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@@ -22,6 +22,29 @@
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* 3. This notice may not be removed or altered from any source distribution.
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*
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**********************************************************************************************/
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+//============================================================================
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+// YOU MUST
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+//
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+// #define RAYMATH_DEFINE
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+//
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+// Like:
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+//
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+// #define RAYMATH_DEFINE
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+// #include "raymath.h"
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+//
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+// YOU CAN:
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+// #define RAYMATH_INLINE //inlines all code, so it runs faster. This requires lots of memory on system.
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+// AND
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+// #define RAYMATH_STANDALONE //not dependent on outside libs
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+//
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+// This needs to be done for every library/source file.
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+//============================================================================
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+
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+#ifdef RAYMATH_INLINE
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+ #define RMDEF static inline
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+#else
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+ #define RMDEF static
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+#endif
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#ifndef RAYMATH_H
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#define RAYMATH_H
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@@ -39,14 +62,25 @@
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#define PI 3.14159265358979323846
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#endif
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-#define DEG2RAD (PI / 180.0f)
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-#define RAD2DEG (180.0f / PI)
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+#ifndef DEG2RAD
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+ #define DEG2RAD (PI / 180.0f)
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+#endif
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+
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+#ifndef RAD2DEG
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+ #define RAD2DEG (180.0f / PI)
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+#endif
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//----------------------------------------------------------------------------------
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// Types and Structures Definition
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//----------------------------------------------------------------------------------
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#ifdef RAYMATH_STANDALONE
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+ // Vector2 type
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+ typedef struct Vector2 {
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+ float x;
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+ float y;
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+ } Vector2;
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+
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// Vector3 type
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typedef struct Vector3 {
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float x;
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@@ -71,70 +105,958 @@ typedef struct Quaternion {
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float w;
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} Quaternion;
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+#ifdef RAYMATH_DEFINE
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+#include <stdio.h> // Used only on PrintMatrix()
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+#include <math.h> // Standard math libary: sin(), cos(), tan()...
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+#include <stdlib.h> // Used for abs()
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-#ifdef __cplusplus
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-extern "C" { // Prevents name mangling of functions
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-#endif
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+//----------------------------------------------------------------------------------
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+// Module Functions Definition - Vector3 math
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+//----------------------------------------------------------------------------------
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+
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+// Converts Vector3 to float array
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+RMDEF float *VectorToFloat(Vector3 vec)
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+{
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+ static float buffer[3];
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-//------------------------------------------------------------------------------------
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-// Functions Declaration to work with Vector3
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-//------------------------------------------------------------------------------------
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-float *VectorToFloat(Vector3 vec); // Converts Vector3 to float array
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-Vector3 VectorAdd(Vector3 v1, Vector3 v2); // Add two vectors
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-Vector3 VectorSubtract(Vector3 v1, Vector3 v2); // Substract two vectors
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-Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2); // Calculate two vectors cross product
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-Vector3 VectorPerpendicular(Vector3 v); // Calculate one vector perpendicular vector
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-float VectorDotProduct(Vector3 v1, Vector3 v2); // Calculate two vectors dot product
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-float VectorLength(const Vector3 v); // Calculate vector lenght
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-void VectorScale(Vector3 *v, float scale); // Scale provided vector
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-void VectorNegate(Vector3 *v); // Negate provided vector (invert direction)
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-void VectorNormalize(Vector3 *v); // Normalize provided vector
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-float VectorDistance(Vector3 v1, Vector3 v2); // Calculate distance between two points
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-Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount); // Calculate linear interpolation between two vectors
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-Vector3 VectorReflect(Vector3 vector, Vector3 normal); // Calculate reflected vector to normal
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-void VectorTransform(Vector3 *v, Matrix mat); // Transforms a Vector3 by a given Matrix
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-Vector3 VectorZero(void); // Return a Vector3 init to zero
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-
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-//------------------------------------------------------------------------------------
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-// Functions Declaration to work with Matrix
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-//------------------------------------------------------------------------------------
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-float *MatrixToFloat(Matrix mat); // Converts Matrix to float array
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-float MatrixDeterminant(Matrix mat); // Compute matrix determinant
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-float MatrixTrace(Matrix mat); // Returns the trace of the matrix (sum of the values along the diagonal)
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-void MatrixTranspose(Matrix *mat); // Transposes provided matrix
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-void MatrixInvert(Matrix *mat); // Invert provided matrix
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-void MatrixNormalize(Matrix *mat); // Normalize provided matrix
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-Matrix MatrixIdentity(void); // Returns identity matrix
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-Matrix MatrixAdd(Matrix left, Matrix right); // Add two matrices
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-Matrix MatrixSubstract(Matrix left, Matrix right); // Substract two matrices (left - right)
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-Matrix MatrixTranslate(float x, float y, float z); // Returns translation matrix
