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1059 行
29 KiB
1059 行
29 KiB
/**********************************************************************************************
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*
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* raymath
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*
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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 - raysan@raysanweb.com)
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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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* 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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* 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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* as being the original software.
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*
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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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#include "raymath.h"
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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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//----------------------------------------------------------------------------------
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// Defines and Macros
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//----------------------------------------------------------------------------------
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//...
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//----------------------------------------------------------------------------------
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// Module specific Functions Declaration
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//----------------------------------------------------------------------------------
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// ...
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//----------------------------------------------------------------------------------
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// Module Functions Definition - Vector3 math
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//----------------------------------------------------------------------------------
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// Add two vectors
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Vector3 VectorAdd(Vector3 v1, Vector3 v2)
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{
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Vector3 result;
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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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return result;
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}
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// Substract two vectors
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Vector3 VectorSubtract(Vector3 v1, Vector3 v2)
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{
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Vector3 result;
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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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return result;
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}
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// Calculate two vectors cross product
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Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2)
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{
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Vector3 result;
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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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return result;
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}
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// Calculate one vector perpendicular vector
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Vector3 VectorPerpendicular(Vector3 v)
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{
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Vector3 result;
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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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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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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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result = VectorCrossProduct(v, cardinalAxis);
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return result;
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}
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// Calculate two vectors dot product
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float VectorDotProduct(Vector3 v1, Vector3 v2)
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{
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float result;
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result = v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
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return result;
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}
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// Calculate vector lenght
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float VectorLength(const Vector3 v)
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{
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float length;
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length = sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
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return length;
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}
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// Scale provided vector
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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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// Negate provided vector (invert direction)
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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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// Normalize provided vector
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void VectorNormalize(Vector3 *v)
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{
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float length, ilength;
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length = VectorLength(*v);
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if (length == 0) length = 1;
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ilength = 1.0/length;
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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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// Calculate distance between two points
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float VectorDistance(Vector3 v1, Vector3 v2)
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{
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float result;
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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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result = sqrt(dx*dx + dy*dy + dz*dz);
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return result;
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}
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// Calculate linear interpolation between two vectors
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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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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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return result;
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}
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// Calculate reflected vector to normal
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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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Vector3 result;
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float dotProduct = VectorDotProduct(vector, normal);
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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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return result;
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}
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// Transforms a Vector3 with a given Matrix
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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 z = v->z;
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//MatrixTranspose(&mat);
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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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// Return a Vector3 init to zero
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Vector3 VectorZero(void)
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{
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Vector3 zero = { 0.0f, 0.0f, 0.0f };
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return zero;
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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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// Returns an OpenGL-ready vector (glMultMatrixf)
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float *GetMatrixVector(Matrix mat)
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{
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static float vector[16];
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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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vector[3] = mat.m12;
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vector[4] = mat.m1;
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vector[5] = mat.m5;
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vector[6] = mat.m9;
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vector[7] = mat.m13;
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vector[8] = mat.m2;
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vector[9] = mat.m6;
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vector[10] = mat.m10;
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vector[11] = mat.m14;
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vector[12] = mat.m3;
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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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return vector;
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}
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// Compute matrix determinant
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float MatrixDeterminant(Matrix mat)
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{
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float result;
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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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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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return result;
