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@@ -5,15 +5,15 @@
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* Some useful functions to work with Vector3, Matrix and Quaternions
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*
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* Copyright (c) 2014 Ramon Santamaria (Ray San - [email protected])
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-*
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-* This software is provided "as-is", without any express or implied warranty. In no event
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+*
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+* This software is provided "as-is", without any express or implied warranty. In no event
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* will the authors be held liable for any damages arising from the use of this software.
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*
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-* Permission is granted to anyone to use this software for any purpose, including commercial
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+* Permission is granted to anyone to use this software for any purpose, including commercial
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* applications, and to alter it and redistribute it freely, subject to the following restrictions:
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*
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-* 1. The origin of this software must not be misrepresented; you must not claim that you
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-* wrote the original software. If you use this software in a product, an acknowledgment
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+* 1. The origin of this software must not be misrepresented; you must not claim that you
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+* wrote the original software. If you use this software in a product, an acknowledgment
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* in the product documentation would be appreciated but is not required.
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*
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* 2. Altered source versions must be plainly marked as such, and must not be misrepresented
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@@ -51,7 +51,7 @@ Vector3 VectorAdd(Vector3 v1, Vector3 v2)
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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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+
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return result;
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}
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@@ -63,7 +63,7 @@ Vector3 VectorSubtract(Vector3 v1, Vector3 v2)
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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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+
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return result;
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}
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@@ -75,7 +75,7 @@ Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2)
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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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+
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return result;
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}
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@@ -83,23 +83,23 @@ Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2)
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Vector3 VectorPerpendicular(Vector3 v)
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{
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Vector3 result;
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-
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+
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float min = fabs(v.x);
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Vector3 cardinalAxis = {1.0, 0.0, 0.0};
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-
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- if (fabs(v.y) < min)
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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){0.0, 1.0, 0.0};
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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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+ if(fabs(v.z) < min)
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{
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cardinalAxis = (Vector3){0.0, 0.0, 1.0};
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}
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-
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+
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result = VectorCrossProduct(v, cardinalAxis);
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-
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+
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return result;
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}
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@@ -107,9 +107,9 @@ Vector3 VectorPerpendicular(Vector3 v)
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float VectorDotProduct(Vector3 v1, Vector3 v2)
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{
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float result;
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-
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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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+
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return result;
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}
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@@ -117,9 +117,9 @@ float VectorDotProduct(Vector3 v1, Vector3 v2)
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float VectorLength(const Vector3 v)
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{
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float length;
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-
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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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+
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return length;
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}
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@@ -145,11 +145,11 @@ void VectorNormalize(Vector3 *v)
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float length, ilength;
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length = VectorLength(*v);
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-
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+
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if (length == 0) length = 1;
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ilength = 1.0/length;
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-
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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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@@ -159,13 +159,13 @@ void VectorNormalize(Vector3 *v)
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float VectorDistance(Vector3 v1, Vector3 v2)
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{
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float result;
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-
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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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+
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result = sqrt(dx*dx + dy*dy + dz*dz);
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-
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+
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return result;
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}
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@@ -173,7 +173,7 @@ float VectorDistance(Vector3 v1, Vector3 v2)
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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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+
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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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@@ -187,11 +187,11 @@ Vector3 VectorReflect(Vector3 vector, Vector3 normal)
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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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+
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Vector3 result;
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-
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+
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float dotProduct = VectorDotProduct(vector, normal);
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-
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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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@@ -203,11 +203,11 @@ Vector3 VectorReflect(Vector3 vector, Vector3 normal)
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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 y = v->y;
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float z = v->z;
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-
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+
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//MatrixTranspose(&mat);
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-
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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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@@ -217,7 +217,7 @@ void VectorTransform(Vector3 *v, Matrix mat)