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-Matrix MatrixRotate(float angle, Vector3 axis); // Returns rotation matrix for an angle around an specified axis (angle in radians)
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-Matrix MatrixRotateX(float angle); // Returns x-rotation matrix (angle in radians)
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-Matrix MatrixRotateY(float angle); // Returns y-rotation matrix (angle in radians)
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-Matrix MatrixRotateZ(float angle); // Returns z-rotation matrix (angle in radians)
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-Matrix MatrixScale(float x, float y, float z); // Returns scaling matrix
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-Matrix MatrixMultiply(Matrix left, Matrix right); // Returns two matrix multiplication
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-Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far); // Returns perspective projection matrix
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-Matrix MatrixPerspective(double fovy, double aspect, double near, double far); // Returns perspective projection matrix
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-Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far); // Returns orthographic projection matrix
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-Matrix MatrixLookAt(Vector3 position, Vector3 target, Vector3 up); // Returns camera look-at matrix (view matrix)
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-void PrintMatrix(Matrix m); // Print matrix utility
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-
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-//------------------------------------------------------------------------------------
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-// Functions Declaration to work with Quaternions
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-//------------------------------------------------------------------------------------
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-float QuaternionLength(Quaternion quat); // Compute the length of a quaternion
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-void QuaternionNormalize(Quaternion *q); // Normalize provided quaternion
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-Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2); // Calculate two quaternion multiplication
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-Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float slerp); // Calculates spherical linear interpolation between two quaternions
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-Quaternion QuaternionFromMatrix(Matrix matrix); // Returns a quaternion for a given rotation matrix
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-Matrix QuaternionToMatrix(Quaternion q); // Returns a matrix for a given quaternion
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-Quaternion QuaternionFromAxisAngle(float angle, Vector3 axis); // Returns rotation quaternion for an angle and axis
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-void QuaternionToAxisAngle(Quaternion q, float *outAngle, Vector3 *outAxis); // Returns the rotation angle and axis for a given quaternion
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-void QuaternionTransform(Quaternion *q, Matrix mat); // Transform a quaternion given a transformation matrix
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-
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-#ifdef __cplusplus
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+ buffer[0] = vec.x;
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+ buffer[1] = vec.y;
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+ buffer[2] = vec.z;
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+
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+ return buffer;
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+}
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+
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+// Add two vectors
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+RMDEF Vector3 VectorAdd(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result;
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+
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+ result.x = v1.x + v2.x;
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+ result.y = v1.y + v2.y;
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+ result.z = v1.z + v2.z;
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+
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+ return result;
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+}
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+
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+// Substract two vectors
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+RMDEF Vector3 VectorSubtract(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result;
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+
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+ result.x = v1.x - v2.x;
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+ result.y = v1.y - v2.y;
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+ result.z = v1.z - v2.z;
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+
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+ return result;
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+}
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+
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+// Calculate two vectors cross product
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+RMDEF Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result;
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+
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+ result.x = v1.y*v2.z - v1.z*v2.y;
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+ result.y = v1.z*v2.x - v1.x*v2.z;
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+ result.z = v1.x*v2.y - v1.y*v2.x;
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+
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+ return result;
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+}
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+
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+// Calculate one vector perpendicular vector
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+RMDEF Vector3 VectorPerpendicular(Vector3 v)
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+{
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+ Vector3 result;
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+
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+ float min = fabs(v.x);
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+ Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f};
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+
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+ if (fabs(v.y) < min)
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+ {
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+ min = fabs(v.y);
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+ cardinalAxis = (Vector3){0.0f, 1.0f, 0.0f};
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+ }
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+
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+ if(fabs(v.z) < min)
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+ {
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+ cardinalAxis = (Vector3){0.0f, 0.0f, 1.0f};
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+ }
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+
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+ result = VectorCrossProduct(v, cardinalAxis);
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+
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+ return result;
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+}
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+
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+// Calculate two vectors dot product
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+RMDEF float VectorDotProduct(Vector3 v1, Vector3 v2)
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+{
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+ float result;
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+
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+ result = v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
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+
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+ return result;
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+}
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+
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+// Calculate vector lenght
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+RMDEF float VectorLength(const Vector3 v)
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+{
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+ float length;
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+
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+ length = sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
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+
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+ return length;
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+}
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+
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+// Scale provided vector
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+RMDEF void VectorScale(Vector3 *v, float scale)
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+{
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+ v->x *= scale;
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+ v->y *= scale;
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+ v->z *= scale;
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+}
