Quat(-x, -y, -z, w);
|
|
|
- }
|
|
|
-
|
|
|
- Quat Inverse() const
|
|
|
- {
|
|
|
- return Quat(-x, -y, -z, w);
|
|
|
- }
|
|
|
-
|
|
|
- // Sets this quaternion to the one rotates in the opposite direction.
|
|
|
- void Invert()
|
|
|
- {
|
|
|
- *this = Quat(-x, -y, -z, w);
|
|
|
- }
|
|
|
-
|
|
|
- // Time integration of constant angular velocity over dt
|
|
|
- Quat TimeIntegrate(Vector3<T> angularVelocity, T dt) const
|
|
|
- {
|
|
|
- // solution is: this * exp( omega*dt/2 ); FromRotationVector(v) gives exp(v*.5).
|
|
|
- return (*this * FastFromRotationVector(angularVelocity * dt, false)).Normalized();
|
|
|
- }
|
|
|
-
|
|
|
- // Time integration of constant angular acceleration and velocity over dt
|
|
|
- // These are the first two terms of the "Magnus expansion" of the solution
|
|
|
- //
|
|
|
- // o = o * exp( W=(W1 + W2 + W3+...) * 0.5 );
|
|
|
- //
|
|
|
- // omega1 = (omega + omegaDot*dt)
|
|
|
- // W1 = (omega + omega1)*dt/2
|
|
|
- // W2 = cross(omega, omega1)/12*dt^2 % (= -cross(omega_dot, omega)/12*dt^3)
|
|
|
- // Terms 3 and beyond are vanishingly small:
|
|
|
- // W3 = cross(omega_dot, cross(omega_dot, omega))/240*dt^5
|
|
|
- //
|
|
|
- Quat TimeIntegrate(Vector3<T> angularVelocity, Vector3<T> angularAcceleration, T dt) const
|
|
|
- {
|
|
|
- const Vector3<T>& omega = angularVelocity;
|
|
|
- const Vector3<T>& omegaDot = angularAcceleration;
|
|
|
-
|
|
|
- Vector3<T> omega1 = (omega + omegaDot * dt);
|
|
|
- Vector3<T> W = ( (omega + omega1) + omega.Cross(omega1) * (dt/T(6)) ) * (dt/T(2));
|
|
|
-
|
|
|
- // FromRotationVector(v) is exp(v*.5)
|
|
|
- return (*this * FastFromRotationVector(W, false)).Normalized();
|
|
|
- }
|
|
|
-
|
|
|
- // Decompose rotation into three rotations:
|
|
|
- // roll radians about Z axis, then pitch radians about X axis, then yaw radians about Y axis.
|
|
|
- // Call with nullptr if a return value is not needed.
|
|
|
- void GetYawPitchRoll(T* yaw, T* pitch, T* roll) const
|
|
|
- {
|
|
|
- return GetEulerAngles<Axis_Y, Axis_X, Axis_Z, Rotate_CCW, Handed_R>(yaw, pitch, roll);
|
|
|
- }
|
|
|
-
|
|
|
- // GetEulerAngles extracts Euler angles from the quaternion, in the specified order of
|
|
|
- // axis rotations and the specified coordinate system. Right-handed coordinate system
|
|
|
- // is the default, with CCW rotations while looking in the negative axis direction.
|
|
|
- // Here a,b,c, are the Yaw/Pitch/Roll angles to be returned.
|
|
|
- // Rotation order is c, b, a:
|
|
|
- // rotation c around axis A3
|
|
|
- // is followed by rotation b around axis A2
|
|
|
- // is followed by rotation a around axis A1
|
|
|
- // rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
|
- //
|
|
|
- template <Axis A1, Axis A2, Axis A3, RotateDirection D, HandedSystem S>
|
|
|
- void GetEulerAngles(T *a, T *b, T *c) const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(IsNormalized());
|
|
|
- OVR_MATH_STATIC_ASSERT((A1 != A2) && (A2 != A3) && (A1 != A3), "(A1 != A2) && (A2 != A3) && (A1 != A3)");
|
|
|
-
|
|
|
- T Q[3] = { x, y, z }; //Quaternion components x,y,z
|
|
|
-
|
|
|
- T ww = w*w;
|
|
|
- T Q11 = Q[A1]*Q[A1];
|
|
|
- T Q22 = Q[A2]*Q[A2];
|
|
|
- T Q33 = Q[A3]*Q[A3];
|
|
|
-
|
|
|
- T psign = T(-1);
|
|
|
- // Determine whether even permutation
|
|
|
- if (((A1 + 1) % 3 == A2) && ((A2 + 1) % 3 == A3))
|
|
|
- psign = T(1);
|
|
|
-
|
|
|
- T s2 = psign * T(2) * (psign*w*Q[A2] + Q[A1]*Q[A3]);
|
|
|
-
|
|
|
- T singularityRadius = Math<T>::SingularityRadius();
|
|
|
- if (s2 < T(-1) + singularityRadius)
|
|
|
- { // South pole singularity
|
|
|
- if (a) *a = T(0);
|
|
|
- if (b) *b = -S*D*((T)MATH_DOUBLE_PIOVER2);
|
|
|
- if (c) *c = S*D*atan2(T(2)*(psign*Q[A1] * Q[A2] + w*Q[A3]), ww + Q22 - Q11 - Q33 );
|
|
|
- }
|
|
|
- else if (s2 > T(1) - singularityRadius)
|
|
|
- { // North pole singularity
|
|
|
- if (a) *a = T(0);
|
|
|
- if (b) *b = S*D*((T)MATH_DOUBLE_PIOVER2);
|
|
|
- if (c) *c = S*D*atan2(T(2)*(psign*Q[A1] * Q[A2] + w*Q[A3]), ww + Q22 - Q11 - Q33);
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- if (a) *a = -S*D*atan2(T(-2)*(w*Q[A1] - psign*Q[A2] * Q[A3]), ww + Q33 - Q11 - Q22);
|
|
|
- if (b) *b = S*D*asin(s2);
|
|
|
- if (c) *c = S*D*atan2(T(2)*(w*Q[A3] - psign*Q[A1] * Q[A2]), ww + Q11 - Q22 - Q33);
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- template <Axis A1, Axis A2, Axis A3, RotateDirection D>
|
|
|
- void GetEulerAngles(T *a, T *b, T *c) const
|
|
|
- { GetEulerAngles<A1, A2, A3, D, Handed_R>(a, b, c); }
|
|
|
-
|
|
|
- template <Axis A1, Axis A2, Axis A3>
|
|
|
- void GetEulerAngles(T *a, T *b, T *c) const
|
|
|
- { GetEulerAngles<A1, A2, A3, Rotate_CCW, Handed_R>(a, b, c); }
|
|
|
-
|
|
|
- // GetEulerAnglesABA extracts Euler angles from the quaternion, in the specified order of
|
|
|
- // axis rotations and the specified coordinate system. Right-handed coordinate system
|
|
|
- // is the default, with CCW rotations while looking in the negative axis direction.
|
|
|
- // Here a,b,c, are the Yaw/Pitch/Roll angles to be returned.
|
|
|
- // rotation a around axis A1
|
|
|
- // is followed by rotation b around axis A2
|
|
|
- // is followed by rotation c around axis A1
|
|
|
- // Rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
|
- template <Axis A1, Axis A2, RotateDirection D, HandedSystem S>
|
|
|
- void GetEulerAnglesABA(T *a, T *b, T *c) const
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(IsNormalized());
|
|
|
- OVR_MATH_STATIC_ASSERT(A1 != A2, "A1 != A2");
|
|
|
-
|
|
|
- T Q[3] = {x, y, z}; // Quaternion components
|
|
|
-
|
|
|
- // Determine the missing axis that was not supplied
|
|
|
- int m = 3 - A1 - A2;
|
|
|
-
|
|
|
- T ww = w*w;
|
|
|
- T Q11 = Q[A1]*Q[A1];
|
|
|
- T Q22 = Q[A2]*Q[A2];
|
|
|
- T Qmm = Q[m]*Q[m];
|
|
|
-
|
|
|
- T psign = T(-1);
|
|
|
- if ((A1 + 1) % 3 == A2) // Determine whether even permutation
|
|
|
- {
|
|
|
- psign = T(1);
|
|
|
- }
|
|
|
-
|
|
|
- T c2 = ww + Q11 - Q22 - Qmm;
|
|
|
- T singularityRadius = Math<T>::SingularityRadius();
|
|
|
- if (c2 < T(-1) + singularityRadius)
|
|
|
- { // South pole singularity
|
|
|
- if (a) *a = T(0);
|
|
|
- if (b) *b = S*D*((T)MATH_DOUBLE_PI);
|
|
|
- if (c) *c = S*D*atan2(T(2)*(w*Q[A1] - psign*Q[A2] * Q[m]),
|
|
|
- ww + Q22 - Q11 - Qmm);
|
|
|
- }
|
|
|
- else if (c2 > T(1) - singularityRadius)
|
|
|
- { // North pole singularity
|
|
|
- if (a) *a = T(0);
|
|
|
- if (b) *b = T(0);
|
|
|
- if (c) *c = S*D*atan2(T(2)*(w*Q[A1] - psign*Q[A2] * Q[m]),
|
|
|
- ww + Q22 - Q11 - Qmm);
|
|
|
- }
|
|
|
- else
|
|
|
- {
|
|
|
- if (a) *a = S*D*atan2(psign*w*Q[m] + Q[A1] * Q[A2],
|
|
|
- w*Q[A2] -psign*Q[A1]*Q[m]);
|
|
|
- if (b) *b = S*D*acos(c2);
|
|
|
- if (c) *c = S*D*atan2(-psign*w*Q[m] + Q[A1] * Q[A2],
|
|
|
- w*Q[A2] + psign*Q[A1]*Q[m]);
|
|
|
- }
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Quat<float> Quatf;
|
|
|
-typedef Quat<double> Quatd;
|
|
|
-
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Quatf) == 4*sizeof(float)), "sizeof(Quatf) failure");
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Quatd) == 4*sizeof(double)), "sizeof(Quatd) failure");
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-// ***** Pose
|
|
|
-//
|
|
|
-// Position and orientation combined.
|
|
|
-//
|
|
|
-// This structure needs to be the same size and layout on 32-bit and 64-bit arch.
|
|
|
-// Update OVR_PadCheck.cpp when updating this object.
|
|
|
-template<class T>
|
|
|
-class Pose
|
|
|
-{
|
|
|
-public:
|
|
|
- typedef typename CompatibleTypes<Pose<T> >::Type CompatibleType;
|
|
|
-
|
|
|
- Pose() { }
|
|
|
- Pose(const Quat<T>& orientation, const Vector3<T>& pos)
|
|
|
- : Rotation(orientation), Translation(pos) { }
|
|
|
- Pose(const Pose& s)
|
|
|
- : Rotation(s.Rotation), Translation(s.Translation) { }
|
|
|
- Pose(const Matrix3<T>& R, const Vector3<T>& t)
|
|
|
- : Rotation((Quat<T>)R), Translation(t) { }
|
|
|
- Pose(const CompatibleType& s)
|
|
|
- : Rotation(s.Orientation), Translation(s.Position) { }
|
|
|
-
|
|
|
- explicit Pose(const Pose<typename Math<T>::OtherFloatType> &s)
|
|
|
- : Rotation(s.Rotation), Translation(s.Translation)
|
|
|
- {
|
|
|
- // Ensure normalized rotation if converting from float to double
|
|
|
- if (sizeof(T) > sizeof(typename Math<T>::OtherFloatType))
|
|
|
- Rotation.Normalize();
|
|
|
- }
|
|
|
-
|
|
|
- static Pose Identity() { return Pose(Quat<T>(0, 0, 0, 1), Vector3<T>(0, 0, 0)); }
|
|
|
-
|
|
|
- void SetIdentity() { Rotation = Quat<T>(0, 0, 0, 1); Translation = Vector3<T>(0, 0, 0); }
|
|
|
-
|
|
|
- // used to make things obviously broken if someone tries to use the value
|
|
|
- void SetInvalid() { Rotation = Quat<T>(NAN, NAN, NAN, NAN); Translation = Vector3<T>(NAN, NAN, NAN); }
|
|
|
-
|
|
|
- bool IsEqual(const Pose&b, T tolerance = Math<T>::Tolerance()) const
|
|
|
- {
|
|
|
- return Translation.IsEqual(b.Translation, tolerance) && Rotation.IsEqual(b.Rotation, tolerance);
|
|
|
- }
|
|
|
-
|
|
|
- operator typename CompatibleTypes<Pose<T> >::Type () const
|
|
|
- {
|
|
|
- typename CompatibleTypes<Pose<T> >::Type result;
|
|
|
- result.Orientation = Rotation;
|
|
|
- result.Position = Translation;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Quat<T> Rotation;
|
|
|
- Vector3<T> Translation;
|
|
|
-
|
|
|
- OVR_MATH_STATIC_ASSERT((sizeof(T) == sizeof(double) || sizeof(T) == sizeof(float)), "(sizeof(T) == sizeof(double) || sizeof(T) == sizeof(float))");
|
|
|
-
|
|
|
- void ToArray(T* arr) const
|
|
|
- {
|
|
|
- T temp[7] = { Rotation.x, Rotation.y, Rotation.z, Rotation.w, Translation.x, Translation.y, Translation.z };
|
|
|
- for (int i = 0; i < 7; i++) arr[i] = temp[i];
|
|
|
- }
|
|
|
-
|
|
|
- static Pose<T> FromArray(const T* v)
|
|
|
- {
|
|
|
- Quat<T> rotation(v[0], v[1], v[2], v[3]);
|
|
|
- Vector3<T> translation(v[4], v[5], v[6]);
|
|
|
- // Ensure rotation is normalized, in case it was originally a float, stored in a .json file, etc.