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Vector3 VectorZero()
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{
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Vector3 zero = { 0.0, 0.0, 0.0 };
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-
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+
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return zero;
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}
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@@ -229,7 +229,7 @@ Vector3 VectorZero()
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float *GetMatrixVector(Matrix mat)
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{
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static float vector[16];
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-
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+
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vector[0] = mat.m0;
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vector[1] = mat.m4;
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vector[2] = mat.m8;
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@@ -246,7 +246,7 @@ float *GetMatrixVector(Matrix mat)
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vector[13] = mat.m7;
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vector[14] = mat.m11;
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vector[15] = mat.m15;
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-
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+
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return vector;
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}
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@@ -267,7 +267,7 @@ float MatrixDeterminant(Matrix mat)
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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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+
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return result;
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}
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@@ -298,7 +298,7 @@ void MatrixTranspose(Matrix *mat)
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temp.m13 = mat->m7;
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temp.m14 = mat->m11;
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temp.m15 = mat->m15;
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-
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+
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*mat = temp;
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}
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@@ -306,13 +306,13 @@ void MatrixTranspose(Matrix *mat)
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void MatrixInvert(Matrix *mat)
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{
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Matrix temp;
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-
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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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+
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float b00 = a00*a11 - a01*a10;
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float b01 = a00*a12 - a02*a10;
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float b02 = a00*a13 - a03*a10;
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@@ -325,12 +325,12 @@ void MatrixInvert(Matrix *mat)
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float b09 = a21*a32 - a22*a31;
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float b10 = a21*a33 - a23*a31;
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float b11 = a22*a33 - a23*a32;
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-
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+
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// Calculate the invert determinant (inlined to avoid double-caching)
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float invDet = 1/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
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-
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+
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printf("%f\n", invDet);
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-
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+
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temp.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet;
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temp.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet;
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temp.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet;
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@@ -347,9 +347,9 @@ void MatrixInvert(Matrix *mat)
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temp.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet;
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temp.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet;
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temp.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet;
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-
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+
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PrintMatrix(temp);
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-
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+
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*mat = temp;
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}
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@@ -357,7 +357,7 @@ void MatrixInvert(Matrix *mat)
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void MatrixNormalize(Matrix *mat)
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{
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float det = MatrixDeterminant(*mat);
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-
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+
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mat->m0 /= det;
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mat->m1 /= det;
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mat->m2 /= det;
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@@ -388,7 +388,7 @@ Matrix MatrixIdentity()
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Matrix MatrixAdd(Matrix left, Matrix right)
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{
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Matrix result = MatrixIdentity();
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-
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+
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result.m0 = left.m0 + right.m0;
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result.m1 = left.m1 + right.m1;
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result.m2 = left.m2 + right.m2;
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@@ -413,7 +413,7 @@ Matrix MatrixAdd(Matrix left, Matrix right)
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Matrix MatrixSubstract(Matrix left, Matrix right)
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{
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Matrix result = MatrixIdentity();
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-
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+
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result.m0 = left.m0 - right.m0;
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result.m1 = left.m1 - right.m1;
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result.m2 = left.m2 - right.m2;
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@@ -444,36 +444,36 @@ Matrix MatrixTranslate(float x, float y, float z)
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0, 1, 0, 0
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0, 0, 1, 0
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x, y, z, 1
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- Is the correct Translation Matrix. Why? Opengl Uses column-major matrix ordering.
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- Which is the Transpose of the Matrix you initially presented, which is in row-major ordering.
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- Row major is used in most math text-books and also DirectX, so it is a common
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+ Is the correct Translation Matrix. Why? Opengl Uses column-major matrix ordering.
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+ Which is the Transpose of the Matrix you initially presented, which is in row-major ordering.
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+ Row major is used in most math text-books and also DirectX, so it is a common
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point of confusion for those new to OpenGL.
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-
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+
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* matrix notation used in opengl documentation does not describe in-memory layout for OpenGL matrices
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-
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+
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Translation matrix should be laid out in memory like this:
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{ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, trabsX, transY, transZ, 1 }
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-
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-
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+
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+
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9.005 Are OpenGL matrices column-major or row-major?