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+
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+// Negate provided vector (invert direction)
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+RMDEF void VectorNegate(Vector3 *v)
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+{
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+ v->x = -v->x;
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+ v->y = -v->y;
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+ v->z = -v->z;
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+}
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+
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+// Normalize provided vector
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+RMDEF void VectorNormalize(Vector3 *v)
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+{
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+ float length, ilength;
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+
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+ length = VectorLength(*v);
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+
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+ if (length == 0) length = 1;
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+
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+ ilength = 1.0/length;
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+
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+ v->x *= ilength;
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+ v->y *= ilength;
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+ v->z *= ilength;
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+}
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+
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+// Calculate distance between two points
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+RMDEF float VectorDistance(Vector3 v1, Vector3 v2)
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+{
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+ float result;
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+
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+ float dx = v2.x - v1.x;
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+ float dy = v2.y - v1.y;
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+ float dz = v2.z - v1.z;
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+
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+ result = sqrt(dx*dx + dy*dy + dz*dz);
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+
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+ return result;
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+}
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+
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+// Calculate linear interpolation between two vectors
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+RMDEF Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount)
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+{
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+ Vector3 result;
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+
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+ result.x = v1.x + amount * (v2.x - v1.x);
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+ result.y = v1.y + amount * (v2.y - v1.y);
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+ result.z = v1.z + amount * (v2.z - v1.z);
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+
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+ return result;
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+}
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+
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+// Calculate reflected vector to normal
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+RMDEF Vector3 VectorReflect(Vector3 vector, Vector3 normal)
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+{
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+ // I is the original vector
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+ // N is the normal of the incident plane
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+ // R = I - (2 * N * ( DotProduct[ I,N] ))
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+
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+ Vector3 result;
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+
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+ float dotProduct = VectorDotProduct(vector, normal);
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+
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+ result.x = vector.x - (2.0 * normal.x) * dotProduct;
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+ result.y = vector.y - (2.0 * normal.y) * dotProduct;
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+ result.z = vector.z - (2.0 * normal.z) * dotProduct;
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+
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+ return result;
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+}
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+
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+// Transforms a Vector3 with a given Matrix
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+RMDEF void VectorTransform(Vector3 *v, Matrix mat)
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+{
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+ float x = v->x;
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+ float y = v->y;
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+ float z = v->z;
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+
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+ //MatrixTranspose(&mat);
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+
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+ v->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12;
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+ v->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13;
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+ v->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14;
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+};
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+
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+// Return a Vector3 init to zero
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+RMDEF Vector3 VectorZero(void)
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+{
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+ Vector3 zero = { 0.0f, 0.0f, 0.0f };
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+
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+ return zero;
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+}
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+
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+//----------------------------------------------------------------------------------
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+// Module Functions Definition - Matrix math
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+//----------------------------------------------------------------------------------
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+
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+// Converts Matrix to float array
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+// NOTE: Returned vector is a transposed version of the Matrix struct,
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+// it should be this way because, despite raymath use OpenGL column-major convention,
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+// Matrix struct memory alignment and variables naming are not coherent
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+RMDEF float *MatrixToFloat(Matrix mat)
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+{
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+ static float buffer[16];
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+
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+ buffer[0] = mat.m0;
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+ buffer[1] = mat.m4;
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+ buffer[2] = mat.m8;
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+ buffer[3] = mat.m12;
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+ buffer[4] = mat.m1;
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+ buffer[5] = mat.m5;
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+ buffer[6] = mat.m9;
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+ buffer[7] = mat.m13;
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+ buffer[8] = mat.m2;
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+ buffer[9] = mat.m6;
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+ buffer[10] = mat.m10;
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+ buffer[11] = mat.m14;
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+ buffer[12] = mat.m3;
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+ buffer[13] = mat.m7;
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+ buffer[14] = mat.m11;
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+ buffer[15] = mat.m15;
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+
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+ return buffer;
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+}
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+
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+// Compute matrix determinant
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+RMDEF float MatrixDeterminant(Matrix mat)
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+{
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+ float result;
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+
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+ // Cache the matrix values (speed optimization)
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+ float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