|
|
|
- return Pose<T>(rotation.Normalized(), translation);
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> Rotate(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return Rotation.Rotate(v);
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> InverseRotate(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return Rotation.InverseRotate(v);
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> Translate(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return v + Translation;
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> Transform(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return Rotate(v) + Translation;
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> InverseTransform(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return InverseRotate(v - Translation);
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- Vector3<T> Apply(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return Transform(v);
|
|
|
- }
|
|
|
-
|
|
|
- Pose operator*(const Pose& other) const
|
|
|
- {
|
|
|
- return Pose(Rotation * other.Rotation, Apply(other.Translation));
|
|
|
- }
|
|
|
-
|
|
|
- Pose Inverted() const
|
|
|
- {
|
|
|
- Quat<T> inv = Rotation.Inverted();
|
|
|
- return Pose(inv, inv.Rotate(-Translation));
|
|
|
- }
|
|
|
-
|
|
|
- // Interpolation between two poses: translation is interpolated with Lerp(),
|
|
|
- // and rotations are interpolated with Slerp().
|
|
|
- Pose Lerp(const Pose& b, T s)
|
|
|
- {
|
|
|
- return Pose(Rotation.Slerp(b.Rotation, s), Translation.Lerp(b.Translation, s));
|
|
|
- }
|
|
|
-
|
|
|
- // Similar to Lerp above, except faster in case of small rotation differences. See Quat<T>::FastSlerp.
|
|
|
- Pose FastLerp(const Pose& b, T s)
|
|
|
- {
|
|
|
- return Pose(Rotation.FastSlerp(b.Rotation, s), Translation.Lerp(b.Translation, s));
|
|
|
- }
|
|
|
-
|
|
|
- Pose TimeIntegrate(const Vector3<T>& linearVelocity, const Vector3<T>& angularVelocity, T dt) const
|
|
|
- {
|
|
|
- return Pose(
|
|
|
- (Rotation * Quat<T>::FastFromRotationVector(angularVelocity * dt, false)).Normalized(),
|
|
|
- Translation + linearVelocity * dt);
|
|
|
- }
|
|
|
-
|
|
|
- Pose TimeIntegrate(const Vector3<T>& linearVelocity, const Vector3<T>& linearAcceleration,
|
|
|
- const Vector3<T>& angularVelocity, const Vector3<T>& angularAcceleration,
|
|
|
- T dt) const
|
|
|
- {
|
|
|
- return Pose(Rotation.TimeIntegrate(angularVelocity, angularAcceleration, dt),
|
|
|
- Translation + linearVelocity*dt + linearAcceleration*dt*dt * T(0.5));
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Pose<float> Posef;
|
|
|
-typedef Pose<double> Posed;
|
|
|
-
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Posed) == sizeof(Quatd) + sizeof(Vector3d)), "sizeof(Posed) failure");
|
|
|
-OVR_MATH_STATIC_ASSERT((sizeof(Posef) == sizeof(Quatf) + sizeof(Vector3f)), "sizeof(Posef) failure");
|
|
|
-
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-// ***** Matrix4
|
|
|
-//
|
|
|
-// Matrix4 is a 4x4 matrix used for 3d transformations and projections.
|
|
|
-// Translation stored in the last column.
|
|
|
-// The matrix is stored in row-major order in memory, meaning that values
|
|
|
-// of the first row are stored before the next one.
|
|
|
-//
|
|
|
-// The arrangement of the matrix is chosen to be in Right-Handed
|
|
|
-// coordinate system and counterclockwise rotations when looking down
|
|
|
-// the axis
|
|
|
-//
|
|
|
-// Transformation Order:
|
|
|
-// - Transformations are applied from right to left, so the expression
|
|
|
-// M1 * M2 * M3 * V means that the vector V is transformed by M3 first,
|
|
|
-// followed by M2 and M1.
|
|
|
-//
|
|
|
-// Coordinate system: Right Handed
|
|
|
-//
|
|
|
-// Rotations: Counterclockwise when looking down the axis. All angles are in radians.
|
|
|
-//
|
|
|
-// | sx 01 02 tx | // First column (sx, 10, 20): Axis X basis vector.
|
|
|
-// | 10 sy 12 ty | // Second column (01, sy, 21): Axis Y basis vector.
|
|
|
-// | 20 21 sz tz | // Third columnt (02, 12, sz): Axis Z basis vector.
|
|
|
-// | 30 31 32 33 |
|
|
|
-//
|
|
|
-// The basis vectors are first three columns.
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class Matrix4
|
|
|
-{
|
|
|
-public:
|
|
|
- typedef T ElementType;
|
|
|
- static const size_t Dimension = 4;
|
|
|
-
|
|
|
- T M[4][4];
|
|
|
-
|
|
|
- enum NoInitType { NoInit };
|
|
|
-
|
|
|
- // Construct with no memory initialization.
|
|
|
- Matrix4(NoInitType) { }
|
|
|
-
|
|
|
- // By default, we construct identity matrix.
|
|
|
- Matrix4()
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = M[2][2] = M[3][3] = T(1);
|
|
|
- M[0][1] = M[1][0] = M[2][3] = M[3][1] = T(0);
|
|
|
- M[0][2] = M[1][2] = M[2][0] = M[3][2] = T(0);
|
|
|
- M[0][3] = M[1][3] = M[2][1] = M[3][0] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4(T m11, T m12, T m13, T m14,
|
|
|
- T m21, T m22, T m23, T m24,
|
|
|
- T m31, T m32, T m33, T m34,
|
|
|
- T m41, T m42, T m43, T m44)
|
|
|
- {
|
|
|
- M[0][0] = m11; M[0][1] = m12; M[0][2] = m13; M[0][3] = m14;
|
|
|
- M[1][0] = m21; M[1][1] = m22; M[1][2] = m23; M[1][3] = m24;
|
|
|
- M[2][0] = m31; M[2][1] = m32; M[2][2] = m33; M[2][3] = m34;
|
|
|
- M[3][0] = m41; M[3][1] = m42; M[3][2] = m43; M[3][3] = m44;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4(T m11, T m12, T m13,
|
|
|
- T m21, T m22, T m23,
|
|
|
- T m31, T m32, T m33)
|
|
|
- {
|
|
|
- M[0][0] = m11; M[0][1] = m12; M[0][2] = m13; M[0][3] = T(0);
|
|
|
- M[1][0] = m21; M[1][1] = m22; M[1][2] = m23; M[1][3] = T(0);
|
|
|
- M[2][0] = m31; M[2][1] = m32; M[2][2] = m33; M[2][3] = T(0);
|
|
|
- M[3][0] = T(0); M[3][1] = T(0); M[3][2] = T(0); M[3][3] = T(1);
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix4(const Matrix3<T>& m)
|
|
|
- {
|
|
|
- M[0][0] = m.M[0][0]; M[0][1] = m.M[0][1]; M[0][2] = m.M[0][2]; M[0][3] = T(0);
|
|
|
- M[1][0] = m.M[1][0]; M[1][1] = m.M[1][1]; M[1][2] = m.M[1][2]; M[1][3] = T(0);
|
|
|
- M[2][0] = m.M[2][0]; M[2][1] = m.M[2][1]; M[2][2] = m.M[2][2]; M[2][3] = T(0);
|
|
|
- M[3][0] = T(0); M[3][1] = T(0); M[3][2] = T(0); M[3][3] = T(1);
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix4(const Quat<T>& q)
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(q.IsNormalized());
|
|
|
- T ww = q.w*q.w;
|
|
|
- T xx = q.x*q.x;
|
|
|
- T yy = q.y*q.y;
|
|
|
- T zz = q.z*q.z;
|
|
|
-
|
|
|
- M[0][0] = ww + xx - yy - zz; M[0][1] = 2 * (q.x*q.y - q.w*q.z); M[0][2] = 2 * (q.x*q.z + q.w*q.y); M[0][3] = T(0);
|
|
|
- M[1][0] = 2 * (q.x*q.y + q.w*q.z); M[1][1] = ww - xx + yy - zz; M[1][2] = 2 * (q.y*q.z - q.w*q.x); M[1][3] = T(0);
|
|
|
- M[2][0] = 2 * (q.x*q.z - q.w*q.y); M[2][1] = 2 * (q.y*q.z + q.w*q.x); M[2][2] = ww - xx - yy + zz; M[2][3] = T(0);
|
|
|
- M[3][0] = T(0); M[3][1] = T(0); M[3][2] = T(0); M[3][3] = T(1);
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix4(const Pose<T>& p)
|
|
|
- {
|
|
|
- Matrix4 result(p.Rotation);
|
|
|
- result.SetTranslation(p.Translation);
|
|
|
- *this = result;
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- // C-interop support
|
|
|
- explicit Matrix4(const Matrix4<typename Math<T>::OtherFloatType> &src)
|
|
|
- {
|
|
|
- for (int i = 0; i < 4; i++)
|
|
|
- for (int j = 0; j < 4; j++)
|
|
|
- M[i][j] = (T)src.M[i][j];
|
|
|
- }
|
|
|
-
|
|
|
- // C-interop support.
|
|
|
- Matrix4(const typename CompatibleTypes<Matrix4<T> >::Type& s)
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(s) == sizeof(Matrix4), "sizeof(s) == sizeof(Matrix4)");
|
|
|
- memcpy(M, s.M, sizeof(M));
|
|
|
- }
|
|
|
-
|
|
|
- operator typename CompatibleTypes<Matrix4<T> >::Type () const
|
|
|
- {
|
|
|
- typename CompatibleTypes<Matrix4<T> >::Type result;
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(result) == sizeof(Matrix4), "sizeof(result) == sizeof(Matrix4)");
|
|
|
- memcpy(result.M, M, sizeof(M));
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- void ToString(char* dest, size_t destsize) const
|
|
|
- {
|
|
|
- size_t pos = 0;
|
|
|
- for (int r=0; r<4; r++)
|
|
|
- {
|
|
|
- for (int c=0; c<4; c++)
|
|
|
- {
|
|
|
- pos += OVRMath_sprintf(dest+pos, destsize-pos, "%g ", M[r][c]);
|
|
|
- }
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix4 FromString(const char* src)
|
|
|
- {
|
|
|
- Matrix4 result;
|
|
|
- if (src)
|
|
|
- {
|
|
|
- for (int r = 0; r < 4; r++)
|
|
|
- {
|
|
|
- for (int c = 0; c < 4; c++)
|
|
|
- {
|
|
|
- result.M[r][c] = (T)atof(src);
|
|
|
- while (*src && *src != ' ')
|
|
|
- {
|
|
|
- src++;
|
|
|
- }
|
|
|
- while (*src && *src == ' ')
|
|
|
- {
|
|
|
- src++;
|
|
|
- }
|
|
|
- }
|
|
|
- }
|
|
|
- }
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix4 Identity() { return Matrix4(); }
|
|
|
-
|
|
|
- void SetIdentity()
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = M[2][2] = M[3][3] = T(1);
|
|
|
- M[0][1] = M[1][0] = M[2][3] = M[3][1] = T(0);
|
|
|
- M[0][2] = M[1][2] = M[2][0] = M[3][2] = T(0);
|
|
|
- M[0][3] = M[1][3] = M[2][1] = M[3][0] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- void SetXBasis(const Vector3<T>& v)
|
|
|
- {
|
|
|
- M[0][0] = v.x;
|
|
|
- M[1][0] = v.y;
|
|
|
- M[2][0] = v.z;
|
|
|
- }
|
|
|
- Vector3<T> GetXBasis() const
|
|
|
- {
|
|
|
- return Vector3<T>(M[0][0], M[1][0], M[2][0]);
|
|
|
- }
|
|
|
-
|
|
|
- void SetYBasis(const Vector3<T> & v)
|
|
|
- {
|
|
|
- M[0][1] = v.x;
|
|
|
- M[1][1] = v.y;
|
|
|
- M[2][1] = v.z;
|
|
|
- }
|
|
|
- Vector3<T> GetYBasis() const
|
|
|
- {
|
|
|
- return Vector3<T>(M[0][1], M[1][1], M[2][1]);
|
|
|
- }
|
|
|
-
|
|
|
- void SetZBasis(const Vector3<T> & v)
|
|
|
- {
|
|
|
- M[0][2] = v.x;
|
|
|
- M[1][2] = v.y;
|
|
|
- M[2][2] = v.z;
|
|
|
- }
|
|
|
- Vector3<T> GetZBasis() const
|
|
|
- {
|
|
|
- return Vector3<T>(M[0][2], M[1][2], M[2][2]);
|
|
|
- }
|
|
|
-
|
|
|
- bool operator== (const Matrix4& b) const
|
|
|
- {
|
|
|
- bool isEqual = true;
|
|
|
- for (int i = 0; i < 4; i++)
|
|
|
- for (int j = 0; j < 4; j++)
|
|
|
- isEqual &= (M[i][j] == b.M[i][j]);
|
|
|
-
|
|
|
- return isEqual;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 operator+ (const Matrix4& b) const
|
|
|
- {
|
|
|
- Matrix4 result(*this);
|
|
|
- result += b;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4& operator+= (const Matrix4& b)
|
|
|
- {
|
|
|
- for (int i = 0; i < 4; i++)
|
|
|
- for (int j = 0; j < 4; j++)
|
|
|
- M[i][j] += b.M[i][j];
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 operator- (const Matrix4& b) const
|
|
|
- {
|
|
|
- Matrix4 result(*this);
|
|
|
- result -= b;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4& operator-= (const Matrix4& b)
|
|
|
- {
|
|
|
- for (int i = 0; i < 4; i++)
|
|
|
- for (int j = 0; j < 4; j++)
|
|
|
- M[i][j] -= b.M[i][j];
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- // Multiplies two matrices into destination with minimum copying.