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- For programming purposes, OpenGL matrices are 16-value arrays with base vectors laid out
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- contiguously in memory. The translation components occupy the 13th, 14th, and 15th elements
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- of the 16-element matrix, where indices are numbered from 1 to 16 as described in section
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+ For programming purposes, OpenGL matrices are 16-value arrays with base vectors laid out
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+ contiguously in memory. The translation components occupy the 13th, 14th, and 15th elements
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+ of the 16-element matrix, where indices are numbered from 1 to 16 as described in section
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2.11.2 of the OpenGL 2.1 Specification.
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- Column-major versus row-major is purely a notational convention. Note that post-multiplying
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- with column-major matrices produces the same result as pre-multiplying with row-major matrices.
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- The OpenGL Specification and the OpenGL Reference Manual both use column-major notation.
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+ Column-major versus row-major is purely a notational convention. Note that post-multiplying
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+ with column-major matrices produces the same result as pre-multiplying with row-major matrices.
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+ The OpenGL Specification and the OpenGL Reference Manual both use column-major notation.
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You can use any notation, as long as it's clearly stated.
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- Sadly, the use of column-major format in the spec and blue book has resulted in endless confusion
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- in the OpenGL programming community. Column-major notation suggests that matrices
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+ Sadly, the use of column-major format in the spec and blue book has resulted in endless confusion
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+ in the OpenGL programming community. Column-major notation suggests that matrices
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are not laid out in memory as a programmer would expect.
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*/
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Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 };
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-
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+
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return result;
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}
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@@ -482,50 +482,50 @@ Matrix MatrixTranslate(float x, float y, float z)
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Matrix MatrixRotate(float angleX, float angleY, float angleZ)
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{
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Matrix result;
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-
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+
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Matrix rotX = MatrixRotateX(angleX);
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Matrix rotY = MatrixRotateY(angleY);
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Matrix rotZ = MatrixRotateZ(angleZ);
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-
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+
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result = MatrixMultiply(MatrixMultiply(rotX, rotY), rotZ);
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-
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+
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return result;
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}
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// Create rotation matrix from axis and angle
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// TODO: Test this function
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-Matrix MatrixFromAxisAngle(Vector3 axis, float angle)
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+Matrix MatrixFromAxisAngle(Vector3 axis, float angle)
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{
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Matrix result;
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-
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+
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Matrix mat = MatrixIdentity();
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float x = axis.x, y = axis.y, z = axis.z;
