From ae87a35f6eca258547c5be9d65f8d8ba3103c9c7 Mon Sep 17 00:00:00 2001 From: Joshua Reisenauer Date: Tue, 19 Jan 2016 15:00:48 -0800 Subject: [PATCH] standalone raymath look over for errors --- src/raymath.c | 988 ---------------------------------------------- src/raymath.h | 1046 ++++++++++++++++++++++++++++++++++++++++++++++--- 2 files changed, 984 insertions(+), 1050 deletions(-) delete mode 100644 src/raymath.c diff --git a/src/raymath.c b/src/raymath.c deleted file mode 100644 index 5feef59d..00000000 --- a/src/raymath.c +++ /dev/null @@ -1,988 +0,0 @@ -/********************************************************************************************** -* -* raymath -* -* Some useful functions to work with Vector3, Matrix and Quaternions -* -* Copyright (c) 2015 Ramon Santamaria (@raysan5) -* -* This software is provided "as-is", without any express or implied warranty. In no event -* will the authors be held liable for any damages arising from the use of this software. -* -* Permission is granted to anyone to use this software for any purpose, including commercial -* applications, and to alter it and redistribute it freely, subject to the following restrictions: -* -* 1. The origin of this software must not be misrepresented; you must not claim that you -* wrote the original software. If you use this software in a product, an acknowledgment -* in the product documentation would be appreciated but is not required. -* -* 2. Altered source versions must be plainly marked as such, and must not be misrepresented -* as being the original software. -* -* 3. This notice may not be removed or altered from any source distribution. -* -**********************************************************************************************/ - -#include "raymath.h" - -#include // Used only on PrintMatrix() -#include // Standard math libary: sin(), cos(), tan()... -#include // Used for abs() - -//---------------------------------------------------------------------------------- -// Defines and Macros -//---------------------------------------------------------------------------------- -//... - -//---------------------------------------------------------------------------------- -// Module specific Functions Declaration -//---------------------------------------------------------------------------------- -// ... - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector3 math -//---------------------------------------------------------------------------------- - -// Converts Vector3 to float array -float *VectorToFloat(Vector3 vec) -{ - static float buffer[3]; - - buffer[0] = vec.x; - buffer[1] = vec.y; - buffer[2] = vec.z; - - return buffer; -} - -// Add two vectors -Vector3 VectorAdd(Vector3 v1, Vector3 v2) -{ - Vector3 result; - - result.x = v1.x + v2.x; - result.y = v1.y + v2.y; - result.z = v1.z + v2.z; - - return result; -} - -// Substract two vectors -Vector3 VectorSubtract(Vector3 v1, Vector3 v2) -{ - Vector3 result; - - result.x = v1.x - v2.x; - result.y = v1.y - v2.y; - result.z = v1.z - v2.z; - - return result; -} - -// Calculate two vectors cross product -Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2) -{ - Vector3 result; - - result.x = v1.y*v2.z - v1.z*v2.y; - result.y = v1.z*v2.x - v1.x*v2.z; - result.z = v1.x*v2.y - v1.y*v2.x; - - return result; -} - -// Calculate one vector perpendicular vector -Vector3 VectorPerpendicular(Vector3 v) -{ - Vector3 result; - - float min = fabs(v.x); - Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; - - if (fabs(v.y) < min) - { - min = fabs(v.y); - cardinalAxis = (Vector3){0.0f, 1.0f, 0.0f}; - } - - if(fabs(v.z) < min) - { - cardinalAxis = (Vector3){0.0f, 0.0f, 1.0f}; - } - - result = VectorCrossProduct(v, cardinalAxis); - - return result; -} - -// Calculate two vectors dot product -float VectorDotProduct(Vector3 v1, Vector3 v2) -{ - float result; - - result = v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; - - return result; -} - -// Calculate vector lenght -float VectorLength(const Vector3 v) -{ - float length; - - length = sqrt(v.x*v.x + v.y*v.y + v.z*v.z); - - return length; -} - -// Scale provided vector -void VectorScale(Vector3 *v, float scale) -{ - v->x *= scale; - v->y *= scale; - v->z *= scale; -} - -// Negate provided vector (invert direction) -void VectorNegate(Vector3 *v) -{ - v->x = -v->x; - v->y = -v->y; - v->z = -v->z; -} - -// Normalize provided vector -void VectorNormalize(Vector3 *v) -{ - float length, ilength; - - length = VectorLength(*v); - - if (length == 0) length = 1; - - ilength = 1.0/length; - - v->x *= ilength; - v->y *= ilength; - v->z *= ilength; -} - -// Calculate distance between two points -float VectorDistance(Vector3 v1, Vector3 v2) -{ - float result; - - float dx = v2.x - v1.x; - float dy = v2.y - v1.y; - float dz = v2.z - v1.z; - - result = sqrt(dx*dx + dy*dy + dz*dz); - - return result; -} - -// Calculate linear interpolation between two vectors -Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount) -{ - Vector3 result; - - result.x = v1.x + amount * (v2.x - v1.x); - result.y = v1.y + amount * (v2.y - v1.y); - result.z = v1.z + amount * (v2.z - v1.z); - - return result; -} - -// Calculate reflected vector to normal -Vector3 VectorReflect(Vector3 vector, Vector3 normal) -{ - // I is the original vector - // N is the normal of the incident plane - // R = I - (2 * N * ( DotProduct[ I,N] )) - - Vector3 result; - - float dotProduct = VectorDotProduct(vector, normal); - - result.x = vector.x - (2.0 * normal.x) * dotProduct; - result.y = vector.y - (2.0 * normal.y) * dotProduct; - result.z = vector.z - (2.0 * normal.z) * dotProduct; - - return result; -} - -// Transforms a Vector3 with a given Matrix -void VectorTransform(Vector3 *v, Matrix mat) -{ - float x = v->x; - float y = v->y; - float z = v->z; - - //MatrixTranspose(&mat); - - v->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; - v->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; - v->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; -}; - -// Return a Vector3 init to zero -Vector3 VectorZero(void) -{ - Vector3 zero = { 0.0f, 0.0f, 0.0f }; - - return zero; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Matrix math -//---------------------------------------------------------------------------------- - -// Converts Matrix to float array -// NOTE: Returned vector is a transposed version of the Matrix struct, -// it should be this way because, despite raymath use OpenGL column-major convention, -// Matrix struct memory alignment and variables naming are not coherent -float *MatrixToFloat(Matrix mat) -{ - static float buffer[16]; - - buffer[0] = mat.m0; - buffer[1] = mat.m4; - buffer[2] = mat.m8; - buffer[3] = mat.m12; - buffer[4] = mat.m1; - buffer[5] = mat.m5; - buffer[6] = mat.m9; - buffer[7] = mat.m13; - buffer[8] = mat.m2; - buffer[9] = mat.m6; - buffer[10] = mat.m10; - buffer[11] = mat.m14; - buffer[12] = mat.m3; - buffer[13] = mat.m7; - buffer[14] = mat.m11; - buffer[15] = mat.m15; - - return buffer; -} - -// Compute matrix determinant -float MatrixDeterminant(Matrix mat) -{ - float result; - - // 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; - - result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 + - a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 + - a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 + - a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 + - a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 + - a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33; - - return result; -} - -// Returns the trace of the matrix (sum of the values along the diagonal) -float MatrixTrace(Matrix mat) -{ - return (mat.m0 + mat.m5 + mat.m10 + mat.m15); -} - -// Transposes provided matrix -void MatrixTranspose(Matrix *mat) -{ - Matrix temp; - - temp.m0 = mat->m0; - temp.m1 = mat->m4; - temp.m2 = mat->m8; - temp.m3 = mat->m12; - temp.m4 = mat->m1; - temp.m5 = mat->m5; - temp.m6 = mat->m9; - temp.m7 = mat->m13; - 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 -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 -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 -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 -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) -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 -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 -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... -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) -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 = 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) -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 two matrix multiplication -// NOTE: When multiplying matrices... the order