|
|
|
- static Matrix4& Multiply(Matrix4* d, const Matrix4& a, const Matrix4& b)
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT((d != &a) && (d != &b));
|
|
|
- int i = 0;
|
|
|
- do {
|
|
|
- d->M[i][0] = a.M[i][0] * b.M[0][0] + a.M[i][1] * b.M[1][0] + a.M[i][2] * b.M[2][0] + a.M[i][3] * b.M[3][0];
|
|
|
- d->M[i][1] = a.M[i][0] * b.M[0][1] + a.M[i][1] * b.M[1][1] + a.M[i][2] * b.M[2][1] + a.M[i][3] * b.M[3][1];
|
|
|
- d->M[i][2] = a.M[i][0] * b.M[0][2] + a.M[i][1] * b.M[1][2] + a.M[i][2] * b.M[2][2] + a.M[i][3] * b.M[3][2];
|
|
|
- d->M[i][3] = a.M[i][0] * b.M[0][3] + a.M[i][1] * b.M[1][3] + a.M[i][2] * b.M[2][3] + a.M[i][3] * b.M[3][3];
|
|
|
- } while((++i) < 4);
|
|
|
-
|
|
|
- return *d;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 operator* (const Matrix4& b) const
|
|
|
- {
|
|
|
- Matrix4 result(Matrix4::NoInit);
|
|
|
- Multiply(&result, *this, b);
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4& operator*= (const Matrix4& b)
|
|
|
- {
|
|
|
- return Multiply(this, Matrix4(*this), b);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 operator* (T s) const
|
|
|
- {
|
|
|
- Matrix4 result(*this);
|
|
|
- result *= s;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4& operator*= (T s)
|
|
|
- {
|
|
|
- for (int i = 0; i < 4; i++)
|
|
|
- for (int j = 0; j < 4; j++)
|
|
|
- M[i][j] *= s;
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- Matrix4 operator/ (T s) const
|
|
|
- {
|
|
|
- Matrix4 result(*this);
|
|
|
- result /= s;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4& operator/= (T s)
|
|
|
- {
|
|
|
- for (int i = 0; i < 4; i++)
|
|
|
- for (int j = 0; j < 4; j++)
|
|
|
- M[i][j] /= s;
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> Transform(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- const T rcpW = T(1) / (M[3][0] * v.x + M[3][1] * v.y + M[3][2] * v.z + M[3][3]);
|
|
|
- return Vector3<T>((M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3]) * rcpW,
|
|
|
- (M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3]) * rcpW,
|
|
|
- (M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3]) * rcpW);
|
|
|
- }
|
|
|
-
|
|
|
- Vector4<T> Transform(const Vector4<T>& v) const
|
|
|
- {
|
|
|
- return Vector4<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3] * v.w,
|
|
|
- M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3] * v.w,
|
|
|
- M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3] * v.w,
|
|
|
- M[3][0] * v.x + M[3][1] * v.y + M[3][2] * v.z + M[3][3] * v.w);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 Transposed() const
|
|
|
- {
|
|
|
- return Matrix4(M[0][0], M[1][0], M[2][0], M[3][0],
|
|
|
- M[0][1], M[1][1], M[2][1], M[3][1],
|
|
|
- M[0][2], M[1][2], M[2][2], M[3][2],
|
|
|
- M[0][3], M[1][3], M[2][3], M[3][3]);
|
|
|
- }
|
|
|
-
|
|
|
- void Transpose()
|
|
|
- {
|
|
|
- *this = Transposed();
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- T SubDet (const size_t* rows, const size_t* cols) const
|
|
|
- {
|
|
|
- return M[rows[0]][cols[0]] * (M[rows[1]][cols[1]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[1]])
|
|
|
- - M[rows[0]][cols[1]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[0]])
|
|
|
- + M[rows[0]][cols[2]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[1]] - M[rows[1]][cols[1]] * M[rows[2]][cols[0]]);
|
|
|
- }
|
|
|
-
|
|
|
- T Cofactor(size_t I, size_t J) const
|
|
|
- {
|
|
|
- const size_t indices[4][3] = {{1,2,3},{0,2,3},{0,1,3},{0,1,2}};
|
|
|
- return ((I+J)&1) ? -SubDet(indices[I],indices[J]) : SubDet(indices[I],indices[J]);
|
|
|
- }
|
|
|
-
|
|
|
- T Determinant() const
|
|
|
- {
|
|
|
- return M[0][0] * Cofactor(0,0) + M[0][1] * Cofactor(0,1) + M[0][2] * Cofactor(0,2) + M[0][3] * Cofactor(0,3);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 Adjugated() const
|
|
|
- {
|
|
|
- return Matrix4(Cofactor(0,0), Cofactor(1,0), Cofactor(2,0), Cofactor(3,0),
|
|
|
- Cofactor(0,1), Cofactor(1,1), Cofactor(2,1), Cofactor(3,1),
|
|
|
- Cofactor(0,2), Cofactor(1,2), Cofactor(2,2), Cofactor(3,2),
|
|
|
- Cofactor(0,3), Cofactor(1,3), Cofactor(2,3), Cofactor(3,3));
|
|
|
- }
|
|
|
-
|
|
|
- Matrix4 Inverted() const
|
|
|
- {
|
|
|
- T det = Determinant();
|
|
|
- OVR_MATH_ASSERT(det != 0);
|
|
|
- return Adjugated() * (T(1)/det);
|
|
|
- }
|
|
|
-
|
|
|
- void Invert()
|
|
|
- {
|
|
|
- *this = Inverted();
|
|
|
- }
|
|
|
-
|
|
|
- // This is more efficient than general inverse, but ONLY works
|
|
|
- // correctly if it is a homogeneous transform matrix (rot + trans)
|
|
|
- Matrix4 InvertedHomogeneousTransform() const
|
|
|
- {
|
|
|
- // Make the inverse rotation matrix
|
|
|
- Matrix4 rinv = this->Transposed();
|
|
|
- rinv.M[3][0] = rinv.M[3][1] = rinv.M[3][2] = T(0);
|
|
|
- // Make the inverse translation matrix
|
|
|
- Vector3<T> tvinv(-M[0][3],-M[1][3],-M[2][3]);
|
|
|
- Matrix4 tinv = Matrix4::Translation(tvinv);
|
|
|
- return rinv * tinv; // "untranslate", then "unrotate"
|
|
|
- }
|
|
|
-
|
|
|
- // This is more efficient than general inverse, but ONLY works
|
|
|
- // correctly if it is a homogeneous transform matrix (rot + trans)
|
|
|
- void InvertHomogeneousTransform()
|
|
|
- {
|
|
|
- *this = InvertedHomogeneousTransform();
|
|
|
- }
|
|
|
-
|
|
|
- // Matrix to Euler Angles conversion
|
|
|
- // a,b,c, are the YawPitchRoll angles to be returned
|
|
|
- // rotation a around axis A1
|
|
|
- // is followed by rotation b around axis A2
|
|
|
- // is followed by rotation c around axis A3
|
|
|
- // rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
|
- template <Axis A1, Axis A2, Axis A3, RotateDirection D, HandedSystem S>
|
|
|
- void ToEulerAngles(T *a, T *b, T *c) const
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT((A1 != A2) && (A2 != A3) && (A1 != A3), "(A1 != A2) && (A2 != A3) && (A1 != A3)");
|
|
|
-
|
|
|
- T psign = T(-1);
|
|
|
- if (((A1 + 1) % 3 == A2) && ((A2 + 1) % 3 == A3)) // Determine whether even permutation
|
|
|
- psign = T(1);
|
|
|
-
|
|
|
- T pm = psign*M[A1][A3];
|
|
|
- T singularityRadius = Math<T>::SingularityRadius();
|
|
|
- if (pm < T(-1) + singularityRadius)
|
|
|
- { // South pole singularity
|
|
|
- *a = T(0);
|
|
|
- *b = -S*D*((T)MATH_DOUBLE_PIOVER2);
|
|
|
- *c = S*D*atan2( psign*M[A2][A1], M[A2][A2] );
|
|
|
- }
|
|
|
- else if (pm > T(1) - singularityRadius)
|
|
|
- { // North pole singularity
|
|
|
- *a = T(0);
|
|
|
- *b = S*D*((T)MATH_DOUBLE_PIOVER2);
|
|
|
- *c = S*D*atan2( psign*M[A2][A1], M[A2][A2] );
|
|
|
- }
|
|
|
- else
|
|
|
- { // Normal case (nonsingular)
|
|
|
- *a = S*D*atan2( -psign*M[A2][A3], M[A3][A3] );
|
|
|
- *b = S*D*asin(pm);
|
|
|
- *c = S*D*atan2( -psign*M[A1][A2], M[A1][A1] );
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- // Matrix to Euler Angles conversion
|
|
|
- // a,b,c, are the YawPitchRoll angles to be returned
|
|
|
- // rotation a around axis A1
|
|
|
- // is followed by rotation b around axis A2
|
|
|
- // is followed by rotation c around axis A1
|
|
|
- // rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
|
- template <Axis A1, Axis A2, RotateDirection D, HandedSystem S>
|
|
|
- void ToEulerAnglesABA(T *a, T *b, T *c) const
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT(A1 != A2, "A1 != A2");
|
|
|
-
|
|
|
- // Determine the axis that was not supplied
|
|
|
- int m = 3 - A1 - A2;
|
|
|
-
|
|
|
- T psign = T(-1);
|
|
|
- if ((A1 + 1) % 3 == A2) // Determine whether even permutation
|
|
|
- psign = T(1);
|
|
|
-
|
|
|
- T c2 = M[A1][A1];
|
|
|
- T singularityRadius = Math<T>::SingularityRadius();
|
|
|
- if (c2 < T(-1) + singularityRadius)
|
|
|
- { // South pole singularity
|
|
|
- *a = T(0);
|
|
|
- *b = S*D*((T)MATH_DOUBLE_PI);
|
|
|
- *c = S*D*atan2( -psign*M[A2][m],M[A2][A2]);
|
|
|
- }
|
|
|
- else if (c2 > T(1) - singularityRadius)
|
|
|
- { // North pole singularity
|
|
|
- *a = T(0);
|
|
|
- *b = T(0);
|
|
|
- *c = S*D*atan2( -psign*M[A2][m],M[A2][A2]);
|
|
|
- }
|
|
|
- else
|
|
|
- { // Normal case (nonsingular)
|
|
|
- *a = S*D*atan2( M[A2][A1],-psign*M[m][A1]);
|
|
|
- *b = S*D*acos(c2);
|
|
|
- *c = S*D*atan2( M[A1][A2],psign*M[A1][m]);
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a matrix that converts the vertices from one coordinate system
|
|
|
- // to another.
|
|
|
- static Matrix4 AxisConversion(const WorldAxes& to, const WorldAxes& from)
|
|
|
- {
|
|
|
- // Holds axis values from the 'to' structure
|
|
|
- int toArray[3] = { to.XAxis, to.YAxis, to.ZAxis };
|
|
|
-
|
|
|
- // The inverse of the toArray
|
|
|
- int inv[4];
|
|
|
- inv[0] = inv[abs(to.XAxis)] = 0;
|
|
|
- inv[abs(to.YAxis)] = 1;
|
|
|
- inv[abs(to.ZAxis)] = 2;
|
|
|
-
|
|
|
- Matrix4 m(0, 0, 0,
|
|
|
- 0, 0, 0,
|
|
|
- 0, 0, 0);
|
|
|
-
|
|
|
- // Only three values in the matrix need to be changed to 1 or -1.