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-
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+
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float length = sqrt(x*x + y*y + z*z);
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-
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+
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if ((length != 1) && (length != 0))
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{
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length = 1 / length;
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- x *= length;
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- y *= length;
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+ x *= length;
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+ y *= length;
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z *= length;
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}
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-
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+
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float s = sin(angle);
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float c = cos(angle);
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float t = 1-c;
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-
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+
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// Cache some 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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-
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+
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// Construct the elements of the rotation matrix
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float b00 = x*x*t + c, b01 = y*x*t + z*s, b02 = z*x*t - y*s;
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float b10 = x*y*t - z*s, b11 = y*y*t + c, b12 = z*y*t + x*s;
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float b20 = x*z*t + y*s, b21 = y*z*t - x*s, b22 = z*z*t + c;
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-
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+
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// Perform rotation-specific matrix multiplication
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result.m0 = a00*b00 + a10*b01 + a20*b02;
|
|
|
result.m1 = a01*b00 + a11*b01 + a21*b02;
|
|
@@ -543,7 +543,7 @@ Matrix MatrixFromAxisAngle(Vector3 axis, float angle)
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|
result.m13 = mat.m13;
|
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|
result.m14 = mat.m14;
|
|
|
result.m15 = mat.m15;
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
};
|
|
|
|
|
@@ -552,7 +552,7 @@ Matrix MatrixFromAxisAngle(Vector3 axis, float angle)
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|
Matrix MatrixFromAxisAngle2(Vector3 axis, float angle)
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|
|
{
|
|
|
Matrix result;
|
|
|
-
|
|
|
+
|
|
|
VectorNormalize(&axis);
|
|
|
float axisX = axis.x, axisY = axis.y, axisZ = axis.y;
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|
@@ -589,7 +589,7 @@ Matrix MatrixFromAxisAngle2(Vector3 axis, float angle)
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|
result.m13 = 0;
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|
result.m14 = 0;
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|
result.m15 = 1;
|
|
|
-
|
|
|
+
|
|
|
return result;
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|
|
}
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|
|
|
|
@@ -597,14 +597,14 @@ Matrix MatrixFromAxisAngle2(Vector3 axis, float angle)
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|
Matrix MatrixFromQuaternion(Quaternion q)
|
|
|
{
|
|
|
Matrix result = MatrixIdentity();
|
|
|
-
|
|
|
+
|
|
|
Vector3 axis;
|
|
|
float angle;
|
|
|
-
|
|
|
+
|
|
|
QuaternionToAxisAngle(q, &axis, &angle);
|
|
|
-
|
|
|
+
|
|
|
result = MatrixFromAxisAngle2(axis, angle);
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
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|
|
|
|
@@ -612,10 +612,10 @@ Matrix MatrixFromQuaternion(Quaternion q)
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|
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;
|
|
@@ -628,10 +628,10 @@ Matrix MatrixRotateX(float angle)
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|
|
Matrix MatrixRotateY(float angle)
|
|
|
{
|
|
|
Matrix result = MatrixIdentity();
|
|
|
-
|
|
|
+
|
|
|
float cosres = (float)cos(angle);
|
|
|
float sinres = (float)sin(angle);
|
|
|
-
|
|
|
+
|
|
|
result.m0 = cosres;
|
|
|
result.m2 = sinres;
|
|
|
result.m8 = -sinres;
|
|
@@ -644,10 +644,10 @@ Matrix MatrixRotateY(float angle)
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|
|
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;
|
|
@@ -669,7 +669,7 @@ Matrix MatrixScale(float x, float y, float z)
|
|
|
Matrix MatrixTransform(Vector3 translation, Vector3 rotation, Vector3 scale)
|
|
|
{
|
|
|