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+ float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
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+ float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
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+ float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15;
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+
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+ result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 +
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+ a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 +
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+ a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 +
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+ a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 +
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+ a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 +
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+ a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33;
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+
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+ return result;
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+}
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+
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+// Returns the trace of the matrix (sum of the values along the diagonal)
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+RMDEF float MatrixTrace(Matrix mat)
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+{
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+ return (mat.m0 + mat.m5 + mat.m10 + mat.m15);
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+}
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+
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+// Transposes provided matrix
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+RMDEF void MatrixTranspose(Matrix *mat)
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+{
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+ Matrix temp;
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+
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+ temp.m0 = mat->m0;
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+ temp.m1 = mat->m4;
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+ temp.m2 = mat->m8;
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+ temp.m3 = mat->m12;
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+ temp.m4 = mat->m1;
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+ temp.m5 = mat->m5;
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+ temp.m6 = mat->m9;
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+ temp.m7 = mat->m13;
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|
|
+ temp.m8 = mat->m2;
|
|
|
+ temp.m9 = mat->m6;
|
|
|
+ temp.m10 = mat->m10;
|
|
|
+ temp.m11 = mat->m14;
|
|
|
+ temp.m12 = mat->m3;
|
|
|
+ temp.m13 = mat->m7;
|
|
|
+ temp.m14 = mat->m11;
|
|
|
+ temp.m15 = mat->m15;
|
|
|
+
|
|
|
+ *mat = temp;
|
|
|
+}
|
|
|
+
|
|
|
+// Invert provided matrix
|
|
|
+RMDEF void MatrixInvert(Matrix *mat)
|
|
|
+{
|
|
|
+ Matrix temp;
|
|
|
+
|
|
|
+ // Cache the matrix values (speed optimization)
|
|
|
+ float a00 = mat->m0, a01 = mat->m1, a02 = mat->m2, a03 = mat->m3;
|
|
|
+ float a10 = mat->m4, a11 = mat->m5, a12 = mat->m6, a13 = mat->m7;
|
|
|
+ float a20 = mat->m8, a21 = mat->m9, a22 = mat->m10, a23 = mat->m11;
|
|
|
+ float a30 = mat->m12, a31 = mat->m13, a32 = mat->m14, a33 = mat->m15;
|
|
|
+
|
|
|
+ float b00 = a00*a11 - a01*a10;
|
|
|
+ float b01 = a00*a12 - a02*a10;
|
|
|
+ float b02 = a00*a13 - a03*a10;
|
|
|
+ float b03 = a01*a12 - a02*a11;
|
|
|
+ float b04 = a01*a13 - a03*a11;
|
|
|
+ float b05 = a02*a13 - a03*a12;
|
|
|
+ float b06 = a20*a31 - a21*a30;
|
|
|
+ float b07 = a20*a32 - a22*a30;
|
|
|
+ float b08 = a20*a33 - a23*a30;
|
|
|
+ float b09 = a21*a32 - a22*a31;
|
|
|
+ float b10 = a21*a33 - a23*a31;
|
|
|
+ float b11 = a22*a33 - a23*a32;
|
|
|
+
|
|
|
+ // Calculate the invert determinant (inlined to avoid double-caching)
|
|
|
+ float invDet = 1/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
|
|
|
+
|
|
|
+ temp.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet;
|
|
|
+ temp.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet;
|
|
|
+ temp.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet;
|
|
|
+ temp.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet;
|
|
|
+ temp.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet;
|
|
|
+ temp.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet;
|
|
|
+ temp.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet;
|
|
|
+ temp.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet;
|
|
|
+ temp.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet;
|
|
|
+ temp.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet;
|
|
|
+ temp.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet;
|
|
|
+ temp.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet;
|
|
|
+ temp.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet;
|
|
|
+ temp.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet;
|
|
|
+ temp.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet;
|
|
|
+ temp.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet;
|
|
|
+
|
|
|
+ *mat = temp;
|
|
|
+}
|
|
|
+
|
|
|
+// Normalize provided matrix
|
|
|
+RMDEF void MatrixNormalize(Matrix *mat)
|
|
|
+{
|
|
|
+ float det = MatrixDeterminant(*mat);
|
|
|
+
|
|
|
+ mat->m0 /= det;
|
|
|
+ mat->m1 /= det;
|
|
|
+ mat->m2 /= det;
|
|
|
+ mat->m3 /= det;
|
|
|
+ mat->m4 /= det;
|
|
|
+ mat->m5 /= det;
|
|
|
+ mat->m6 /= det;
|
|
|
+ mat->m7 /= det;
|
|
|
+ mat->m8 /= det;
|
|
|
+ mat->m9 /= det;
|
|
|
+ mat->m10 /= det;
|
|
|
+ mat->m11 /= det;
|
|
|
+ mat->m12 /= det;
|
|
|
+ mat->m13 /= det;
|
|
|
+ mat->m14 /= det;
|
|
|
+ mat->m15 /= det;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns identity matrix
|
|
|
+RMDEF Matrix MatrixIdentity(void)
|
|
|
+{
|
|
|
+ Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Add two matrices
|
|
|
+RMDEF Matrix MatrixAdd(Matrix left, Matrix right)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ result.m0 = left.m0 + right.m0;
|
|
|
+ result.m1 = left.m1 + right.m1;
|
|
|
+ result.m2 = left.m2 + right.m2;
|
|
|
+ result.m3 = left.m3 + right.m3;
|
|
|
+ result.m4 = left.m4 + right.m4;
|
|
|
+ result.m5 = left.m5 + right.m5;
|
|
|
+ result.m6 = left.m6 + right.m6;
|
|
|
+ result.m7 = left.m7 + right.m7;
|
|
|
+ result.m8 = left.m8 + right.m8;
|
|
|
+ result.m9 = left.m9 + right.m9;
|
|
|
+ result.m10 = left.m10 + right.m10;
|
|
|
+ result.m11 = left.m11 + right.m11;
|
|
|
+ result.m12 = left.m12 + right.m12;
|
|
|
+ result.m13 = left.m13 + right.m13;
|
|
|
+ result.m14 = left.m14 + right.m14;
|
|
|
+ result.m15 = left.m15 + right.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Substract two matrices (left - right)
|
|
|
+RMDEF Matrix MatrixSubstract(Matrix left, Matrix right)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ result.m0 = left.m0 - right.m0;
|
|
|
+ result.m1 = left.m1 - right.m1;
|
|
|
+ result.m2 = left.m2 - right.m2;
|
|
|
+ result.m3 = left.m3 - right.m3;
|
|
|
+ result.m4 = left.m4 - right.m4;
|
|
|
+ result.m5 = left.m5 - right.m5;
|
|
|
+ result.m6 = left.m6 - right.m6;
|
|
|
+ result.m7 = left.m7 - right.m7;
|
|
|
+ result.m8 = left.m8 - right.m8;
|
|
|
+ result.m9 = left.m9 - right.m9;
|
|
|
+ result.m10 = left.m10 - right.m10;
|
|
|
+ result.m11 = left.m11 - right.m11;
|
|
|
+ result.m12 = left.m12 - right.m12;
|
|
|
+ result.m13 = left.m13 - right.m13;
|
|
|
+ result.m14 = left.m14 - right.m14;
|
|
|
+ result.m15 = left.m15 - right.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns translation matrix
|
|
|
+RMDEF Matrix MatrixTranslate(float x, float y, float z)
|
|
|
+{
|
|
|
+ Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 };
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Create rotation matrix from axis and angle
|
|
|
+// NOTE: Angle should be provided in radians
|
|
|
+RMDEF Matrix MatrixRotate(float angle, Vector3 axis)
|
|
|
+{
|
|
|
+ Matrix result;
|
|
|
+
|
|
|
+ Matrix mat = MatrixIdentity();
|
|
|
+
|
|
|
+ float x = axis.x, y = axis.y, z = axis.z;
|
|
|
+
|
|
|
+ float length = sqrt(x*x + y*y + z*z);
|
|
|
+
|
|
|
+ if ((length != 1) && (length != 0))
|
|
|
+ {
|
|
|
+ length = 1/length;
|
|
|
+ x *= length;
|
|
|
+ y *= length;
|
|
|
+ z *= length;
|
|
|
+ }
|
|
|
+
|
|
|
+ float s = sinf(angle);
|
|
|
+ float c = cosf(angle);
|
|
|
+ float t = 1.0f - c;
|
|
|
+
|
|
|
+ // Cache some matrix values (speed optimization)
|
|
|
+ float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
|
|
|
+ float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
|
|
|
+ float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
|
|
|
+
|
|
|
+ // Construct the elements of the rotation matrix
|
|
|
+ float b00 = x*x*t + c, b01 = y*x*t + z*s, b02 = z*x*t - y*s;
|
|
|
+ float b10 = x*y*t - z*s, b11 = y*y*t + c, b12 = z*y*t + x*s;
|
|
|
+ float b20 = x*z*t + y*s, b21 = y*z*t - x*s, b22 = z*z*t + c;
|
|
|
+
|
|
|
+ // Perform rotation-specific matrix multiplication
|
|
|
+ result.m0 = a00*b00 + a10*b01 + a20*b02;
|
|
|
+ result.m1 = a01*b00 + a11*b01 + a21*b02;
|
|
|
+ result.m2 = a02*b00 + a12*b01 + a22*b02;
|
|
|
+ result.m3 = a03*b00 + a13*b01 + a23*b02;
|
|
|
+ result.m4 = a00*b10 + a10*b11 + a20*b12;
|
|
|
+ result.m5 = a01*b10 + a11*b11 + a21*b12;
|
|
|
+ result.m6 = a02*b10 + a12*b11 + a22*b12;
|
|
|
+ result.m7 = a03*b10 + a13*b11 + a23*b12;
|
|
|
+ result.m8 = a00*b20 + a10*b21 + a20*b22;
|
|
|
+ result.m9 = a01*b20 + a11*b21 + a21*b22;
|
|
|
+ result.m10 = a02*b20 + a12*b21 + a22*b22;
|
|
|
+ result.m11 = a03*b20 + a13*b21 + a23*b22;
|
|
|
+ result.m12 = mat.m12;
|
|
|
+ result.m13 = mat.m13;
|
|
|
+ result.m14 = mat.m14;
|
|
|
+ result.m15 = mat.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+/*
|
|
|
+// Another implementation for MatrixRotate...