|
|
|
- m.M[inv[abs(from.XAxis)]][0] = T(from.XAxis/toArray[inv[abs(from.XAxis)]]);
|
|
|
- m.M[inv[abs(from.YAxis)]][1] = T(from.YAxis/toArray[inv[abs(from.YAxis)]]);
|
|
|
- m.M[inv[abs(from.ZAxis)]][2] = T(from.ZAxis/toArray[inv[abs(from.ZAxis)]]);
|
|
|
- return m;
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- // Creates a matrix for translation by vector
|
|
|
- static Matrix4 Translation(const Vector3<T>& v)
|
|
|
- {
|
|
|
- Matrix4 t;
|
|
|
- t.M[0][3] = v.x;
|
|
|
- t.M[1][3] = v.y;
|
|
|
- t.M[2][3] = v.z;
|
|
|
- return t;
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a matrix for translation by vector
|
|
|
- static Matrix4 Translation(T x, T y, T z = T(0))
|
|
|
- {
|
|
|
- Matrix4 t;
|
|
|
- t.M[0][3] = x;
|
|
|
- t.M[1][3] = y;
|
|
|
- t.M[2][3] = z;
|
|
|
- return t;
|
|
|
- }
|
|
|
-
|
|
|
- // Sets the translation part
|
|
|
- void SetTranslation(const Vector3<T>& v)
|
|
|
- {
|
|
|
- M[0][3] = v.x;
|
|
|
- M[1][3] = v.y;
|
|
|
- M[2][3] = v.z;
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> GetTranslation() const
|
|
|
- {
|
|
|
- return Vector3<T>( M[0][3], M[1][3], M[2][3] );
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a matrix for scaling by vector
|
|
|
- static Matrix4 Scaling(const Vector3<T>& v)
|
|
|
- {
|
|
|
- Matrix4 t;
|
|
|
- t.M[0][0] = v.x;
|
|
|
- t.M[1][1] = v.y;
|
|
|
- t.M[2][2] = v.z;
|
|
|
- return t;
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a matrix for scaling by vector
|
|
|
- static Matrix4 Scaling(T x, T y, T z)
|
|
|
- {
|
|
|
- Matrix4 t;
|
|
|
- t.M[0][0] = x;
|
|
|
- t.M[1][1] = y;
|
|
|
- t.M[2][2] = z;
|
|
|
- return t;
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a matrix for scaling by constant
|
|
|
- static Matrix4 Scaling(T s)
|
|
|
- {
|
|
|
- Matrix4 t;
|
|
|
- t.M[0][0] = s;
|
|
|
- t.M[1][1] = s;
|
|
|
- t.M[2][2] = s;
|
|
|
- return t;
|
|
|
- }
|
|
|
-
|
|
|
- // Simple L1 distance in R^12
|
|
|
- T Distance(const Matrix4& m2) const
|
|
|
- {
|
|
|
- T d = fabs(M[0][0] - m2.M[0][0]) + fabs(M[0][1] - m2.M[0][1]);
|
|
|
- d += fabs(M[0][2] - m2.M[0][2]) + fabs(M[0][3] - m2.M[0][3]);
|
|
|
- d += fabs(M[1][0] - m2.M[1][0]) + fabs(M[1][1] - m2.M[1][1]);
|
|
|
- d += fabs(M[1][2] - m2.M[1][2]) + fabs(M[1][3] - m2.M[1][3]);
|
|
|
- d += fabs(M[2][0] - m2.M[2][0]) + fabs(M[2][1] - m2.M[2][1]);
|
|
|
- d += fabs(M[2][2] - m2.M[2][2]) + fabs(M[2][3] - m2.M[2][3]);
|
|
|
- d += fabs(M[3][0] - m2.M[3][0]) + fabs(M[3][1] - m2.M[3][1]);
|
|
|
- d += fabs(M[3][2] - m2.M[3][2]) + fabs(M[3][3] - m2.M[3][3]);
|
|
|
- return d;
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a rotation matrix rotating around the X axis by 'angle' radians.
|
|
|
- // Just for quick testing. Not for final API. Need to remove case.
|
|
|
- static Matrix4 RotationAxis(Axis A, T angle, RotateDirection d, HandedSystem s)
|
|
|
- {
|
|
|
- T sina = s * d *sin(angle);
|
|
|
- T cosa = cos(angle);
|
|
|
-
|
|
|
- switch(A)
|
|
|
- {
|
|
|
- case Axis_X:
|
|
|
- return Matrix4(1, 0, 0,
|
|
|
- 0, cosa, -sina,
|
|
|
- 0, sina, cosa);
|
|
|
- case Axis_Y:
|
|
|
- return Matrix4(cosa, 0, sina,
|
|
|
- 0, 1, 0,
|
|
|
- -sina, 0, cosa);
|
|
|
- case Axis_Z:
|
|
|
- return Matrix4(cosa, -sina, 0,
|
|
|
- sina, cosa, 0,
|
|
|
- 0, 0, 1);
|
|
|
- default:
|
|
|
- return Matrix4();
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- // Creates a rotation matrix rotating around the X axis by 'angle' radians.
|
|
|
- // Rotation direction is depends on the coordinate system:
|
|
|
- // RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
|
|
|
- // while looking in the negative axis direction. This is the
|
|
|
- // same as looking down from positive axis values towards origin.
|
|
|
- // LHS: Positive angle values rotate clock-wise (CW), while looking in the
|
|
|
- // negative axis direction.
|
|
|
- static Matrix4 RotationX(T angle)
|
|
|
- {
|
|
|
- T sina = sin(angle);
|
|
|
- T cosa = cos(angle);
|
|
|
- return Matrix4(1, 0, 0,
|
|
|
- 0, cosa, -sina,
|
|
|
- 0, sina, cosa);
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a rotation matrix rotating around the Y axis by 'angle' radians.
|
|
|
- // Rotation direction is depends on the coordinate system:
|
|
|
- // RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
|
|
|
- // while looking in the negative axis direction. This is the
|
|
|
- // same as looking down from positive axis values towards origin.
|
|
|
- // LHS: Positive angle values rotate clock-wise (CW), while looking in the
|
|
|
- // negative axis direction.
|
|
|
- static Matrix4 RotationY(T angle)
|
|
|
- {
|
|
|
- T sina = (T)sin(angle);
|
|
|
- T cosa = (T)cos(angle);
|
|
|
- return Matrix4(cosa, 0, sina,
|
|
|
- 0, 1, 0,
|
|
|
- -sina, 0, cosa);
|
|
|
- }
|
|
|
-
|
|
|
- // Creates a rotation matrix rotating around the Z axis by 'angle' radians.
|
|
|
- // Rotation direction is depends on the coordinate system:
|
|
|
- // RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
|
|
|
- // while looking in the negative axis direction. This is the
|
|
|
- // same as looking down from positive axis values towards origin.
|
|
|
- // LHS: Positive angle values rotate clock-wise (CW), while looking in the
|
|
|
- // negative axis direction.
|
|
|
- static Matrix4 RotationZ(T angle)
|
|
|
- {
|
|
|
- T sina = sin(angle);
|
|
|
- T cosa = cos(angle);
|
|
|
- return Matrix4(cosa, -sina, 0,
|
|
|
- sina, cosa, 0,
|
|
|
- 0, 0, 1);
|
|
|
- }
|
|
|
-
|
|
|
- // LookAtRH creates a View transformation matrix for right-handed coordinate system.
|
|
|
- // The resulting matrix points camera from 'eye' towards 'at' direction, with 'up'
|
|
|
- // specifying the up vector. The resulting matrix should be used with PerspectiveRH
|
|
|
- // projection.
|
|
|
- static Matrix4 LookAtRH(const Vector3<T>& eye, const Vector3<T>& at, const Vector3<T>& up)
|
|
|
- {
|
|
|
- Vector3<T> z = (eye - at).Normalized(); // Forward
|
|
|
- Vector3<T> x = up.Cross(z).Normalized(); // Right
|
|
|
- Vector3<T> y = z.Cross(x);
|
|
|
-
|
|
|
- Matrix4 m(x.x, x.y, x.z, -(x.Dot(eye)),
|
|
|
- y.x, y.y, y.z, -(y.Dot(eye)),
|
|
|
- z.x, z.y, z.z, -(z.Dot(eye)),
|
|
|
- 0, 0, 0, 1 );
|
|
|
- return m;
|
|
|
- }
|
|
|
-
|
|
|
- // LookAtLH creates a View transformation matrix for left-handed coordinate system.
|
|
|
- // The resulting matrix points camera from 'eye' towards 'at' direction, with 'up'
|
|
|
- // specifying the up vector.
|
|
|
- static Matrix4 LookAtLH(const Vector3<T>& eye, const Vector3<T>& at, const Vector3<T>& up)
|
|
|
- {
|
|
|
- Vector3<T> z = (at - eye).Normalized(); // Forward
|
|
|
- Vector3<T> x = up.Cross(z).Normalized(); // Right
|
|
|
- Vector3<T> y = z.Cross(x);
|
|
|
-
|
|
|
- Matrix4 m(x.x, x.y, x.z, -(x.Dot(eye)),
|
|
|
- y.x, y.y, y.z, -(y.Dot(eye)),
|
|
|
- z.x, z.y, z.z, -(z.Dot(eye)),
|
|
|
- 0, 0, 0, 1 );
|
|
|
- return m;
|
|
|
- }
|
|
|
-
|
|
|
- // PerspectiveRH creates a right-handed perspective projection matrix that can be
|
|
|
- // used with the Oculus sample renderer.
|
|
|
- // yfov - Specifies vertical field of view in radians.
|
|
|
- // aspect - Screen aspect ration, which is usually width/height for square pixels.
|
|
|
- // Note that xfov = yfov * aspect.
|
|
|
- // znear - Absolute value of near Z clipping clipping range.
|
|
|
- // zfar - Absolute value of far Z clipping clipping range (larger then near).
|
|
|
- // Even though RHS usually looks in the direction of negative Z, positive values
|
|
|
- // are expected for znear and zfar.
|
|
|
- static Matrix4 PerspectiveRH(T yfov, T aspect, T znear, T zfar)
|
|
|
- {
|
|
|
- Matrix4 m;
|
|
|
- T tanHalfFov = tan(yfov * T(0.5));
|
|
|
-
|
|
|
- m.M[0][0] = T(1) / (aspect * tanHalfFov);
|
|
|
- m.M[1][1] = T(1) / tanHalfFov;
|
|
|
- m.M[2][2] = zfar / (znear - zfar);
|
|
|
- m.M[3][2] = T(-1);
|
|
|
- m.M[2][3] = (zfar * znear) / (znear - zfar);
|
|
|
- m.M[3][3] = T(0);
|
|
|
-
|
|
|
- // Note: Post-projection matrix result assumes Left-Handed coordinate system,
|
|
|
- // with Y up, X right and Z forward. This supports positive z-buffer values.
|
|
|
- // This is the case even for RHS coordinate input.
|
|
|
- return m;
|
|
|
- }
|
|
|
-
|
|
|
- // PerspectiveLH creates a left-handed perspective projection matrix that can be
|
|
|
- // used with the Oculus sample renderer.
|
|
|
- // yfov - Specifies vertical field of view in radians.
|
|
|
- // aspect - Screen aspect ration, which is usually width/height for square pixels.
|
|
|
- // Note that xfov = yfov * aspect.
|
|
|
- // znear - Absolute value of near Z clipping clipping range.
|
|
|
- // zfar - Absolute value of far Z clipping clipping range (larger then near).
|
|
|
- static Matrix4 PerspectiveLH(T yfov, T aspect, T znear, T zfar)
|
|
|
- {
|
|
|
- Matrix4 m;
|
|
|
- T tanHalfFov = tan(yfov * T(0.5));
|
|
|
-
|
|
|
- m.M[0][0] = T(1) / (aspect * tanHalfFov);
|
|
|
- m.M[1][1] = T(1) / tanHalfFov;
|
|
|
- //m.M[2][2] = zfar / (znear - zfar);
|
|
|
- m.M[2][2] = zfar / (zfar - znear);
|
|
|
- m.M[3][2] = T(-1);
|
|
|
- m.M[2][3] = (zfar * znear) / (znear - zfar);
|
|
|
- m.M[3][3] = T(0);
|
|
|
-
|
|
|
- // Note: Post-projection matrix result assumes Left-Handed coordinate system,
|
|
|
- // with Y up, X right and Z forward. This supports positive z-buffer values.
|
|
|
- // This is the case even for RHS coordinate input.
|
|
|
- return m;
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix4 Ortho2D(T w, T h)
|
|
|
- {
|
|
|
- Matrix4 m;
|
|
|
- m.M[0][0] = T(2.0)/w;
|
|
|
- m.M[1][1] = T(-2.0)/h;
|
|
|
- m.M[0][3] = T(-1.0);
|
|
|
- m.M[1][3] = T(1.0);
|
|
|
- m.M[2][2] = T(0);
|
|
|
- return m;
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Matrix4<float> Matrix4f;
|
|
|
-typedef Matrix4<double> Matrix4d;
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-// ***** Matrix3
|
|
|
-//
|
|
|
-// Matrix3 is a 3x3 matrix used for representing a rotation matrix.
|
|
|
-// The matrix is stored in row-major order in memory, meaning that values
|
|
|
-// of the first row are stored before the next one.
|
|
|
-//
|
|
|
-// The arrangement of the matrix is chosen to be in Right-Handed
|
|
|
-// coordinate system and counterclockwise rotations when looking down
|
|
|
-// the axis
|
|
|
-//
|
|
|
-// Transformation Order:
|
|
|
-// - Transformations are applied from right to left, so the expression
|
|
|
-// M1 * M2 * M3 * V means that the vector V is transformed by M3 first,
|
|
|
-// followed by M2 and M1.
|
|
|
-//
|
|
|
-// Coordinate system: Right Handed
|
|
|
-//
|
|
|
-// Rotations: Counterclockwise when looking down the axis. All angles are in radians.