matters! -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 -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 -//---------------------------------------------------------------------------------- - -// Computes 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 (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 -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 -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 -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 -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 -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; -} \ No newline at end of file diff --git a/src/raymath.h b/src/raymath.h index 507bf52f..f5912795 100644 --- a/src/raymath.h +++ b/src/raymath.h @@ -22,6 +22,29 @@ * 3. This notice may not be removed or altered from any source distribution. * **********************************************************************************************/ +//============================================================================ +// YOU MUST +// +// #define RAYMATH_DEFINE +// +// Like: +// +// #define RAYMATH_DEFINE +// #include "raymath.h" +// +// YOU CAN: +// #define RAYMATH_INLINE //inlines all code, so it runs faster. This requires lots of memory on system. +// AND +// #define RAYMATH_STANDALONE //not dependent on outside libs +// +// This needs to be done for every library/source file. +//============================================================================ + +#ifdef RAYMATH_INLINE + #define RMDEF static inline +#else + #define RMDEF static +#endif #ifndef RAYMATH_H #define RAYMATH_H @@ -39,14 +62,25 @@ #define PI 3.14159265358979323846 #endif -#define DEG2RAD (PI / 180.0f) -#define RAD2DEG (180.0f / PI) +#ifndef DEG2RAD + #define DEG2RAD (PI / 180.0f) +#endif + +#ifndef RAD2DEG + #define RAD2DEG (180.0f / PI) +#endif //---------------------------------------------------------------------------------- // Types and Structures Definition //---------------------------------------------------------------------------------- #ifdef RAYMATH_STANDALONE + // Vector2 type + typedef struct Vector2 { + float x; + float y; + } Vector2; + // Vector3 type typedef struct Vector3 { float x; @@ -71,70 +105,958 @@ typedef struct Quaternion { float w; } Quaternion; +#ifdef RAYMATH_DEFINE +#include // Used only on PrintMatrix() +#include // Standard math libary: sin(), cos(), tan()... +#include // Used for abs() -#ifdef __cplusplus -extern "C" { // Prevents name mangling of functions -#endif +//---------------------------------------------------------------------------------- +// Module Functions Definition - Vector3 math +//---------------------------------------------------------------------------------- -//------------------------------------------------------------------------------------ -// Functions Declaration to work with Vector3 -//------------------------------------------------------------------------------------ -float *VectorToFloat(Vector3 vec); // Converts Vector3 to float array -Vector3 VectorAdd(Vector3 v1, Vector3 v2); // Add two vectors -Vector3 VectorSubtract(Vector3 v1, Vector3 v2); // Substract two vectors -Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2); // Calculate two vectors cross product -Vector3 VectorPerpendicular(Vector3 v); // Calculate one vector perpendicular vector -float VectorDotProduct(Vector3 v1, Vector3 v2); // Calculate two vectors dot product -float VectorLength(const Vector3 v); // Calculate vector lenght -void VectorScale(Vector3 *v, float scale); // Scale provided vector -void VectorNegate(Vector3 *v); // Negate provided vector (invert direction) -void VectorNormalize(Vector3 *v); // Normalize provided vector -float VectorDistance(Vector3 v1, Vector3 v2); // Calculate distance between two points -Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount); // Calculate linear interpolation between two vectors -Vector3 VectorReflect(Vector3 vector, Vector3 normal); // Calculate reflected vector to normal -void VectorTransform(Vector3 *v, Matrix mat); // Transforms a Vector3 by a given Matrix -Vector3 VectorZero(void); // Return a Vector3 init to zero +// Converts Vector3 to float array +RMDEF float *VectorToFloat(Vector3 vec) +{ + static float buffer[3]; -//------------------------------------------------------------------------------------ -// Functions Declaration to work with Matrix -//------------------------------------------------------------------------------------ -float *MatrixToFloat(Matrix mat); // Converts Matrix to float array -float MatrixDeterminant(Matrix mat); // Compute matrix determinant -float MatrixTrace(Matrix mat); // Returns the trace of the matrix (sum of the values along the diagonal) -void MatrixTranspose(Matrix *mat); // Transposes provided matrix -void MatrixInvert(Matrix *mat); // Invert provided matrix -void MatrixNormalize(Matrix *mat); // Normalize provided matrix -Matrix MatrixIdentity(void); // Returns identity matrix -Matrix MatrixAdd(Matrix left, Matrix right); // Add two matrices -Matrix MatrixSubstract(Matrix left, Matrix right); // Substract two matrices (left - right) -Matrix MatrixTranslate(float x, float y, float z); // Returns translation matrix -Matrix MatrixRotate(float angle, Vector3 axis); // Returns rotation matrix for an angle around an specified axis (angle in radians) -Matrix MatrixRotateX(float angle); // Returns x-rotation matrix (angle in radians) -Matrix MatrixRotateY(float angle); // Returns y-rotation matrix (angle in radians) -Matrix MatrixRotateZ(float angle); // Returns z-rotation matrix (angle in radians) -Matrix MatrixScale(float x, float y, float z); // Returns scaling matrix -Matrix MatrixMultiply(Matrix left, Matrix right); // Returns two matrix multiplication -Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far); // Returns perspective projection matrix -Matrix MatrixPerspective(double fovy, double aspect, double near, double far); // Returns perspective projection matrix -Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far); // Returns orthographic projection matrix -Matrix MatrixLookAt(Vector3 position, Vector3 target, Vector3 up); // Returns camera look-at matrix (view matrix) -void PrintMatrix(Matrix m); // Print matrix utility + buffer[0] = vec.x; + buffer[1] = vec.y; + buffer[2] = vec.z; -//------------------------------------------------------------------------------------ -// Functions Declaration to work with Quaternions -//------------------------------------------------------------------------------------ -float QuaternionLength(Quaternion quat); // Compute the length of a quaternion -void QuaternionNormalize(Quaternion *q); // Normalize provided quaternion -Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2); // Calculate two quaternion multiplication -Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float slerp); // Calculates spherical linear interpolation between two quaternions -Quaternion QuaternionFromMatrix(Matrix matrix); // Returns a quaternion for a given rotation matrix -Matrix QuaternionToMatrix(Quaternion q); // Returns a matrix for a given quaternion -Quaternion QuaternionFromAxisAngle(float angle, Vector3 axis); // Returns rotation quaternion for an angle and axis -void QuaternionToAxisAngle(Quaternion q, float *outAngle, Vector3 *outAxis); // Returns the rotation angle and axis for a given quaternion -void QuaternionTransform(Quaternion *q, Matrix mat); // Transform a quaternion given a transformation matrix - -#ifdef __cplusplus + return buffer; } -#endif +// Add two vectors +RMDEF Vector3 VectorAdd(Vector3 v1, Vector3 v2) +{ + Vector3 result; + + result.x = v1.x + v2.x; + result.y = v1.y + v2.y; + result.z = v1.z + v2.z; + + return result; +} + +// Substract two vectors +RMDEF Vector3 VectorSubtract(Vector3 v1, Vector3 v2) +{ + Vector3 result; + + result.x = v1.x - v2.x; + result.y = v1.y - v2.y; + result.z = v1.z - v2.z; + + return result; +} + +// Calculate two vectors cross product +RMDEF Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2) +{ + Vector3 result; + + result.x = v1.y*v2.z - v1.z*v2.y; + result.y = v1.z*v2.x - v1.x*v2.z; + result.z = v1.x*v2.y - v1.y*v2.x; + + return result; +} + +// Calculate one vector perpendicular vector +RMDEF Vector3 VectorPerpendicular(Vector3 v) +{ + Vector3 result; + + float min = fabs(v.x); + Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; + + if (fabs(v.y) < min) + { + min = fabs(v.y); + cardinalAxis = (Vector3){0.0f, 1.0f, 0.0f}; + } + + if(fabs(v.z) < min) + { + cardinalAxis = (Vector3){0.0f, 0.0f, 1.0f}; + } + + result = VectorCrossProduct(v, cardinalAxis); + + return result; +} + +// Calculate two vectors dot product +RMDEF float