|
|
|
+RMDEF Matrix MatrixRotate(float angle, float x, float y, float z)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float c = cosf(angle); // cosine
|
|
|
+ float s = sinf(angle); // sine
|
|
|
+ float c1 = 1.0f - c; // 1 - c
|
|
|
+
|
|
|
+ float m0 = result.m0, m4 = result.m4, m8 = result.m8, m12 = result.m12,
|
|
|
+ m1 = result.m1, m5 = result.m5, m9 = result.m9, m13 = result.m13,
|
|
|
+ m2 = result.m2, m6 = result.m6, m10 = result.m10, m14 = result.m14;
|
|
|
+
|
|
|
+ // build rotation matrix
|
|
|
+ float r0 = x * x * c1 + c;
|
|
|
+ float r1 = x * y * c1 + z * s;
|
|
|
+ float r2 = x * z * c1 - y * s;
|
|
|
+ float r4 = x * y * c1 - z * s;
|
|
|
+ float r5 = y * y * c1 + c;
|
|
|
+ float r6 = y * z * c1 + x * s;
|
|
|
+ float r8 = x * z * c1 + y * s;
|
|
|
+ float r9 = y * z * c1 - x * s;
|
|
|
+ float r10= z * z * c1 + c;
|
|
|
+
|
|
|
+ // multiply rotation matrix
|
|
|
+ result.m0 = r0*m0 + r4*m1 + r8*m2;
|
|
|
+ result.m1 = r1*m0 + r5*m1 + r9*m2;
|
|
|
+ result.m2 = r2*m0 + r6*m1 + r10*m2;
|
|
|
+ result.m4 = r0*m4 + r4*m5 + r8*m6;
|
|
|
+ result.m5 = r1*m4 + r5*m5 + r9*m6;
|
|
|
+ result.m6 = r2*m4 + r6*m5 + r10*m6;
|
|
|
+ result.m8 = r0*m8 + r4*m9 + r8*m10;
|
|
|
+ result.m9 = r1*m8 + r5*m9 + r9*m10;
|
|
|
+ result.m10 = r2*m8 + r6*m9 + r10*m10;
|
|
|
+ result.m12 = r0*m12+ r4*m13 + r8*m14;
|
|
|
+ result.m13 = r1*m12+ r5*m13 + r9*m14;
|
|
|
+ result.m14 = r2*m12+ r6*m13 + r10*m14;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+*/
|
|
|
+
|
|
|
+// Returns x-rotation matrix (angle in radians)
|
|
|
+RMDEF Matrix MatrixRotateX(float angle)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosres = (float)cos(angle);
|
|
|
+ float sinres = (float)sin(angle);
|
|
|
+
|
|
|
+ result.m5 = cosres;
|
|
|
+ result.m6 = -sinres;
|
|
|
+ result.m9 = sinres;
|
|
|
+ result.m10 = cosres;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns y-rotation matrix (angle in radians)
|
|
|
+RMDEF Matrix MatrixRotateY(float angle)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosres = cosf(angle);
|
|
|
+ float sinres = sinf(angle);
|
|
|
+
|
|
|
+ result.m0 = cosres;
|
|
|
+ result.m2 = sinres;
|
|
|
+ result.m8 = -sinres;
|
|
|
+ result.m10 = cosres;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns z-rotation matrix (angle in radians)
|
|
|
+RMDEF Matrix MatrixRotateZ(float angle)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosres = (float)cos(angle);
|
|
|
+ float sinres = (float)sin(angle);
|
|
|
+
|
|
|
+ result.m0 = cosres;
|
|
|
+ result.m1 = -sinres;
|
|
|
+ result.m4 = sinres;
|
|
|
+ result.m5 = cosres;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns scaling matrix
|
|
|
+RMDEF Matrix MatrixScale(float x, float y, float z)
|
|
|
+{
|
|
|
+ Matrix result = { x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 };
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns two matrix multiplication
|
|
|
+// NOTE: When multiplying matrices... the order matters!