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class Matrix3
|
|
|
-{
|
|
|
-public:
|
|
|
- typedef T ElementType;
|
|
|
- static const size_t Dimension = 3;
|
|
|
-
|
|
|
- T M[3][3];
|
|
|
-
|
|
|
- enum NoInitType { NoInit };
|
|
|
-
|
|
|
- // Construct with no memory initialization.
|
|
|
- Matrix3(NoInitType) { }
|
|
|
-
|
|
|
- // By default, we construct identity matrix.
|
|
|
- Matrix3()
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = M[2][2] = T(1);
|
|
|
- M[0][1] = M[1][0] = M[2][0] = T(0);
|
|
|
- M[0][2] = M[1][2] = M[2][1] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3(T m11, T m12, T m13,
|
|
|
- T m21, T m22, T m23,
|
|
|
- T m31, T m32, T m33)
|
|
|
- {
|
|
|
- M[0][0] = m11; M[0][1] = m12; M[0][2] = m13;
|
|
|
- M[1][0] = m21; M[1][1] = m22; M[1][2] = m23;
|
|
|
- M[2][0] = m31; M[2][1] = m32; M[2][2] = m33;
|
|
|
- }
|
|
|
-
|
|
|
- // Construction from X, Y, Z basis vectors
|
|
|
- Matrix3(const Vector3<T>& xBasis, const Vector3<T>& yBasis, const Vector3<T>& zBasis)
|
|
|
- {
|
|
|
- M[0][0] = xBasis.x; M[0][1] = yBasis.x; M[0][2] = zBasis.x;
|
|
|
- M[1][0] = xBasis.y; M[1][1] = yBasis.y; M[1][2] = zBasis.y;
|
|
|
- M[2][0] = xBasis.z; M[2][1] = yBasis.z; M[2][2] = zBasis.z;
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix3(const Quat<T>& q)
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT(q.IsNormalized());
|
|
|
- const T tx = q.x+q.x, ty = q.y+q.y, tz = q.z+q.z;
|
|
|
- const T twx = q.w*tx, twy = q.w*ty, twz = q.w*tz;
|
|
|
- const T txx = q.x*tx, txy = q.x*ty, txz = q.x*tz;
|
|
|
- const T tyy = q.y*ty, tyz = q.y*tz, tzz = q.z*tz;
|
|
|
- M[0][0] = T(1) - (tyy + tzz); M[0][1] = txy - twz; M[0][2] = txz + twy;
|
|
|
- M[1][0] = txy + twz; M[1][1] = T(1) - (txx + tzz); M[1][2] = tyz - twx;
|
|
|
- M[2][0] = txz - twy; M[2][1] = tyz + twx; M[2][2] = T(1) - (txx + tyy);
|
|
|
- }
|
|
|
-
|
|
|
- inline explicit Matrix3(T s)
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = M[2][2] = s;
|
|
|
- M[0][1] = M[0][2] = M[1][0] = M[1][2] = M[2][0] = M[2][1] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3(T m11, T m22, T m33)
|
|
|
- {
|
|
|
- M[0][0] = m11; M[0][1] = T(0); M[0][2] = T(0);
|
|
|
- M[1][0] = T(0); M[1][1] = m22; M[1][2] = T(0);
|
|
|
- M[2][0] = T(0); M[2][1] = T(0); M[2][2] = m33;
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix3(const Matrix3<typename Math<T>::OtherFloatType> &src)
|
|
|
- {
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- M[i][j] = (T)src.M[i][j];
|
|
|
- }
|
|
|
-
|
|
|
- // C-interop support.
|
|
|
- Matrix3(const typename CompatibleTypes<Matrix3<T> >::Type& s)
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(s) == sizeof(Matrix3), "sizeof(s) == sizeof(Matrix3)");
|
|
|
- memcpy(M, s.M, sizeof(M));
|
|
|
- }
|
|
|
-
|
|
|
- operator const typename CompatibleTypes<Matrix3<T> >::Type () const
|
|
|
- {
|
|
|
- typename CompatibleTypes<Matrix3<T> >::Type result;
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(result) == sizeof(Matrix3), "sizeof(result) == sizeof(Matrix3)");
|
|
|
- memcpy(result.M, M, sizeof(M));
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- T operator()(int i, int j) const { return M[i][j]; }
|
|
|
- T& operator()(int i, int j) { return M[i][j]; }
|
|
|
-
|
|
|
- void ToString(char* dest, size_t destsize) const
|
|
|
- {
|
|
|
- size_t pos = 0;
|
|
|
- for (int r=0; r<3; r++)
|
|
|
- {
|
|
|
- for (int c=0; c<3; c++)
|
|
|
- pos += OVRMath_sprintf(dest+pos, destsize-pos, "%g ", M[r][c]);
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix3 FromString(const char* src)
|
|
|
- {
|
|
|
- Matrix3 result;
|
|
|
- if (src)
|
|
|
- {
|
|
|
- for (int r=0; r<3; r++)
|
|
|
- {
|
|
|
- for (int c=0; c<3; c++)
|
|
|
- {
|
|
|
- result.M[r][c] = (T)atof(src);
|
|
|
- while (*src && *src != ' ')
|
|
|
- src++;
|
|
|
- while (*src && *src == ' ')
|
|
|
- src++;
|
|
|
- }
|
|
|
- }
|
|
|
- }
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix3 Identity() { return Matrix3(); }
|
|
|
-
|
|
|
- void SetIdentity()
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = M[2][2] = T(1);
|
|
|
- M[0][1] = M[1][0] = M[2][0] = T(0);
|
|
|
- M[0][2] = M[1][2] = M[2][1] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix3 Diagonal(T m00, T m11, T m22)
|
|
|
- {
|
|
|
- return Matrix3(m00, 0, 0,
|
|
|
- 0, m11, 0,
|
|
|
- 0, 0, m22);
|
|
|
- }
|
|
|
- static Matrix3 Diagonal(const Vector3<T>& v) { return Diagonal(v.x, v.y, v.z); }
|
|
|
-
|
|
|
- T Trace() const { return M[0][0] + M[1][1] + M[2][2]; }
|
|
|
-
|
|
|
- bool operator== (const Matrix3& b) const
|
|
|
- {
|
|
|
- bool isEqual = true;
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- {
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- isEqual &= (M[i][j] == b.M[i][j]);
|
|
|
- }
|
|
|
-
|
|
|
- return isEqual;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3 operator+ (const Matrix3& b) const
|
|
|
- {
|
|
|
- Matrix3<T> result(*this);
|
|
|
- result += b;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3& operator+= (const Matrix3& b)
|
|
|
- {
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- M[i][j] += b.M[i][j];
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- void operator= (const Matrix3& b)
|
|
|
- {
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- M[i][j] = b.M[i][j];
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3 operator- (const Matrix3& b) const
|
|
|
- {
|
|
|
- Matrix3 result(*this);
|
|
|
- result -= b;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3& operator-= (const Matrix3& b)
|
|
|
- {
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- {
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- M[i][j] -= b.M[i][j];
|
|
|
- }
|
|
|
-
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- // Multiplies two matrices into destination with minimum copying.
|
|
|
- static Matrix3& Multiply(Matrix3* d, const Matrix3& a, const Matrix3& b)
|
|
|
- {
|
|
|
- OVR_MATH_ASSERT((d != &a) && (d != &b));
|
|
|
- int i = 0;
|
|
|
- do {
|
|
|
- d->M[i][0] = a.M[i][0] * b.M[0][0] + a.M[i][1] * b.M[1][0] + a.M[i][2] * b.M[2][0];
|
|
|
- d->M[i][1] = a.M[i][0] * b.M[0][1] + a.M[i][1] * b.M[1][1] + a.M[i][2] * b.M[2][1];
|
|
|
- d->M[i][2] = a.M[i][0] * b.M[0][2] + a.M[i][1] * b.M[1][2] + a.M[i][2] * b.M[2][2];
|
|
|
- } while((++i) < 3);
|
|
|
-
|
|
|
- return *d;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3 operator* (const Matrix3& b) const
|
|
|
- {
|
|
|
- Matrix3 result(Matrix3::NoInit);
|
|
|
- Multiply(&result, *this, b);
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3& operator*= (const Matrix3& b)
|
|
|
- {
|
|
|
- return Multiply(this, Matrix3(*this), b);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3 operator* (T s) const
|
|
|
- {
|
|
|
- Matrix3 result(*this);
|
|
|
- result *= s;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3& operator*= (T s)
|
|
|
- {
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- {
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- M[i][j] *= s;
|
|
|
- }
|
|
|
-
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> operator* (const Vector3<T> &b) const
|
|
|
- {
|
|
|
- Vector3<T> result;
|
|
|
- result.x = M[0][0]*b.x + M[0][1]*b.y + M[0][2]*b.z;
|
|
|
- result.y = M[1][0]*b.x + M[1][1]*b.y + M[1][2]*b.z;
|
|
|
- result.z = M[2][0]*b.x + M[2][1]*b.y + M[2][2]*b.z;
|
|
|
-
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3 operator/ (T s) const
|
|
|
- {
|
|
|
- Matrix3 result(*this);
|
|
|
- result /= s;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3& operator/= (T s)
|
|
|
- {
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- {
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- M[i][j] /= s;
|
|
|
- }
|
|
|
-
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Vector2<T> Transform(const Vector2<T>& v) const
|
|
|
- {
|
|
|
- const T rcpZ = T(1) / (M[2][0] * v.x + M[2][1] * v.y + M[2][2]);
|
|
|
- return Vector2<T>((M[0][0] * v.x + M[0][1] * v.y + M[0][2]) * rcpZ,
|
|
|
- (M[1][0] * v.x + M[1][1] * v.y + M[1][2]) * rcpZ);
|
|
|
- }
|
|
|
-
|
|
|
- Vector3<T> Transform(const Vector3<T>& v) const
|
|
|
- {
|
|
|
- return Vector3<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z,
|
|
|
- M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z,
|
|
|
- M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix3 Transposed() const
|
|
|
- {
|
|
|
- return Matrix3(M[0][0], M[1][0], M[2][0],
|
|
|
- M[0][1], M[1][1], M[2][1],
|
|
|
- M[0][2], M[1][2], M[2][2]);
|
|
|
- }
|
|
|
-
|
|
|
- void Transpose()
|
|
|
- {
|
|
|
- *this = Transposed();
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- T SubDet (const size_t* rows, const size_t* cols) const