Matrix result = MatrixIdentity();
|
|
|
-
|
|
|
+
|
|
|
Matrix mRotation = MatrixRotate(rotation.x, rotation.y, rotation.z);
|
|
|
Matrix mScale = MatrixScale(scale.x, scale.y, scale.z);
|
|
|
Matrix mTranslate = MatrixTranslate(translation.x, translation.y, translation.z);
|
|
@@ -690,12 +690,12 @@ Matrix MatrixMultiply(Matrix left, Matrix right)
|
|
|
float a10 = left.m4, a11 = left.m5, a12 = left.m6, a13 = left.m7;
|
|
|
float a20 = left.m8, a21 = left.m9, a22 = left.m10, a23 = left.m11;
|
|
|
float a30 = left.m12, a31 = left.m13, a32 = left.m14, a33 = left.m15;
|
|
|
-
|
|
|
+
|
|
|
float b00 = right.m0, b01 = right.m1, b02 = right.m2, b03 = right.m3;
|
|
|
float b10 = right.m4, b11 = right.m5, b12 = right.m6, b13 = right.m7;
|
|
|
float b20 = right.m8, b21 = right.m9, b22 = right.m10, b23 = right.m11;
|
|
|
float b30 = right.m12, b31 = right.m13, b32 = right.m14, b33 = right.m15;
|
|
|
-
|
|
|
+
|
|
|
result.m0 = b00*a00 + b01*a10 + b02*a20 + b03*a30;
|
|
|
result.m1 = b00*a01 + b01*a11 + b02*a21 + b03*a31;
|
|
|
result.m2 = b00*a02 + b01*a12 + b02*a22 + b03*a32;
|
|
@@ -712,19 +712,19 @@ Matrix MatrixMultiply(Matrix left, Matrix right)
|
|
|
result.m13 = b30*a01 + b31*a11 + b32*a21 + b33*a31;
|
|
|
result.m14 = b30*a02 + b31*a12 + b32*a22 + b33*a32;
|
|
|
result.m15 = b30*a03 + b31*a13 + b32*a23 + b33*a33;
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
|
|
|
|
|
|
// Returns perspective projection matrix
|
|
|
-Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far)
|
|
|
+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) / rl;
|
|
|
result.m1 = 0;
|
|
|
result.m2 = 0;
|
|
@@ -741,7 +741,7 @@ Matrix MatrixFrustum(double left, double right, double bottom, double top, doubl
|
|
|
result.m13 = 0;
|
|
|
result.m14 = -(far*near*2) / fn;
|
|
|
result.m15 = 0;
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
|
|
|
|
|
@@ -755,14 +755,14 @@ Matrix MatrixPerspective(double fovy, double aspect, double near, double far)
|
|
|
}
|
|
|
|
|
|
// Returns orthographic projection matrix
|
|
|
-Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far)
|
|
|
+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;
|
|
@@ -779,7 +779,7 @@ Matrix MatrixOrtho(double left, double right, double bottom, double top, double
|
|
|
result.m13 = -(top + bottom) / tb;
|
|
|
result.m14 = -(far + near) / fn;
|
|
|
result.m15 = 1;
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
|
|
|
|
|
@@ -787,14 +787,14 @@ Matrix MatrixOrtho(double left, double right, double bottom, double top, double
|
|
|
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;
|
|
@@ -811,7 +811,7 @@ Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up)
|
|
|
result.m13 = 0;
|
|
|
result.m14 = 0;
|
|
|
result.m15 = 1;
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
|
|
|
|
|
@@ -837,16 +837,16 @@ float QuaternionLength(Quaternion quat)
|
|
|
}
|
|
|
|
|
|
// Normalize provided quaternion
|
|
|
-void QuaternionNormalize(Quaternion *q)
|
|
|
+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;
|
|
@@ -854,28 +854,28 @@ void QuaternionNormalize(Quaternion *q)
|
|
|
}
|
|
|
|
|
|
// Calculate two quaternion multiplication
|
|
|
-Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2)
|
|
|
+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
|
|
|
-Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
|
|
|
+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 (abs(cosHalfTheta) >= 1.0) result = q1;
|
|
|
else
|
|
|
{
|
|
@@ -892,15 +892,15 @@ Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
|
|
|
else
|
|
|
{
|
|
|
float ratioA = sin((1 - amount)*halfTheta) / sinHalfTheta;
|
|
|
- float ratioB = sin(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;
|
|
|
}
|
|
|
|
|
@@ -956,7 +956,7 @@ Quaternion QuaternionFromMatrix(Matrix matrix)
|
|
|
result.z = s * 0.25;
|
|
|
}
|
|
|
}
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
|
|
|
|
|
@@ -966,24 +966,24 @@ Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle)
|
|
|
{
|
|
|
Quaternion result = { 0, 0, 0, 1 };
|
|
|
|
|
|
- if (VectorLength(axis) != 0.0)
|
|
|
+ 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;
|
|
|
}
|
|
|
|
|
|
// Calculates the matrix from the given quaternion
|
|
|
-Matrix QuaternionToMatrix(Quaternion q)
|
|
|
+Matrix QuaternionToMatrix(Quaternion q)
|
|
|
{
|
|
|
Matrix result;
|
|
|
|
|
@@ -1021,7 +1021,7 @@ Matrix QuaternionToMatrix(Quaternion q)
|
|
|
result.m13 = 0;
|
|
|
result.m14 = 0;
|
|
|
result.m15 = 1;
|
|
|
-
|
|
|
+
|
|
|
return result;
|
|
|
}
|
|
|
|
|
@@ -1035,7 +1035,7 @@ void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
|
|
|
|
|
|
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;
|
|
@@ -1044,11 +1044,11 @@ void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
|
|
|
}
|
|
|
else
|
|
|
{
|
|
|
- // This occurs when the angle is zero.
|
|
|
+ // This occurs when the angle is zero.
|
|
|
// Not a problem: just set an arbitrary normalized axis.
|
|
|
resAxis.x = 1.0;
|
|
|
}
|
|
|
-
|
|
|
+
|
|
|
*outAxis = resAxis;
|
|
|
*outAngle = resAngle;
|
|
|
}
|