|
|
|
+RMDEF Matrix MatrixMultiply(Matrix left, Matrix right)
|
|
|
+{
|
|
|
+ Matrix result;
|
|
|
+
|
|
|
+ result.m0 = right.m0*left.m0 + right.m1*left.m4 + right.m2*left.m8 + right.m3*left.m12;
|
|
|
+ result.m1 = right.m0*left.m1 + right.m1*left.m5 + right.m2*left.m9 + right.m3*left.m13;
|
|
|
+ result.m2 = right.m0*left.m2 + right.m1*left.m6 + right.m2*left.m10 + right.m3*left.m14;
|
|
|
+ result.m3 = right.m0*left.m3 + right.m1*left.m7 + right.m2*left.m11 + right.m3*left.m15;
|
|
|
+ result.m4 = right.m4*left.m0 + right.m5*left.m4 + right.m6*left.m8 + right.m7*left.m12;
|
|
|
+ result.m5 = right.m4*left.m1 + right.m5*left.m5 + right.m6*left.m9 + right.m7*left.m13;
|
|
|
+ result.m6 = right.m4*left.m2 + right.m5*left.m6 + right.m6*left.m10 + right.m7*left.m14;
|
|
|
+ result.m7 = right.m4*left.m3 + right.m5*left.m7 + right.m6*left.m11 + right.m7*left.m15;
|
|
|
+ result.m8 = right.m8*left.m0 + right.m9*left.m4 + right.m10*left.m8 + right.m11*left.m12;
|
|
|
+ result.m9 = right.m8*left.m1 + right.m9*left.m5 + right.m10*left.m9 + right.m11*left.m13;
|
|
|
+ result.m10 = right.m8*left.m2 + right.m9*left.m6 + right.m10*left.m10 + right.m11*left.m14;
|
|
|
+ result.m11 = right.m8*left.m3 + right.m9*left.m7 + right.m10*left.m11 + right.m11*left.m15;
|
|
|
+ result.m12 = right.m12*left.m0 + right.m13*left.m4 + right.m14*left.m8 + right.m15*left.m12;
|
|
|
+ result.m13 = right.m12*left.m1 + right.m13*left.m5 + right.m14*left.m9 + right.m15*left.m13;
|
|
|
+ result.m14 = right.m12*left.m2 + right.m13*left.m6 + right.m14*left.m10 + right.m15*left.m14;
|
|
|
+ result.m15 = right.m12*left.m3 + right.m13*left.m7 + right.m14*left.m11 + right.m15*left.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns perspective projection matrix
|
|
|
+RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far)
|
|
|
+{
|
|
|
+ Matrix result;
|
|
|
+
|
|
|
+ float rl = (right - left);
|
|
|
+ float tb = (top - bottom);
|
|
|
+ float fn = (far - near);
|
|
|
+
|
|
|
+ result.m0 = (near*2.0f) / rl;
|
|
|
+ result.m1 = 0;
|
|
|
+ result.m2 = 0;
|
|
|
+ result.m3 = 0;
|
|
|
+
|
|
|
+ result.m4 = 0;
|
|
|
+ result.m5 = (near*2.0f) / tb;
|
|
|
+ result.m6 = 0;
|
|
|
+ result.m7 = 0;
|
|
|
+
|
|
|
+ result.m8 = (right + left) / rl;
|
|
|
+ result.m9 = (top + bottom) / tb;
|
|
|
+ result.m10 = -(far + near) / fn;
|
|
|
+ result.m11 = -1.0f;
|
|
|
+
|
|
|
+ result.m12 = 0;
|
|
|
+ result.m13 = 0;
|
|
|
+ result.m14 = -(far*near*2.0f) / fn;
|
|
|
+ result.m15 = 0;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns perspective projection matrix
|
|
|
+RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far)
|
|
|
+{
|
|
|
+ double top = near*tanf(fovy*PI / 360.0f);
|
|
|
+ double right = top*aspect;
|
|
|
+
|
|
|
+ return MatrixFrustum(-right, right, -top, top, near, far);
|
|
|
+}
|
|
|
+
|
|
|
+// Returns orthographic projection matrix
|
|
|
+RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far)
|
|
|
+{
|
|
|
+ Matrix result;
|
|
|
+
|
|
|
+ float rl = (right - left);
|
|
|
+ float tb = (top - bottom);
|
|
|
+ float fn = (far - near);
|
|
|
+
|
|
|
+ result.m0 = 2 / rl;
|
|
|
+ result.m1 = 0;
|
|
|
+ result.m2 = 0;
|
|
|
+ result.m3 = 0;
|
|
|
+ result.m4 = 0;
|
|
|
+ result.m5 = 2 / tb;
|
|
|
+ result.m6 = 0;
|
|
|
+ result.m7 = 0;
|
|
|
+ result.m8 = 0;
|
|
|
+ result.m9 = 0;
|
|
|
+ result.m10 = -2 / fn;
|
|
|
+ result.m11 = 0;
|
|
|
+ result.m12 = -(left + right) / rl;
|
|
|
+ result.m13 = -(top + bottom) / tb;
|
|
|
+ result.m14 = -(far + near) / fn;
|
|
|
+ result.m15 = 1;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns camera look-at matrix (view matrix)
|
|
|
+RMDEF Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up)
|
|
|
+{
|
|
|
+ Matrix result;
|
|
|
+
|
|
|
+ Vector3 z = VectorSubtract(eye, target);
|
|
|
+ VectorNormalize(&z);
|
|
|
+ Vector3 x = VectorCrossProduct(up, z);
|
|
|
+ VectorNormalize(&x);
|
|
|
+ Vector3 y = VectorCrossProduct(z, x);
|
|
|
+ VectorNormalize(&y);
|
|
|
+
|
|
|
+ result.m0 = x.x;
|
|
|
+ result.m1 = x.y;
|
|
|
+ result.m2 = x.z;
|
|
|
+ result.m3 = -((x.x * eye.x) + (x.y * eye.y) + (x.z * eye.z));