|
|
|
- {
|
|
|
- return M[rows[0]][cols[0]] * (M[rows[1]][cols[1]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[1]])
|
|
|
- - M[rows[0]][cols[1]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[0]])
|
|
|
- + M[rows[0]][cols[2]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[1]] - M[rows[1]][cols[1]] * M[rows[2]][cols[0]]);
|
|
|
- }
|
|
|
-
|
|
|
-
|
|
|
- // M += a*b.t()
|
|
|
- inline void Rank1Add(const Vector3<T> &a, const Vector3<T> &b)
|
|
|
- {
|
|
|
- M[0][0] += a.x*b.x; M[0][1] += a.x*b.y; M[0][2] += a.x*b.z;
|
|
|
- M[1][0] += a.y*b.x; M[1][1] += a.y*b.y; M[1][2] += a.y*b.z;
|
|
|
- M[2][0] += a.z*b.x; M[2][1] += a.z*b.y; M[2][2] += a.z*b.z;
|
|
|
- }
|
|
|
-
|
|
|
- // M -= a*b.t()
|
|
|
- inline void Rank1Sub(const Vector3<T> &a, const Vector3<T> &b)
|
|
|
- {
|
|
|
- M[0][0] -= a.x*b.x; M[0][1] -= a.x*b.y; M[0][2] -= a.x*b.z;
|
|
|
- M[1][0] -= a.y*b.x; M[1][1] -= a.y*b.y; M[1][2] -= a.y*b.z;
|
|
|
- M[2][0] -= a.z*b.x; M[2][1] -= a.z*b.y; M[2][2] -= a.z*b.z;
|
|
|
- }
|
|
|
-
|
|
|
- inline Vector3<T> Col(int c) const
|
|
|
- {
|
|
|
- return Vector3<T>(M[0][c], M[1][c], M[2][c]);
|
|
|
- }
|
|
|
-
|
|
|
- inline Vector3<T> Row(int r) const
|
|
|
- {
|
|
|
- return Vector3<T>(M[r][0], M[r][1], M[r][2]);
|
|
|
- }
|
|
|
-
|
|
|
- inline Vector3<T> GetColumn(int c) const
|
|
|
- {
|
|
|
- return Vector3<T>(M[0][c], M[1][c], M[2][c]);
|
|
|
- }
|
|
|
-
|
|
|
- inline Vector3<T> GetRow(int r) const
|
|
|
- {
|
|
|
- return Vector3<T>(M[r][0], M[r][1], M[r][2]);
|
|
|
- }
|
|
|
-
|
|
|
- inline void SetColumn(int c, const Vector3<T>& v)
|
|
|
- {
|
|
|
- M[0][c] = v.x;
|
|
|
- M[1][c] = v.y;
|
|
|
- M[2][c] = v.z;
|
|
|
- }
|
|
|
-
|
|
|
- inline void SetRow(int r, const Vector3<T>& v)
|
|
|
- {
|
|
|
- M[r][0] = v.x;
|
|
|
- M[r][1] = v.y;
|
|
|
- M[r][2] = v.z;
|
|
|
- }
|
|
|
-
|
|
|
- inline T Determinant() const
|
|
|
- {
|
|
|
- const Matrix3<T>& m = *this;
|
|
|
- T d;
|
|
|
-
|
|
|
- d = m.M[0][0] * (m.M[1][1]*m.M[2][2] - m.M[1][2] * m.M[2][1]);
|
|
|
- d -= m.M[0][1] * (m.M[1][0]*m.M[2][2] - m.M[1][2] * m.M[2][0]);
|
|
|
- d += m.M[0][2] * (m.M[1][0]*m.M[2][1] - m.M[1][1] * m.M[2][0]);
|
|
|
-
|
|
|
- return d;
|
|
|
- }
|
|
|
-
|
|
|
- inline Matrix3<T> Inverse() const
|
|
|
- {
|
|
|
- Matrix3<T> a;
|
|
|
- const Matrix3<T>& m = *this;
|
|
|
- T d = Determinant();
|
|
|
-
|
|
|
- OVR_MATH_ASSERT(d != 0);
|
|
|
- T s = T(1)/d;
|
|
|
-
|
|
|
- a.M[0][0] = s * (m.M[1][1] * m.M[2][2] - m.M[1][2] * m.M[2][1]);
|
|
|
- a.M[1][0] = s * (m.M[1][2] * m.M[2][0] - m.M[1][0] * m.M[2][2]);
|
|
|
- a.M[2][0] = s * (m.M[1][0] * m.M[2][1] - m.M[1][1] * m.M[2][0]);
|
|
|
-
|
|
|
- a.M[0][1] = s * (m.M[0][2] * m.M[2][1] - m.M[0][1] * m.M[2][2]);
|
|
|
- a.M[1][1] = s * (m.M[0][0] * m.M[2][2] - m.M[0][2] * m.M[2][0]);
|
|
|
- a.M[2][1] = s * (m.M[0][1] * m.M[2][0] - m.M[0][0] * m.M[2][1]);
|
|
|
-
|
|
|
- a.M[0][2] = s * (m.M[0][1] * m.M[1][2] - m.M[0][2] * m.M[1][1]);
|
|
|
- a.M[1][2] = s * (m.M[0][2] * m.M[1][0] - m.M[0][0] * m.M[1][2]);
|
|
|
- a.M[2][2] = s * (m.M[0][0] * m.M[1][1] - m.M[0][1] * m.M[1][0]);
|
|
|
-
|
|
|
- return a;
|
|
|
- }
|
|
|
-
|
|
|
- // Outer Product of two column vectors: a * b.Transpose()
|
|
|
- static Matrix3 OuterProduct(const Vector3<T>& a, const Vector3<T>& b)
|
|
|
- {
|
|
|
- return Matrix3(a.x*b.x, a.x*b.y, a.x*b.z,
|
|
|
- a.y*b.x, a.y*b.y, a.y*b.z,
|
|
|
- a.z*b.x, a.z*b.y, a.z*b.z);
|
|
|
- }
|
|
|
-
|
|
|
- // Vector cross product as a premultiply matrix:
|
|
|
- // L.Cross(R) = LeftCrossAsMatrix(L) * R
|
|
|
- static Matrix3 LeftCrossAsMatrix(const Vector3<T>& L)
|
|
|
- {
|
|
|
- return Matrix3(
|
|
|
- T(0), -L.z, +L.y,
|
|
|
- +L.z, T(0), -L.x,
|
|
|
- -L.y, +L.x, T(0));
|
|
|
- }
|
|
|
-
|
|
|
- // Vector cross product as a premultiply matrix:
|
|
|
- // L.Cross(R) = RightCrossAsMatrix(R) * L
|
|
|
- static Matrix3 RightCrossAsMatrix(const Vector3<T>& R)
|
|
|
- {
|
|
|
- return Matrix3(
|
|
|
- T(0), +R.z, -R.y,
|
|
|
- -R.z, T(0), +R.x,
|
|
|
- +R.y, -R.x, T(0));
|
|
|
- }
|
|
|
-
|
|
|
- // Angle in radians of a rotation matrix
|
|
|
- // Uses identity trace(a) = 2*cos(theta) + 1
|
|
|
- T Angle() const
|
|
|
- {
|
|
|
- return Acos((Trace() - T(1)) * T(0.5));
|
|
|
- }
|
|
|
-
|
|
|
- // Angle in radians between two rotation matrices
|
|
|
- T Angle(const Matrix3& b) const
|
|
|
- {
|
|
|
- // Compute trace of (this->Transposed() * b)
|
|
|
- // This works out to sum of products of elements.
|
|
|
- T trace = T(0);
|
|
|
- for (int i = 0; i < 3; i++)
|
|
|
- {
|
|
|
- for (int j = 0; j < 3; j++)
|
|
|
- {
|
|
|
- trace += M[i][j] * b.M[i][j];
|
|
|
- }
|
|
|
- }
|
|
|
- return Acos((trace - T(1)) * T(0.5));
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Matrix3<float> Matrix3f;
|
|
|
-typedef Matrix3<double> Matrix3d;
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-// ***** Matrix2
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class Matrix2
|
|
|
-{
|
|
|
-public:
|
|
|
- typedef T ElementType;
|
|
|
- static const size_t Dimension = 2;
|
|
|
-
|
|
|
- T M[2][2];
|
|
|
-
|
|
|
- enum NoInitType { NoInit };
|
|
|
-
|
|
|
- // Construct with no memory initialization.
|
|
|
- Matrix2(NoInitType) { }
|
|
|
-
|
|
|
- // By default, we construct identity matrix.
|
|
|
- Matrix2()
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = T(1);
|
|
|
- M[0][1] = M[1][0] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2(T m11, T m12,
|
|
|
- T m21, T m22)
|
|
|
- {
|
|
|
- M[0][0] = m11; M[0][1] = m12;
|
|
|
- M[1][0] = m21; M[1][1] = m22;
|
|
|
- }
|
|
|
-
|
|
|
- // Construction from X, Y basis vectors
|
|
|
- Matrix2(const Vector2<T>& xBasis, const Vector2<T>& yBasis)
|
|
|
- {
|
|
|
- M[0][0] = xBasis.x; M[0][1] = yBasis.x;
|
|
|
- M[1][0] = xBasis.y; M[1][1] = yBasis.y;
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix2(T s)
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = s;
|
|
|
- M[0][1] = M[1][0] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2(T m11, T m22)
|
|
|
- {
|
|
|
- M[0][0] = m11; M[0][1] = T(0);
|
|
|
- M[1][0] = T(0); M[1][1] = m22;
|
|
|
- }
|
|
|
-
|
|
|
- explicit Matrix2(const Matrix2<typename Math<T>::OtherFloatType> &src)
|
|
|
- {
|
|
|
- M[0][0] = T(src.M[0][0]); M[0][1] = T(src.M[0][1]);
|
|
|
- M[1][0] = T(src.M[1][0]); M[1][1] = T(src.M[1][1]);
|
|
|
- }
|
|
|
-
|
|
|
- // C-interop support
|
|
|
- Matrix2(const typename CompatibleTypes<Matrix2<T> >::Type& s)
|
|
|
- {
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(s) == sizeof(Matrix2), "sizeof(s) == sizeof(Matrix2)");
|
|
|
- memcpy(M, s.M, sizeof(M));
|
|
|
- }
|
|
|
-
|
|
|
- operator const typename CompatibleTypes<Matrix2<T> >::Type() const
|
|
|
- {
|
|
|
- typename CompatibleTypes<Matrix2<T> >::Type result;
|
|
|
- OVR_MATH_STATIC_ASSERT(sizeof(result) == sizeof(Matrix2), "sizeof(result) == sizeof(Matrix2)");
|
|
|
- memcpy(result.M, M, sizeof(M));
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- T operator()(int i, int j) const { return M[i][j]; }
|
|
|
- T& operator()(int i, int j) { return M[i][j]; }
|
|
|
- const T* operator[](int i) const { return M[i]; }
|
|
|
- T* operator[](int i) { return M[i]; }
|
|
|
-
|
|
|
- static Matrix2 Identity() { return Matrix2(); }
|
|
|
-
|
|
|
- void SetIdentity()
|
|
|
- {
|
|
|
- M[0][0] = M[1][1] = T(1);
|
|
|
- M[0][1] = M[1][0] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- static Matrix2 Diagonal(T m00, T m11)
|
|
|
- {
|
|
|
- return Matrix2(m00, m11);
|
|
|
- }
|
|
|
- static Matrix2 Diagonal(const Vector2<T>& v) { return Matrix2(v.x, v.y); }
|
|
|
-
|
|
|
- T Trace() const { return M[0][0] + M[1][1]; }
|
|
|
-
|
|
|
- bool operator== (const Matrix2& b) const
|
|
|
- {
|
|
|
- return M[0][0] == b.M[0][0] && M[0][1] == b.M[0][1] &&
|
|
|
- M[1][0] == b.M[1][0] && M[1][1] == b.M[1][1];
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 operator+ (const Matrix2& b) const
|
|
|
- {
|
|
|
- return Matrix2(M[0][0] + b.M[0][0], M[0][1] + b.M[0][1],
|
|
|
- M[1][0] + b.M[1][0], M[1][1] + b.M[1][1]);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2& operator+= (const Matrix2& b)
|
|
|
- {
|
|
|
- M[0][0] += b.M[0][0]; M[0][1] += b.M[0][1];
|
|
|
- M[1][0] += b.M[1][0]; M[1][1] += b.M[1][1];
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- void operator= (const Matrix2& b)
|
|
|
- {
|
|
|
- M[0][0] = b.M[0][0]; M[0][1] = b.M[0][1];
|
|
|
- M[1][0] = b.M[1][0]; M[1][1] = b.M[1][1];
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 operator- (const Matrix2& b) const
|
|
|
- {
|
|
|
- return Matrix2(M[0][0] - b.M[0][0], M[0][1] - b.M[0][1],
|
|
|