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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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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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// Transposes provided matrix
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void MatrixTranspose(Matrix *mat)
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{
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Matrix temp;
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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;
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temp.m9 = mat->m6;
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temp.m10 = mat->m10;
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temp.m11 = mat->m14;
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temp.m12 = mat->m3;
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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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*mat = temp;
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}
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// Invert provided matrix
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void MatrixInvert(Matrix *mat)
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{
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Matrix temp;
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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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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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float b03 = a01*a12 - a02*a11;
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float b04 = a01*a13 - a03*a11;
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float b05 = a02*a13 - a03*a12;
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float b06 = a20*a31 - a21*a30;
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float b07 = a20*a32 - a22*a30;
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float b08 = a20*a33 - a23*a30;
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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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// 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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printf("%f\n", invDet);
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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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temp.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet;
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temp.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet;
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temp.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet;
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temp.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet;
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temp.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet;
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temp.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet;
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temp.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet;
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temp.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet;
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temp.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet;
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temp.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet;
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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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PrintMatrix(temp);
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*mat = temp;
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}
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// Normalize provided matrix
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void MatrixNormalize(Matrix *mat)
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{
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float det = MatrixDeterminant(*mat);
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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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mat->m3 /= det;
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mat->m4 /= det;
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mat->m5 /= det;
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mat->m6 /= det;
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mat->m7 /= det;
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mat->m8 /= det;
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mat->m9 /= det;
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mat->m10 /= det;
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mat->m11 /= det;
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mat->m12 /= det;
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mat->m13 /= det;
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mat->m14 /= det;
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mat->m15 /= det;
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}
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// Returns identity matrix
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Matrix MatrixIdentity(void)
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{
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Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
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return result;
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}
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// Add two matrices
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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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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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result.m3 = left.m3 + right.m3;
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result.m4 = left.m4 + right.m4;
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result.m5 = left.m5 + right.m5;
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result.m6 = left.m6 + right.m6;
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result.m7 = left.m7 + right.m7;
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result.m8 = left.m8 + right.m8;
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result.m9 = left.m9 + right.m9;
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result.m10 = left.m10 + right.m10;
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result.m11 = left.m11 + right.m11;
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result.m12 = left.m12 + right.m12;
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result.m13 = left.m13 + right.m13;
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result.m14 = left.m14 + right.m14;
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result.m15 = left.m15 + right.m15;
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return result;
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}
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// Substract two matrices (left - 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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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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result.m3 = left.m3 - right.m3;
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result.m4 = left.m4 - right.m4;
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result.m5 = left.m5 - right.m5;
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result.m6 = left.m6 - right.m6;
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result.m7 = left.m7 - right.m7;
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result.m8 = left.m8 - right.m8;
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result.m9 = left.m9 - right.m9;
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result.m10 = left.m10 - right.m10;
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result.m11 = left.m11 - right.m11;
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result.m12 = left.m12 - right.m12;
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result.m13 = left.m13 - right.m13;
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result.m14 = left.m14 - right.m14;
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result.m15 = left.m15 - right.m15;
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return result;
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}
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// Returns translation matrix
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// TODO: Review this function
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Matrix MatrixTranslate(float x, float y, float z)
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{
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/*
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For OpenGL
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1, 0, 0, 0
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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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point of confusion for those new to OpenGL.
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* matrix notation used in opengl documentation does not describe in-memory layout for OpenGL matrices
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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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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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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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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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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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return result;
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}
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// Returns rotation matrix
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// TODO: Review this function
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Matrix MatrixRotate(float angleX, float angleY, float angleZ)
|
|
{
|
|
Matrix result;
|
|
|
|
Matrix rotX = MatrixRotateX(angleX);
|
|
Matrix rotY = MatrixRotateY(angleY);
|
|
Matrix rotZ = MatrixRotateZ(angleZ);
|
|
|
|
result = MatrixMultiply(MatrixMultiply(rotX, rotY), rotZ);
|
|
|
|
return result;
|
|
}
|
|
|
|
// Create rotation matrix from axis and angle
|
|
// TODO: Test this function
|
|
// NOTE: NO prototype defined!
|
|
Matrix MatrixFromAxisAngle(Vector3 axis, float angle)
|
|
{
|
|
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 = sin(angle);
|
|
float c = cos(angle);
|
|
float t = 1-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;
|
|
};
|
|
|
|
// Create rotation matrix from axis and angle (version 2)
|
|
// TODO: Test this function
|
|
// NOTE: NO prototype defined!