|
|
|
+ result.m4 = y.x;
|
|
|
+ result.m5 = y.y;
|
|
|
+ result.m6 = y.z;
|
|
|
+ result.m7 = -((y.x * eye.x) + (y.y * eye.y) + (y.z * eye.z));
|
|
|
+ result.m8 = z.x;
|
|
|
+ result.m9 = z.y;
|
|
|
+ result.m10 = z.z;
|
|
|
+ result.m11 = -((z.x * eye.x) + (z.y * eye.y) + (z.z * eye.z));
|
|
|
+ result.m12 = 0;
|
|
|
+ result.m13 = 0;
|
|
|
+ result.m14 = 0;
|
|
|
+ result.m15 = 1;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Print matrix utility (for debug)
|
|
|
+RMDEF void PrintMatrix(Matrix m)
|
|
|
+{
|
|
|
+ printf("----------------------\n");
|
|
|
+ printf("%2.2f %2.2f %2.2f %2.2f\n", m.m0, m.m4, m.m8, m.m12);
|
|
|
+ printf("%2.2f %2.2f %2.2f %2.2f\n", m.m1, m.m5, m.m9, m.m13);
|
|
|
+ printf("%2.2f %2.2f %2.2f %2.2f\n", m.m2, m.m6, m.m10, m.m14);
|
|
|
+ printf("%2.2f %2.2f %2.2f %2.2f\n", m.m3, m.m7, m.m11, m.m15);
|
|
|
+ printf("----------------------\n");
|
|
|
+}
|
|
|
+
|
|
|
+//----------------------------------------------------------------------------------
|
|
|
+// Module Functions Definition - Quaternion math
|
|
|
+//----------------------------------------------------------------------------------
|
|
|
+
|
|
|
+// Computes the length of a quaternion
|
|
|
+RMDEF float QuaternionLength(Quaternion quat)
|
|
|
+{
|
|
|
+ return sqrt(quat.x*quat.x + quat.y*quat.y + quat.z*quat.z + quat.w*quat.w);
|
|
|
+}
|
|
|
+
|
|
|
+// Normalize provided quaternion
|
|
|
+RMDEF void QuaternionNormalize(Quaternion *q)
|
|
|
+{
|
|
|
+ float length, ilength;
|
|
|
+
|
|
|
+ length = QuaternionLength(*q);
|
|
|
+
|
|
|
+ if (length == 0) length = 1;
|
|
|
+
|
|
|
+ ilength = 1.0/length;
|
|
|
+
|
|
|
+ q->x *= ilength;
|
|
|
+ q->y *= ilength;
|
|
|
+ q->z *= ilength;
|
|
|
+ q->w *= ilength;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate two quaternion multiplication
|
|
|
+RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2)
|
|
|
+{
|
|
|
+ Quaternion result;
|
|
|
+
|
|
|
+ float qax = q1.x, qay = q1.y, qaz = q1.z, qaw = q1.w;
|
|
|
+ float qbx = q2.x, qby = q2.y, qbz = q2.z, qbw = q2.w;
|
|
|
+
|
|
|
+ result.x = qax*qbw + qaw*qbx + qay*qbz - qaz*qby;
|
|
|
+ result.y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz;
|
|
|
+ result.z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx;
|
|
|
+ result.w = qaw*qbw - qax*qbx - qay*qby - qaz*qbz;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculates spherical linear interpolation between two quaternions
|
|
|
+RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
|
|
|
+{
|
|
|
+ Quaternion result;
|
|
|
+
|
|
|
+ float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w;
|
|
|
+
|
|
|
+ if (fabs(cosHalfTheta) >= 1.0f) result = q1;
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float halfTheta = acos(cosHalfTheta);
|
|
|
+ float sinHalfTheta = sqrt(1.0f - cosHalfTheta*cosHalfTheta);
|
|
|
+
|
|
|
+ if (fabs(sinHalfTheta) < 0.001f)
|
|
|
+ {
|
|
|
+ result.x = (q1.x*0.5f + q2.x*0.5f);
|
|
|
+ result.y = (q1.y*0.5f + q2.y*0.5f);
|
|
|
+ result.z = (q1.z*0.5f + q2.z*0.5f);
|
|
|
+ result.w = (q1.w*0.5f + q2.w*0.5f);
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float ratioA = sin((1 - amount)*halfTheta) / sinHalfTheta;
|
|
|
+ float ratioB = sin(amount*halfTheta) / sinHalfTheta;
|
|
|
+
|
|
|
+ result.x = (q1.x*ratioA + q2.x*ratioB);
|
|
|
+ result.y = (q1.y*ratioA + q2.y*ratioB);
|
|
|
+ result.z = (q1.z*ratioA + q2.z*ratioB);
|
|
|
+ result.w = (q1.w*ratioA + q2.w*ratioB);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns a quaternion for a given rotation matrix
|
|
|
+RMDEF Quaternion QuaternionFromMatrix(Matrix matrix)
|
|
|
+{
|
|
|
+ Quaternion result;
|
|
|
+
|
|
|
+ float trace = MatrixTrace(matrix);
|
|
|
+
|
|
|
+ if (trace > 0)
|
|
|
+ {
|
|
|
+ float s = (float)sqrt(trace + 1) * 2;
|
|
|
+ float invS = 1 / s;
|
|
|
+
|
|
|
+ result.w = s * 0.25;
|
|
|
+ result.x = (matrix.m6 - matrix.m9) * invS;
|
|
|
+ result.y = (matrix.m8 - matrix.m2) * invS;
|
|
|
+ result.z = (matrix.m1 - matrix.m4) * invS;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float m00 = matrix.m0, m11 = matrix.m5, m22 = matrix.m10;