- M[1][0] - b.M[1][0], M[1][1] - b.M[1][1]);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2& operator-= (const Matrix2& b)
|
|
|
- {
|
|
|
- M[0][0] -= b.M[0][0]; M[0][1] -= b.M[0][1];
|
|
|
- M[1][0] -= b.M[1][0]; M[1][1] -= b.M[1][1];
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 operator* (const Matrix2& b) const
|
|
|
- {
|
|
|
- return Matrix2(M[0][0] * b.M[0][0] + M[0][1] * b.M[1][0], M[0][0] * b.M[0][1] + M[0][1] * b.M[1][1],
|
|
|
- M[1][0] * b.M[0][0] + M[1][1] * b.M[1][0], M[1][0] * b.M[0][1] + M[1][1] * b.M[1][1]);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2& operator*= (const Matrix2& b)
|
|
|
- {
|
|
|
- *this = *this * b;
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 operator* (T s) const
|
|
|
- {
|
|
|
- return Matrix2(M[0][0] * s, M[0][1] * s,
|
|
|
- M[1][0] * s, M[1][1] * s);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2& operator*= (T s)
|
|
|
- {
|
|
|
- M[0][0] *= s; M[0][1] *= s;
|
|
|
- M[1][0] *= s; M[1][1] *= s;
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 operator/ (T s) const
|
|
|
- {
|
|
|
- return *this * (T(1) / s);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2& operator/= (T s)
|
|
|
- {
|
|
|
- return *this *= (T(1) / s);
|
|
|
- }
|
|
|
-
|
|
|
- Vector2<T> operator* (const Vector2<T> &b) const
|
|
|
- {
|
|
|
- return Vector2<T>(M[0][0] * b.x + M[0][1] * b.y,
|
|
|
- M[1][0] * b.x + M[1][1] * b.y);
|
|
|
- }
|
|
|
-
|
|
|
- Vector2<T> Transform(const Vector2<T>& v) const
|
|
|
- {
|
|
|
- return Vector2<T>(M[0][0] * v.x + M[0][1] * v.y,
|
|
|
- M[1][0] * v.x + M[1][1] * v.y);
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 Transposed() const
|
|
|
- {
|
|
|
- return Matrix2(M[0][0], M[1][0],
|
|
|
- M[0][1], M[1][1]);
|
|
|
- }
|
|
|
-
|
|
|
- void Transpose()
|
|
|
- {
|
|
|
- OVRMath_Swap(M[1][0], M[0][1]);
|
|
|
- }
|
|
|
-
|
|
|
- Vector2<T> GetColumn(int c) const
|
|
|
- {
|
|
|
- return Vector2<T>(M[0][c], M[1][c]);
|
|
|
- }
|
|
|
-
|
|
|
- Vector2<T> GetRow(int r) const
|
|
|
- {
|
|
|
- return Vector2<T>(M[r][0], M[r][1]);
|
|
|
- }
|
|
|
-
|
|
|
- void SetColumn(int c, const Vector2<T>& v)
|
|
|
- {
|
|
|
- M[0][c] = v.x;
|
|
|
- M[1][c] = v.y;
|
|
|
- }
|
|
|
-
|
|
|
- void SetRow(int r, const Vector2<T>& v)
|
|
|
- {
|
|
|
- M[r][0] = v.x;
|
|
|
- M[r][1] = v.y;
|
|
|
- }
|
|
|
-
|
|
|
- T Determinant() const
|
|
|
- {
|
|
|
- return M[0][0] * M[1][1] - M[0][1] * M[1][0];
|
|
|
- }
|
|
|
-
|
|
|
- Matrix2 Inverse() const
|
|
|
- {
|
|
|
- T rcpDet = T(1) / Determinant();
|
|
|
- return Matrix2( M[1][1] * rcpDet, -M[0][1] * rcpDet,
|
|
|
- -M[1][0] * rcpDet, M[0][0] * rcpDet);
|
|
|
- }
|
|
|
-
|
|
|
- // Outer Product of two column vectors: a * b.Transpose()
|
|
|
- static Matrix2 OuterProduct(const Vector2<T>& a, const Vector2<T>& b)
|
|
|
- {
|
|
|
- return Matrix2(a.x*b.x, a.x*b.y,
|
|
|
- a.y*b.x, a.y*b.y);
|
|
|
- }
|
|
|
-
|
|
|
- // Angle in radians between two rotation matrices
|
|
|
- T Angle(const Matrix2& b) const
|
|
|
- {
|
|
|
- const Matrix2& a = *this;
|
|
|
- return Acos(a(0, 0)*b(0, 0) + a(1, 0)*b(1, 0));
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Matrix2<float> Matrix2f;
|
|
|
-typedef Matrix2<double> Matrix2d;
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class SymMat3
|
|
|
-{
|
|
|
-private:
|
|
|
- typedef SymMat3<T> this_type;
|
|
|
-
|
|
|
-public:
|
|
|
- typedef T Value_t;
|
|
|
- // Upper symmetric
|
|
|
- T v[6]; // _00 _01 _02 _11 _12 _22
|
|
|
-
|
|
|
- inline SymMat3() {}
|
|
|
-
|
|
|
- inline explicit SymMat3(T s)
|
|
|
- {
|
|
|
- v[0] = v[3] = v[5] = s;
|
|
|
- v[1] = v[2] = v[4] = T(0);
|
|
|
- }
|
|
|
-
|
|
|
- inline explicit SymMat3(T a00, T a01, T a02, T a11, T a12, T a22)
|
|
|
- {
|
|
|
- v[0] = a00; v[1] = a01; v[2] = a02;
|
|
|
- v[3] = a11; v[4] = a12;
|
|
|
- v[5] = a22;
|
|
|
- }
|
|
|
-
|
|
|
- // Cast to symmetric Matrix3
|
|
|
- operator Matrix3<T>() const
|
|
|
- {
|
|
|
- return Matrix3<T>(v[0], v[1], v[2],
|
|
|
- v[1], v[3], v[4],
|
|
|
- v[2], v[4], v[5]);
|
|
|
- }
|
|
|
-
|
|
|
- static inline int Index(unsigned int i, unsigned int j)
|
|
|
- {
|
|
|
- return (i <= j) ? (3*i - i*(i+1)/2 + j) : (3*j - j*(j+1)/2 + i);
|
|
|
- }
|
|
|
-
|
|
|
- inline T operator()(int i, int j) const { return v[Index(i,j)]; }
|
|
|
-
|
|
|
- inline T &operator()(int i, int j) { return v[Index(i,j)]; }
|
|
|
-
|
|
|
- inline this_type& operator+=(const this_type& b)
|
|
|
- {
|
|
|
- v[0]+=b.v[0];
|
|
|
- v[1]+=b.v[1];
|
|
|
- v[2]+=b.v[2];
|
|
|
- v[3]+=b.v[3];
|
|
|
- v[4]+=b.v[4];
|
|
|
- v[5]+=b.v[5];
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- inline this_type& operator-=(const this_type& b)
|
|
|
- {
|
|
|
- v[0]-=b.v[0];
|
|
|
- v[1]-=b.v[1];
|
|
|
- v[2]-=b.v[2];
|
|
|
- v[3]-=b.v[3];
|
|
|
- v[4]-=b.v[4];
|
|
|
- v[5]-=b.v[5];
|
|
|
-
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- inline this_type& operator*=(T s)
|
|
|
- {
|
|
|
- v[0]*=s;
|
|
|
- v[1]*=s;
|
|
|
- v[2]*=s;
|
|
|
- v[3]*=s;
|
|
|
- v[4]*=s;
|
|
|
- v[5]*=s;
|
|
|
-
|
|
|
- return *this;
|
|
|
- }
|
|
|
-
|
|
|
- inline SymMat3 operator*(T s) const
|
|
|
- {
|
|
|
- SymMat3 d;
|
|
|
- d.v[0] = v[0]*s;
|
|
|
- d.v[1] = v[1]*s;
|
|
|
- d.v[2] = v[2]*s;
|
|
|
- d.v[3] = v[3]*s;
|
|
|
- d.v[4] = v[4]*s;
|
|
|
- d.v[5] = v[5]*s;
|
|
|
-
|
|
|
- return d;
|
|
|
- }
|
|
|
-
|
|
|
- // Multiplies two matrices into destination with minimum copying.
|
|
|
- static SymMat3& Multiply(SymMat3* d, const SymMat3& a, const SymMat3& b)
|
|
|
- {
|
|
|
- // _00 _01 _02 _11 _12 _22
|
|
|
-
|
|
|
- d->v[0] = a.v[0] * b.v[0];
|
|
|
- d->v[1] = a.v[0] * b.v[1] + a.v[1] * b.v[3];
|
|
|
- d->v[2] = a.v[0] * b.v[2] + a.v[1] * b.v[4];
|
|
|
-
|
|
|
- d->v[3] = a.v[3] * b.v[3];
|
|
|
- d->v[4] = a.v[3] * b.v[4] + a.v[4] * b.v[5];
|
|
|
-
|
|
|
- d->v[5] = a.v[5] * b.v[5];
|
|
|
-
|
|
|
- return *d;
|
|
|
- }
|
|
|
-
|
|
|
- inline T Determinant() const
|
|
|
- {
|
|
|
- const this_type& m = *this;
|
|
|
- T d;
|
|
|
-
|
|
|
- d = m(0,0) * (m(1,1)*m(2,2) - m(1,2) * m(2,1));
|
|
|
- d -= m(0,1) * (m(1,0)*m(2,2) - m(1,2) * m(2,0));
|
|
|
- d += m(0,2) * (m(1,0)*m(2,1) - m(1,1) * m(2,0));
|
|
|
-
|
|
|
- return d;
|
|
|
- }
|
|
|
-
|
|
|
- inline this_type Inverse() const
|
|
|
- {
|
|
|
- this_type a;
|
|
|
- const this_type& m = *this;
|
|
|
- T d = Determinant();
|
|
|
-
|
|
|
- OVR_MATH_ASSERT(d != 0);
|
|
|
- T s = T(1)/d;
|
|
|
-
|
|
|
- a(0,0) = s * (m(1,1) * m(2,2) - m(1,2) * m(2,1));
|
|
|
-
|
|
|
- a(0,1) = s * (m(0,2) * m(2,1) - m(0,1) * m(2,2));
|
|
|
- a(1,1) = s * (m(0,0) * m(2,2) - m(0,2) * m(2,0));
|
|
|
-
|
|
|
- a(0,2) = s * (m(0,1) * m(1,2) - m(0,2) * m(1,1));
|
|
|
- a(1,2) = s * (m(0,2) * m(1,0) - m(0,0) * m(1,2));
|
|
|
- a(2,2) = s * (m(0,0) * m(1,1) - m(0,1) * m(1,0));
|
|
|
-
|
|
|
- return a;
|
|
|
- }
|
|
|
-
|
|
|
- inline T Trace() const { return v[0] + v[3] + v[5]; }
|
|
|
-
|
|
|
- // M = a*a.t()
|
|
|
- inline void Rank1(const Vector3<T> &a)
|
|
|
- {
|
|
|
- v[0] = a.x*a.x; v[1] = a.x*a.y; v[2] = a.x*a.z;
|
|
|
- v[3] = a.y*a.y; v[4] = a.y*a.z;
|
|
|
- v[5] = a.z*a.z;
|
|
|
- }
|
|
|
-
|
|
|
- // M += a*a.t()
|
|
|
- inline void Rank1Add(const Vector3<T> &a)
|
|
|
- {
|
|
|
- v[0] += a.x*a.x; v[1] += a.x*a.y; v[2] += a.x*a.z;
|
|
|
- v[3] += a.y*a.y; v[4] += a.y*a.z;
|
|
|
- v[5] += a.z*a.z;
|
|
|
- }
|
|
|
-
|
|
|
- // M -= a*a.t()
|
|
|
- inline void Rank1Sub(const Vector3<T> &a)
|
|
|
- {
|
|
|
- v[0] -= a.x*a.x; v[1] -= a.x*a.y; v[2] -= a.x*a.z;
|
|
|
- v[3] -= a.y*a.y; v[4] -= a.y*a.z;
|
|
|
- v[5] -= a.z*a.z;
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef SymMat3<float> SymMat3f;
|
|
|
-typedef SymMat3<double> SymMat3d;
|
|
|
-
|
|
|
-template<class T>
|
|
|
-inline Matrix3<T> operator*(const SymMat3<T>& a, const SymMat3<T>& b)
|
|
|
-{
|
|
|
- #define AJB_ARBC(r,c) (a(r,0)*b(0,c)+a(r,1)*b(1,c)+a(r,2)*b(2,c))
|
|
|
- return Matrix3<T>(
|
|
|
- AJB_ARBC(0,0), AJB_ARBC(0,1), AJB_ARBC(0,2),
|
|
|
- AJB_ARBC(1,0), AJB_ARBC(1,1), AJB_ARBC(1,2),
|
|
|
- AJB_ARBC(2,0), AJB_ARBC(2,1), AJB_ARBC(2,2));
|
|
|
- #undef AJB_ARBC
|
|
|
-}
|
|
|
-
|
|
|
-template<class T>
|
|
|
-inline Matrix3<T> operator*(const Matrix3<T>& a, const SymMat3<T>& b)
|
|
|
-{
|
|
|
- #define AJB_ARBC(r,c) (a(r,0)*b(0,c)+a(r,1)*b(1,c)+a(r,2)*b(2,c))
|
|
|
- return Matrix3<T>(
|
|
|
- AJB_ARBC(0,0), AJB_ARBC(0,1), AJB_ARBC(0,2),
|
|
|
- AJB_ARBC(1,0), AJB_ARBC(1,1), AJB_ARBC(1,2),
|
|
|
- AJB_ARBC(2,0), AJB_ARBC(2,1), AJB_ARBC(2,2));
|
|
|
- #undef AJB_ARBC
|
|
|
-}
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-// ***** Angle
|
|
|
-
|
|
|
-// Cleanly representing the algebra of 2D rotations.
|
|
|
-// The operations maintain the angle between -Pi and Pi, the same range as atan2.