|
|
Matrix MatrixFromAxisAngle2(Vector3 axis, float angle)
|
|
{
|
|
Matrix result;
|
|
|
|
VectorNormalize(&axis);
|
|
float axisX = axis.x, axisY = axis.y, axisZ = axis.y;
|
|
|
|
// Calculate angles
|
|
float cosres = (float)cos(-angle);
|
|
float sinres = (float)sin(-angle);
|
|
float t = 1.0f - cosres;
|
|
|
|
// Do the conversion math once
|
|
float tXX = t * axisX * axisX;
|
|
float tXY = t * axisX * axisY;
|
|
float tXZ = t * axisX * axisZ;
|
|
float tYY = t * axisY * axisY;
|
|
float tYZ = t * axisY * axisZ;
|
|
float tZZ = t * axisZ * axisZ;
|
|
|
|
float sinX = sinres * axisX;
|
|
float sinY = sinres * axisY;
|
|
float sinZ = sinres * axisZ;
|
|
|
|
result.m0 = tXX + cosres;
|
|
result.m1 = tXY + sinZ;
|
|
result.m2 = tXZ - sinY;
|
|
result.m3 = 0;
|
|
result.m4 = tXY - sinZ;
|
|
result.m5 = tYY + cosres;
|
|
result.m6 = tYZ + sinX;
|
|
result.m7 = 0;
|
|
result.m8 = tXZ + sinY;
|
|
result.m9 = tYZ - sinX;
|
|
result.m10 = tZZ + cosres;
|
|
result.m11 = 0;
|
|
result.m12 = 0;
|
|
result.m13 = 0;
|
|
result.m14 = 0;
|
|
result.m15 = 1;
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns rotation matrix for a given quaternion
|
|
Matrix MatrixFromQuaternion(Quaternion q)
|
|
{
|
|
Matrix result = MatrixIdentity();
|
|
|
|
Vector3 axis;
|
|
float angle;
|
|
|
|
QuaternionToAxisAngle(q, &axis, &angle);
|
|
|
|
result = MatrixFromAxisAngle2(axis, angle);
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns x-rotation matrix (angle in radians)
|
|
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)
|
|
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;
|
|
result.m10 = cosres;
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns z-rotation matrix (angle in radians)
|
|
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
|
|
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 transformation matrix for a given translation, rotation and scale
|
|
// NOTE: Transformation order is rotation -> scale -> translation
|
|
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);
|
|
|
|
result = MatrixMultiply(MatrixMultiply(mRotation, mScale), mTranslate);
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns two matrix multiplication
|
|
// NOTE: When multiplying matrices... the order matters!
|
|
Matrix MatrixMultiply(Matrix left, Matrix right)
|
|
{
|
|
Matrix result;
|
|
|
|
// Cache the matrix values (speed optimization)
|
|
float a00 = left.m0, a01 = left.m1, a02 = left.m2, a03 = left.m3;
|
|
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;
|
|
result.m3 = b00*a03 + b01*a13 + b02*a23 + b03*a33;
|
|
result.m4 = b10*a00 + b11*a10 + b12*a20 + b13*a30;
|
|
result.m5 = b10*a01 + b11*a11 + b12*a21 + b13*a31;
|
|
result.m6 = b10*a02 + b11*a12 + b12*a22 + b13*a32;
|
|
result.m7 = b10*a03 + b11*a13 + b12*a23 + b13*a33;
|
|
result.m8 = b20*a00 + b21*a10 + b22*a20 + b23*a30;
|
|
result.m9 = b20*a01 + b21*a11 + b22*a21 + b23*a31;
|
|
result.m10 = b20*a02 + b21*a12 + b22*a22 + b23*a32;
|
|
result.m11 = b20*a03 + b21*a13 + b22*a23 + b23*a33;
|
|
result.m12 = b30*a00 + b31*a10 + b32*a20 + b33*a30;
|
|
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 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
|
|
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
|
|
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)
|
|
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)
|
|
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
|
|
//----------------------------------------------------------------------------------
|
|
|
|
// Calculates the length of a quaternion
|
|
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
|
|
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
|
|
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 result;
|
|
|
|
float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w;
|
|
|
|
if (abs(cosHalfTheta) >= 1.0f) result = q1;
|
|
else
|
|
{
|
|
float halfTheta = acos(cosHalfTheta);
|
|
float sinHalfTheta = sqrt(1.0f - cosHalfTheta*cosHalfTheta);
|
|
|
|
if (abs(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 from a given rotation matrix
|
|
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 rotation quaternion for an angle around an axis
|
|
// NOTE: angle must be provided in radians
|
|
Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle)
|
|
{
|
|
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;
|
|
}
|
|
|
|
// Calculates the matrix from the given quaternion
|
|
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 the axis and the angle for a given quaternion
|
|
void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
|
|
{
|
|
if (abs(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;
|
|
}
|