|
|
|
+
|
|
|
+ if (m00 > m11 && m00 > m22)
|
|
|
+ {
|
|
|
+ float s = (float)sqrt(1 + m00 - m11 - m22) * 2;
|
|
|
+ float invS = 1 / s;
|
|
|
+
|
|
|
+ result.w = (matrix.m6 - matrix.m9) * invS;
|
|
|
+ result.x = s * 0.25;
|
|
|
+ result.y = (matrix.m4 + matrix.m1) * invS;
|
|
|
+ result.z = (matrix.m8 + matrix.m2) * invS;
|
|
|
+ }
|
|
|
+ else if (m11 > m22)
|
|
|
+ {
|
|
|
+ float s = (float)sqrt(1 + m11 - m00 - m22) * 2;
|
|
|
+ float invS = 1 / s;
|
|
|
+
|
|
|
+ result.w = (matrix.m8 - matrix.m2) * invS;
|
|
|
+ result.x = (matrix.m4 + matrix.m1) * invS;
|
|
|
+ result.y = s * 0.25;
|
|
|
+ result.z = (matrix.m9 + matrix.m6) * invS;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float s = (float)sqrt(1 + m22 - m00 - m11) * 2;
|
|
|
+ float invS = 1 / s;
|
|
|
+
|
|
|
+ result.w = (matrix.m1 - matrix.m4) * invS;
|
|
|
+ result.x = (matrix.m8 + matrix.m2) * invS;
|
|
|
+ result.y = (matrix.m9 + matrix.m6) * invS;
|
|
|
+ result.z = s * 0.25;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns a matrix for a given quaternion
|
|
|
+RMDEF Matrix QuaternionToMatrix(Quaternion q)
|
|
|
+{
|
|
|
+ Matrix result;
|
|
|
+
|
|
|
+ float x = q.x, y = q.y, z = q.z, w = q.w;
|
|
|
+
|
|
|
+ float x2 = x + x;
|
|
|
+ float y2 = y + y;
|
|
|
+ float z2 = z + z;
|
|
|
+
|
|
|
+ float xx = x*x2;
|
|
|
+ float xy = x*y2;
|
|
|
+ float xz = x*z2;
|
|
|
+
|
|
|
+ float yy = y*y2;
|
|
|
+ float yz = y*z2;
|
|
|
+ float zz = z*z2;
|
|
|
+
|
|
|
+ float wx = w*x2;
|
|
|
+ float wy = w*y2;
|
|
|
+ float wz = w*z2;
|
|
|
+
|
|
|
+ result.m0 = 1 - (yy + zz);
|
|
|
+ result.m1 = xy - wz;
|
|
|
+ result.m2 = xz + wy;
|
|
|
+ result.m3 = 0;
|
|
|
+ result.m4 = xy + wz;
|
|
|
+ result.m5 = 1 - (xx + zz);
|
|
|
+ result.m6 = yz - wx;
|
|
|
+ result.m7 = 0;
|
|
|
+ result.m8 = xz - wy;
|
|
|
+ result.m9 = yz + wx;
|
|
|
+ result.m10 = 1 - (xx + yy);
|
|
|
+ result.m11 = 0;
|
|
|
+ result.m12 = 0;
|
|
|
+ result.m13 = 0;
|
|
|
+ result.m14 = 0;
|
|
|
+ result.m15 = 1;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns rotation quaternion for an angle and axis
|
|
|
+// NOTE: angle must be provided in radians
|
|
|
+RMDEF Quaternion QuaternionFromAxisAngle(float angle, Vector3 axis)
|
|
|
+{
|
|
|
+ Quaternion result = { 0, 0, 0, 1 };
|
|
|
+
|
|
|
+ if (VectorLength(axis) != 0.0)
|
|
|
+
|
|
|
+ angle *= 0.5;
|
|
|
+
|
|
|
+ VectorNormalize(&axis);
|
|
|
+
|
|
|
+ result.x = axis.x * (float)sin(angle);
|
|
|
+ result.y = axis.y * (float)sin(angle);
|
|
|
+ result.z = axis.z * (float)sin(angle);
|
|
|
+ result.w = (float)cos(angle);
|
|
|
+
|
|
|
+ QuaternionNormalize(&result);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns the rotation angle and axis for a given quaternion
|
|
|
+RMDEF void QuaternionToAxisAngle(Quaternion q, float *outAngle, Vector3 *outAxis)
|
|
|
+{
|
|
|
+ if (fabs(q.w) > 1.0f) QuaternionNormalize(&q);
|
|
|
+
|
|
|
+ Vector3 resAxis = { 0, 0, 0 };
|
|
|
+ float resAngle = 0;
|
|
|
+
|
|
|
+ resAngle = 2.0f * (float)acos(q.w);
|
|
|
+ float den = (float)sqrt(1.0 - q.w * q.w);
|
|
|
+
|
|
|
+ if (den > 0.0001f)
|
|
|
+ {
|
|
|
+ resAxis.x = q.x / den;
|
|
|
+ resAxis.y = q.y / den;
|
|
|
+ resAxis.z = q.z / den;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ // This occurs when the angle is zero.
|
|
|
+ // Not a problem: just set an arbitrary normalized axis.
|
|
|
+ resAxis.x = 1.0;
|
|
|
+ }
|
|
|
+
|
|
|
+ *outAxis = resAxis;
|
|
|
+ *outAngle = resAngle;
|
|
|
+}
|
|
|
+
|
|
|
+// Transform a quaternion given a transformation matrix
|
|
|
+RMDEF void QuaternionTransform(Quaternion *q, Matrix mat)
|
|
|
+{
|
|
|
+ float x = q->x;
|
|
|
+ float y = q->y;
|
|
|
+ float z = q->z;
|
|
|
+ float w = q->w;
|
|
|
+
|
|
|
+ q->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12*w;
|
|
|
+ q->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13*w;
|
|
|
+ q->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14*w;
|
|
|
+ q->w = mat.m3*x + mat.m7*y + mat.m11*z + mat.m15*w;
|
|
|
}
|
|
|
-#endif
|
|
|
|
|
|
+#endif // RAYMATH_DEFINE
|
|
|
#endif // RAYMATH_H
|
Ray