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class Angle
|
|
|
-{
|
|
|
-public:
|
|
|
- enum AngularUnits
|
|
|
- {
|
|
|
- Radians = 0,
|
|
|
- Degrees = 1
|
|
|
- };
|
|
|
-
|
|
|
- Angle() : a(0) {}
|
|
|
-
|
|
|
- // Fix the range to be between -Pi and Pi
|
|
|
- Angle(T a_, AngularUnits u = Radians) : a((u == Radians) ? a_ : a_*((T)MATH_DOUBLE_DEGREETORADFACTOR)) { FixRange(); }
|
|
|
-
|
|
|
- T Get(AngularUnits u = Radians) const { return (u == Radians) ? a : a*((T)MATH_DOUBLE_RADTODEGREEFACTOR); }
|
|
|
- void Set(const T& x, AngularUnits u = Radians) { a = (u == Radians) ? x : x*((T)MATH_DOUBLE_DEGREETORADFACTOR); FixRange(); }
|
|
|
- int Sign() const { if (a == 0) return 0; else return (a > 0) ? 1 : -1; }
|
|
|
- T Abs() const { return (a >= 0) ? a : -a; }
|
|
|
-
|
|
|
- bool operator== (const Angle& b) const { return a == b.a; }
|
|
|
- bool operator!= (const Angle& b) const { return a != b.a; }
|
|
|
-// bool operator< (const Angle& b) const { return a < a.b; }
|
|
|
-// bool operator> (const Angle& b) const { return a > a.b; }
|
|
|
-// bool operator<= (const Angle& b) const { return a <= a.b; }
|
|
|
-// bool operator>= (const Angle& b) const { return a >= a.b; }
|
|
|
-// bool operator= (const T& x) { a = x; FixRange(); }
|
|
|
-
|
|
|
- // These operations assume a is already between -Pi and Pi.
|
|
|
- Angle& operator+= (const Angle& b) { a = a + b.a; FastFixRange(); return *this; }
|
|
|
- Angle& operator+= (const T& x) { a = a + x; FixRange(); return *this; }
|
|
|
- Angle operator+ (const Angle& b) const { Angle res = *this; res += b; return res; }
|
|
|
- Angle operator+ (const T& x) const { Angle res = *this; res += x; return res; }
|
|
|
- Angle& operator-= (const Angle& b) { a = a - b.a; FastFixRange(); return *this; }
|
|
|
- Angle& operator-= (const T& x) { a = a - x; FixRange(); return *this; }
|
|
|
- Angle operator- (const Angle& b) const { Angle res = *this; res -= b; return res; }
|
|
|
- Angle operator- (const T& x) const { Angle res = *this; res -= x; return res; }
|
|
|
-
|
|
|
- T Distance(const Angle& b) { T c = fabs(a - b.a); return (c <= ((T)MATH_DOUBLE_PI)) ? c : ((T)MATH_DOUBLE_TWOPI) - c; }
|
|
|
-
|
|
|
-private:
|
|
|
-
|
|
|
- // The stored angle, which should be maintained between -Pi and Pi
|
|
|
- T a;
|
|
|
-
|
|
|
- // Fixes the angle range to [-Pi,Pi], but assumes no more than 2Pi away on either side
|
|
|
- inline void FastFixRange()
|
|
|
- {
|
|
|
- if (a < -((T)MATH_DOUBLE_PI))
|
|
|
- a += ((T)MATH_DOUBLE_TWOPI);
|
|
|
- else if (a > ((T)MATH_DOUBLE_PI))
|
|
|
- a -= ((T)MATH_DOUBLE_TWOPI);
|
|
|
- }
|
|
|
-
|
|
|
- // Fixes the angle range to [-Pi,Pi] for any given range, but slower then the fast method
|
|
|
- inline void FixRange()
|
|
|
- {
|
|
|
- // do nothing if the value is already in the correct range, since fmod call is expensive
|
|
|
- if (a >= -((T)MATH_DOUBLE_PI) && a <= ((T)MATH_DOUBLE_PI))
|
|
|
- return;
|
|
|
- a = fmod(a,((T)MATH_DOUBLE_TWOPI));
|
|
|
- if (a < -((T)MATH_DOUBLE_PI))
|
|
|
- a += ((T)MATH_DOUBLE_TWOPI);
|
|
|
- else if (a > ((T)MATH_DOUBLE_PI))
|
|
|
- a -= ((T)MATH_DOUBLE_TWOPI);
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-
|
|
|
-typedef Angle<float> Anglef;
|
|
|
-typedef Angle<double> Angled;
|
|
|
-
|
|
|
-
|
|
|
-//-------------------------------------------------------------------------------------
|
|
|
-// ***** Plane
|
|
|
-
|
|
|
-// Consists of a normal vector and distance from the origin where the plane is located.
|
|
|
-
|
|
|
-template<class T>
|
|
|
-class Plane
|
|
|
-{
|
|
|
-public:
|
|
|
- Vector3<T> N;
|
|
|
- T D;
|
|
|
-
|
|
|
- Plane() : D(0) {}
|
|
|
-
|
|
|
- // Normals must already be normalized
|
|
|
- Plane(const Vector3<T>& n, T d) : N(n), D(d) {}
|
|
|
- Plane(T x, T y, T z, T d) : N(x,y,z), D(d) {}
|
|
|
-
|
|
|
- // construct from a point on the plane and the normal
|
|
|
- Plane(const Vector3<T>& p, const Vector3<T>& n) : N(n), D(-(p * n)) {}
|
|
|
-
|
|
|
- // Find the point to plane distance. The sign indicates what side of the plane the point is on (0 = point on plane).
|
|
|
- T TestSide(const Vector3<T>& p) const
|
|
|
- {
|
|
|
- return (N.Dot(p)) + D;
|
|
|
- }
|
|
|
-
|
|
|
- Plane<T> Flipped() const
|
|
|
- {
|
|
|
- return Plane(-N, -D);
|
|
|
- }
|
|
|
-
|
|
|
- void Flip()
|
|
|
- {
|
|
|
- N = -N;
|
|
|
- D = -D;
|
|
|
- }
|
|
|
-
|
|
|
- bool operator==(const Plane<T>& rhs) const
|
|
|
- {
|
|
|
- return (this->D == rhs.D && this->N == rhs.N);
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-typedef Plane<float> Planef;
|
|
|
-typedef Plane<double> Planed;
|
|
|
-
|
|
|
-
|
|
|
-
|
|
|
-
|
|
|
-//-----------------------------------------------------------------------------------
|
|
|
-// ***** ScaleAndOffset2D
|
|
|
-
|
|
|
-struct ScaleAndOffset2D
|
|
|
-{
|
|
|
- Vector2f Scale;
|
|
|
- Vector2f Offset;
|
|
|
-
|
|
|
- ScaleAndOffset2D(float sx = 0.0f, float sy = 0.0f, float ox = 0.0f, float oy = 0.0f)
|
|
|
- : Scale(sx, sy), Offset(ox, oy)
|
|
|
- { }
|
|
|
-};
|
|
|
-
|
|
|
-
|
|
|
-//-----------------------------------------------------------------------------------
|
|
|
-// ***** FovPort
|
|
|
-
|
|
|
-// FovPort describes Field Of View (FOV) of a viewport.
|
|
|
-// This class has values for up, down, left and right, stored in
|
|
|
-// tangent of the angle units to simplify calculations.
|
|
|
-//
|
|
|
-// As an example, for a standard 90 degree vertical FOV, we would
|
|
|
-// have: { UpTan = tan(90 degrees / 2), DownTan = tan(90 degrees / 2) }.
|
|
|
-//
|
|
|
-// CreateFromRadians/Degrees helper functions can be used to
|
|
|
-// access FOV in different units.
|
|
|
-
|
|
|
-
|
|
|
-// ***** FovPort
|
|
|
-
|
|
|
-struct FovPort
|
|
|
-{
|
|
|
- float UpTan;
|
|
|
- float DownTan;
|
|
|
- float LeftTan;
|
|
|
- float RightTan;
|
|
|
-
|
|
|
- FovPort ( float sideTan = 0.0f ) :
|
|
|
- UpTan(sideTan), DownTan(sideTan), LeftTan(sideTan), RightTan(sideTan) { }
|
|
|
- FovPort ( float u, float d, float l, float r ) :
|
|
|
- UpTan(u), DownTan(d), LeftTan(l), RightTan(r) { }
|
|
|
-
|
|
|
- // C-interop support: FovPort <-> ovrFovPort (implementation in OVR_CAPI.cpp).
|
|
|
- FovPort(const ovrFovPort &src)
|
|
|
- : UpTan(src.UpTan), DownTan(src.DownTan), LeftTan(src.LeftTan), RightTan(src.RightTan)
|
|
|
- { }
|
|
|
-
|
|
|
- operator ovrFovPort () const
|
|
|
- {
|
|
|
- ovrFovPort result;
|
|
|
- result.LeftTan = LeftTan;
|
|
|
- result.RightTan = RightTan;
|
|
|
- result.UpTan = UpTan;
|
|
|
- result.DownTan = DownTan;
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- static FovPort CreateFromRadians(float horizontalFov, float verticalFov)
|
|
|
- {
|
|
|
- FovPort result;
|
|
|
- result.UpTan = tanf ( verticalFov * 0.5f );
|
|
|
- result.DownTan = tanf ( verticalFov * 0.5f );
|
|
|
- result.LeftTan = tanf ( horizontalFov * 0.5f );
|
|
|
- result.RightTan = tanf ( horizontalFov * 0.5f );
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- static FovPort CreateFromDegrees(float horizontalFovDegrees,
|
|
|
- float verticalFovDegrees)
|
|
|
- {
|
|
|
- return CreateFromRadians(DegreeToRad(horizontalFovDegrees),
|
|
|
- DegreeToRad(verticalFovDegrees));
|
|
|
- }
|
|
|
-
|
|
|
- // Get Horizontal/Vertical components of Fov in radians.
|
|
|
- float GetVerticalFovRadians() const { return atanf(UpTan) + atanf(DownTan); }
|
|
|
- float GetHorizontalFovRadians() const { return atanf(LeftTan) + atanf(RightTan); }
|
|
|
- // Get Horizontal/Vertical components of Fov in degrees.
|
|
|
- float GetVerticalFovDegrees() const { return RadToDegree(GetVerticalFovRadians()); }
|
|
|
- float GetHorizontalFovDegrees() const { return RadToDegree(GetHorizontalFovRadians()); }
|
|
|
-
|
|
|
- // Compute maximum tangent value among all four sides.
|
|
|
- float GetMaxSideTan() const
|
|
|
- {
|
|
|
- return OVRMath_Max(OVRMath_Max(UpTan, DownTan), OVRMath_Max(LeftTan, RightTan));
|
|
|
- }
|
|
|
-
|
|
|
- static ScaleAndOffset2D CreateNDCScaleAndOffsetFromFov ( FovPort tanHalfFov )
|
|
|
- {
|
|
|
- float projXScale = 2.0f / ( tanHalfFov.LeftTan + tanHalfFov.RightTan );
|
|
|
- float projXOffset = ( tanHalfFov.LeftTan - tanHalfFov.RightTan ) * projXScale * 0.5f;
|
|
|
- float projYScale = 2.0f / ( tanHalfFov.UpTan + tanHalfFov.DownTan );
|
|
|
- float projYOffset = ( tanHalfFov.UpTan - tanHalfFov.DownTan ) * projYScale * 0.5f;
|
|
|
-
|
|
|
- ScaleAndOffset2D result;
|
|
|
- result.Scale = Vector2f(projXScale, projYScale);
|
|
|
- result.Offset = Vector2f(projXOffset, projYOffset);
|
|
|
- // Hey - why is that Y.Offset negated?
|
|
|
- // It's because a projection matrix transforms from world coords with Y=up,
|
|
|
- // whereas this is from NDC which is Y=down.
|
|
|
-
|
|
|
- return result;
|
|
|
- }
|
|
|
-
|
|
|
- // Converts Fov Tan angle units to [-1,1] render target NDC space
|
|
|
- Vector2f TanAngleToRendertargetNDC(Vector2f const &tanEyeAngle)
|
|
|
- {
|
|
|
- ScaleAndOffset2D eyeToSourceNDC = CreateNDCScaleAndOffsetFromFov(*this);
|
|
|
- return tanEyeAngle * eyeToSourceNDC.Scale + eyeToSourceNDC.Offset;
|
|
|
- }
|
|
|
-
|
|
|
- // Compute per-channel minimum and maximum of Fov.
|
|
|
- static FovPort Min(const FovPort& a, const FovPort& b)
|
|
|
- {
|
|
|
- FovPort fov( OVRMath_Min( a.UpTan , b.UpTan ),
|
|
|
- OVRMath_Min( a.DownTan , b.DownTan ),
|
|
|
- OVRMath_Min( a.LeftTan , b.LeftTan ),
|
|
|
- OVRMath_Min( a.RightTan, b.RightTan ) );
|
|
|
- return fov;
|
|
|
- }
|
|
|
-
|
|
|
- static FovPort Max(const FovPort& a, const FovPort& b)
|
|
|
- {
|
|
|
- FovPort fov( OVRMath_Max( a.UpTan , b.UpTan ),
|
|
|
- OVRMath_Max( a.DownTan , b.DownTan ),
|
|
|
- OVRMath_Max( a.LeftTan , b.LeftTan ),
|
|
|
- OVRMath_Max( a.RightTan, b.RightTan ) );
|
|
|
- return fov;
|
|
|
- }
|
|
|
-};
|
|
|
-
|
|
|
-
|
|
|
-} // Namespace OVR
|
|
|
-
|
|
|
-
|
|
|
-#if defined(_MSC_VER)
|
|
|
- #pragma warning(pop)
|
|
|
-#endif
|
|
|
-
|
|
|
-
|
|
|
-#endif
|
Ray