VectorDotProduct(Vector3 v1, Vector3 v2) +{ + float result; + + result = v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; + + return result; +} + +// Calculate vector lenght +RMDEF float VectorLength(const Vector3 v) +{ + float length; + + length = sqrt(v.x*v.x + v.y*v.y + v.z*v.z); + + return length; +} + +// Scale provided vector +RMDEF void VectorScale(Vector3 *v, float scale) +{ + v->x *= scale; + v->y *= scale; + v->z *= scale; +} + +// Negate provided vector (invert direction) +RMDEF void VectorNegate(Vector3 *v) +{ + v->x = -v->x; + v->y = -v->y; + v->z = -v->z; +} + +// Normalize provided vector +RMDEF void VectorNormalize(Vector3 *v) +{ + float length, ilength; + + length = VectorLength(*v); + + if (length == 0) length = 1; + + ilength = 1.0/length; + + v->x *= ilength; + v->y *= ilength; + v->z *= ilength; +} + +// Calculate distance between two points +RMDEF float VectorDistance(Vector3 v1, Vector3 v2) +{ + float result; + + float dx = v2.x - v1.x; + float dy = v2.y - v1.y; + float dz = v2.z - v1.z; + + result = sqrt(dx*dx + dy*dy + dz*dz); + + return result; +} + +// Calculate linear interpolation between two vectors +RMDEF Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount) +{ + Vector3 result; + + result.x = v1.x + amount * (v2.x - v1.x); + result.y = v1.y + amount * (v2.y - v1.y); + result.z = v1.z + amount * (v2.z - v1.z); + + return result; +} + +// Calculate reflected vector to normal +RMDEF Vector3 VectorReflect(Vector3 vector, Vector3 normal) +{ + // I is the original vector + // N is the normal of the incident plane + // R = I - (2 * N * ( DotProduct[ I,N] )) + + Vector3 result; + + float dotProduct = VectorDotProduct(vector, normal); + + result.x = vector.x - (2.0 * normal.x) * dotProduct; + result.y = vector.y - (2.0 * normal.y) * dotProduct; + result.z = vector.z - (2.0 * normal.z) * dotProduct; + + return result; +} + +// Transforms a Vector3 with a given Matrix +RMDEF void VectorTransform(Vector3 *v, Matrix mat) +{ + float x = v->x; + float y = v->y; + float z = v->z; + + //MatrixTranspose(&mat); + + v->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; + v->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; + v->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; +}; + +// Return a Vector3 init to zero +RMDEF Vector3 VectorZero(void) +{ + Vector3 zero = { 0.0f, 0.0f, 0.0f }; + + return zero; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Matrix math +//---------------------------------------------------------------------------------- + +// Converts Matrix to float array +// NOTE: Returned vector is a transposed version of the Matrix struct, +// it should be this way because, despite raymath use OpenGL column-major convention, +// Matrix struct memory alignment and variables naming are not coherent +RMDEF float *MatrixToFloat(Matrix mat) +{ + static float buffer[16]; + + buffer[0] = mat.m0; + buffer[1] = mat.m4; + buffer[2] = mat.m8; + buffer[3] = mat.m12; + buffer[4] = mat.m1; + buffer[5] = mat.m5; + buffer[6] = mat.m9; + buffer[7] = mat.m13; + buffer[8] = mat.m2; + buffer[9] = mat.m6; + buffer[10] = mat.m10; + buffer[11] = mat.m14; + buffer[12] = mat.m3; + buffer[13] = mat.m7; + buffer[14] = mat.m11; + buffer[15] = mat.m15; + + return buffer; +} + +// Compute matrix determinant +RMDEF float MatrixDeterminant(Matrix mat) +{ + float result; + + // 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; + + result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 + + a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 + + a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 + + a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 + + a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 + + a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33; + + return result; +} + +// Returns the trace of the matrix (sum of the values along the diagonal) +RMDEF float MatrixTrace(Matrix mat) +{ + return (mat.m0 + mat.m5 + mat.m10 + mat.m15); +} + +// Transposes provided matrix +RMDEF void MatrixTranspose(Matrix *mat) +{ + Matrix temp; + + temp.m0 = mat->m0; + temp.m1 = mat->m4; + temp.m2 = mat->m8; + temp.m3 = mat->m12; + temp.m4 = mat->m1; + temp.m5 = mat->m5; + temp.m6 = mat->m9; + temp.m7 = mat->m13; + 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 // RAYMATH_DEFINE #endif // RAYMATH_H \ No newline at end of file