From 174cd86d086f3d57d629c4750d2b87a656ada9b2 Mon Sep 17 00:00:00 2001 From: raysan5 Date: Sun, 2 Mar 2014 16:03:25 +0100 Subject: [PATCH] 3D useful maths Some useful functions to work with Vector3, Matrix and Quaternions --- src/raymath.c | 1014 +++++++++++++++++++++++++++++++++++++++++++++++++ src/raymath.h | 139 +++++++ 2 files changed, 1153 insertions(+) create mode 100644 src/raymath.c create mode 100644 src/raymath.h diff --git a/src/raymath.c b/src/raymath.c new file mode 100644 index 00000000..3546113c --- /dev/null +++ b/src/raymath.c @@ -0,0 +1,1014 @@ +/********************************************************************************************* +* +* raymath +* +* Some useful functions to work with Vector3, Matrix and Quaternions +* +* Copyright (c) 2014 Ramon Santamaria (Ray San - raysan@raysanweb.com) +* +* 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 +//---------------------------------------------------------------------------------- + +// 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 = {1.0, 0.0, 0.0}; + + if (fabs(v.y) < min) + { + min = fabs(v.y); + cardinalAxis = (Vector3){0.0, 1.0, 0.0}; + } + + if(fabs(v.z) < min) + { + cardinalAxis = (Vector3){0.0, 0.0, 1.0}; + } + + 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; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Matrix math +//---------------------------------------------------------------------------------- + +// Returns an OpenGL-ready vector (glMultMatrixf) +float *GetMatrixVector(Matrix mat) +{ + static float vector[16]; + + vector[0] = mat.m0; + vector[1] = mat.m4; + vector[2] = mat.m8; + vector[3] = mat.m12; + vector[4] = mat.m1; + vector[5] = mat.m5; + vector[6] = mat.m9; + vector[7] = mat.m13; + vector[8] = mat.m2; + vector[9] = mat.m6; + vector[10] = mat.m10; + vector[11] = mat.m14; + vector[12] = mat.m3; + vector[13] = mat.m7; + vector[14] = mat.m11; + vector[15] = mat.m15; + + return vector; +} + +// 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); + + printf("%f\n", invDet); + + 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; + + PrintMatrix(temp); + + *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() +{ + 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 +// TODO: REVIEW +Matrix MatrixTranslate(float x, float y, float z) +{ +/* + For OpenGL + 1, 0, 0, 0 + 0, 1, 0, 0 + 0, 0, 1, 0 + x, y, z, 1 + Is the correct Translation Matrix. Why? Opengl Uses column-major matrix ordering. + Which is the Transpose of the Matrix you initially presented, which is in row-major ordering. + Row major is used in most math text-books and also DirectX, so it is a common + point of confusion for those new to OpenGL. + + * matrix notation used in opengl documentation does not describe in-memory layout for OpenGL matrices + + Translation matrix should be laid out in memory like this: + { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, trabsX, transY, transZ, 1 } + + + 9.005 Are OpenGL matrices column-major or row-major? + + For programming purposes, OpenGL matrices are 16-value arrays with base vectors laid out + contiguously in memory. The translation components occupy the 13th, 14th, and 15th elements + of the 16-element matrix, where indices are numbered from 1 to 16 as described in section + 2.11.2 of the OpenGL 2.1 Specification. + + Column-major versus row-major is purely a notational convention. Note that post-multiplying + with column-major matrices produces the same result as pre-multiplying with row-major matrices. + The OpenGL Specification and the OpenGL Reference Manual both use column-major notation. + You can use any notation, as long as it's clearly stated. + + Sadly, the use of column-major format in the spec and blue book has resulted in endless confusion + in the OpenGL programming community. Column-major notation suggests that matrices + are not laid out in memory as a programmer would expect. +*/ + + Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 }; + + return result; +} + +// Returns rotation matrix +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 +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 +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 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) / rl; + result.m1 = 0; + result.m2 = 0; + result.m3 = 0; + result.m4 = 0; + result.m5 = (near*2) / 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; + result.m12 = 0; + result.m13 = 0; + result.m14 = -(far*near*2) / fn; + result.m15 = 0; + + return result; +} + +// Returns perspective projection matrix +Matrix MatrixPerspective(double fovy, double aspect, double near, double far) +{ + double top = near*tan(fovy*PI / 360.0); + 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) >= 1.0) result = q1; + else + { + float halfTheta = acos(cosHalfTheta); + float sinHalfTheta = sqrt(1.0 - cosHalfTheta*cosHalfTheta); + + if (abs(sinHalfTheta) < 0.001) + { + result.x = (q1.x*0.5 + q2.x*0.5); + result.y = (q1.y*0.5 + q2.y*0.5); + result.z = (q1.z*0.5 + q2.z*0.5); + result.w = (q1.w*0.5 + q2.w*0.5); + } + 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; +} \ No newline at end of file diff --git a/src/raymath.h b/src/raymath.h new file mode 100644 index 00000000..49cceafb --- /dev/null +++ b/src/raymath.h @@ -0,0 +1,139 @@ +/********************************************************************************************* +* +* raymath +* +* Some useful functions to work with Vector3, Matrix and Quaternions +* +* Copyright (c) 2014 Ramon Santamaria (Ray San - raysan@raysanweb.com) +* +* 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. +* +**********************************************************************************************/ + +#ifndef RAYMATH_H +#define RAYMATH_H + +//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line + +#ifndef RAYMATH_STANDALONE + #include "raylib.h" // Required for typedef: Vector3 +#endif + +//---------------------------------------------------------------------------------- +// Defines and Macros +//---------------------------------------------------------------------------------- +#ifndef PI + #define PI 3.14159265358979323846 +#endif + +#define DEG2RAD (PI / 180.0) +#define RAD2DEG (180.0 / PI) + +//---------------------------------------------------------------------------------- +// Types and Structures Definition +//---------------------------------------------------------------------------------- + +#ifdef RAYMATH_STANDALONE + // Vector3 type + typedef struct Vector3 { + float x; + float y; + float z; + } Vector3; +#endif + +// Matrix type (OpenGL style 4x4 - right handed) +typedef struct Matrix { + float m0, m4, m8, m12; + float m1, m5, m9, m13; + float m2, m6, m10, m14; + float m3, m7, m11, m15; +} Matrix; + +// Quaternion type +typedef struct Quaternion { + float x; + float y; + float z; + float w; +} Quaternion; + + +#ifdef __cplusplus +extern "C" { // Prevents name mangling of functions +#endif + +//------------------------------------------------------------------------------------ +// Functions Declaration to work with Vector3 +//------------------------------------------------------------------------------------ +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 + +//------------------------------------------------------------------------------------ +// Functions Declaration to work with Matrix +//------------------------------------------------------------------------------------ +float *GetMatrixVector(Matrix mat); // Returns an OpenGL-ready vector (glMultMatrixf) +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(); // 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 angleX, float angleY, float angleZ); // Returns rotation matrix +Matrix MatrixRotateAroundAxis(Vector3 axis, float angle); // Returns rotation matrix for an angle around an specified axis +Matrix MatrixRotateAroundAxis2(Vector3 axis, float angle); // Returns rotation matrix for an angle around an specified axis (test another implemntation) +Matrix MatrixFromQuaternion(Quaternion q); // Returns rotation matrix for a given quaternion +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 + +//------------------------------------------------------------------------------------ +// Functions Declaration to work with Quaternions +//------------------------------------------------------------------------------------ +float QuaternionLength(Quaternion quat); // Calculates 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 from a given rotation matrix +Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle); // Returns rotation quaternion for an angle around an axis +Matrix QuaternionToMatrix(Quaternion q); // Calculates the matrix from the given quaternion +void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle); // Returns the axis and the angle for a given quaternion + +#ifdef __cplusplus +} +#endif + +#endif // RAYMATH_H \ No newline at end of file