diff --git a/examples/Makefile b/examples/Makefile index 6824b5d99..b5590be63 100644 --- a/examples/Makefile +++ b/examples/Makefile @@ -267,7 +267,8 @@ ifeq ($(PLATFORM),PLATFORM_DESKTOP) ifeq ($(PLATFORM_OS),LINUX) # Reset everything. # Precedence: immediately local, installed version, raysan5 provided libs -I$(RAYLIB_H_INSTALL_PATH) -I$(RAYLIB_PATH)/release/include - INCLUDE_PATHS = -I$(RAYLIB_H_INSTALL_PATH) -isystem. -isystem$(RAYLIB_PATH)/src -isystem$(RAYLIB_PATH)/release/include -isystem$(RAYLIB_PATH)/src/external + #INCLUDE_PATHS = -I$(RAYLIB_H_INSTALL_PATH) -isystem. -isystem$(RAYLIB_PATH)/src -isystem$(RAYLIB_PATH)/release/include -isystem$(RAYLIB_PATH)/src/external + INCLUDE_PATHS = -I$(RAYLIB_H_INSTALL_PATH) -I. -I$(RAYLIB_PATH)/src -I$(RAYLIB_PATH)/release/include -I$(RAYLIB_PATH)/src/external endif endif @@ -290,7 +291,7 @@ ifeq ($(PLATFORM),PLATFORM_DESKTOP) ifeq ($(PLATFORM_OS),LINUX) # Reset everything. # Precedence: immediately local, installed version, raysan5 provided libs - LDFLAGS = -L. -L$(RAYLIB_INSTALL_PATH) -L$(RAYLIB_RELEASE_PATH) + LDFLAGS = -L. -L$(RAYLIB_INSTALL_PATH) -L$(RAYLIB_RELEASE_PATH) -L$(RAYLIB_PATH) endif endif @@ -378,7 +379,8 @@ CORE = \ core/core_scissor_test \ core/core_storage_values \ core/core_vr_simulator \ - core/core_loading_thread + core/core_loading_thread \ + core/core_quat_conversion SHAPES = \ shapes/shapes_basic_shapes \ diff --git a/examples/core/core_quat_conversion.c b/examples/core/core_quat_conversion.c new file mode 100644 index 000000000..5f2fc36e5 --- /dev/null +++ b/examples/core/core_quat_conversion.c @@ -0,0 +1,131 @@ +/******************************************************************************************* +* +* raylib [core] example - quat conversions +* +* Welcome to raylib! +* +* generally you should really stick to eulers OR quats... +* This tests that various conversions are equivilant. +* +* You can find all basic examples on [C:\raylib\raylib\examples] directory and +* raylib official webpage: [www.raylib.com] +* +* Enjoy using raylib. :) +* +* This example has been created using raylib 1.0 (www.raylib.com) +* raylib is licensed under an unmodified zlib/libpng license (View raylib.h for details) +* +* Copyright (c) 2013-2020 Ramon Santamaria (@raysan5) +* +********************************************************************************************/ + +#include "raylib.h" +#include "raymath.h" + +#ifndef PI2 + #define PI2 PI*2 +#endif + +int main(void) +{ + // Initialization + //-------------------------------------------------------------------------------------- + const int screenWidth = 800; + const int screenHeight = 450; + + InitWindow(screenWidth, screenHeight, "raylib [core] example - quat conversions"); + + Camera3D camera = { 0 }; + camera.position = (Vector3){ 0.0f, 10.0f, 10.0f }; // Camera position + camera.target = (Vector3){ 0.0f, 0.0f, 0.0f }; // Camera looking at point + camera.up = (Vector3){ 0.0f, 1.0f, 0.0f }; // Camera up vector (rotation towards target) + camera.fovy = 45.0f; // Camera field-of-view Y + camera.type = CAMERA_PERSPECTIVE; // Camera mode type + + Mesh msh = GenMeshCylinder(.2, 1, 32); + Model mod = LoadModelFromMesh(msh); + + SetTargetFPS(60); // Set our game to run at 60 frames-per-second + //-------------------------------------------------------------------------------------- + + Quaternion q1; + Matrix m1,m2,m3,m4; + Vector3 v1,v2; + + // Main game loop + while (!WindowShouldClose()) // Detect window close button or ESC key + { + // Update + if (!IsKeyDown(KEY_SPACE)) { + v1.x += 0.01; + v1.y += 0.03; + v1.z += 0.05; + } + + if (v1.x > PI2) v1.x-=PI2; + if (v1.y > PI2) v1.y-=PI2; + if (v1.z > PI2) v1.z-=PI2; + + q1 = QuaternionFromEuler(v1.x, v1.y, v1.z); + m1 = MatrixRotateZYX(v1); + m2 = QuaternionToMatrix(q1); + + q1 = QuaternionFromMatrix(m1); + m3 = QuaternionToMatrix(q1); + + v2 = QuaternionToEuler(q1); + v2.x*=DEG2RAD; v2.y*=DEG2RAD; v2.z*=DEG2RAD; + + m4 = MatrixRotateZYX(v2); + + // Draw + //---------------------------------------------------------------------------------- + BeginDrawing(); + + ClearBackground(RAYWHITE); + BeginMode3D(camera); + + mod.transform = m1; + DrawModel(mod, (Vector3){-1,0,0},1.0,RED); + mod.transform = m2; + DrawModel(mod, (Vector3){1,0,0},1.0,RED); + mod.transform = m3; + DrawModel(mod, (Vector3){0,0,0},1.0,RED); + mod.transform = m4; + DrawModel(mod, (Vector3){0,0,-1},1.0,RED); + + + DrawGrid(10, 1.0f); + + EndMode3D(); + + if (v2.x<0) v2.x+=PI2; + if (v2.y<0) v2.y+=PI2; + if (v2.z<0) v2.z+=PI2; + + Color cx,cy,cz; + cx=cy=cz=BLACK; + if (v1.x == v2.x) cx = GREEN; + if (v1.y == v2.y) cy = GREEN; + if (v1.z == v2.z) cz = GREEN; + + DrawText(TextFormat("%2.3f",v1.x),20,20,20,cx); + DrawText(TextFormat("%2.3f",v1.y),20,40,20,cy); + DrawText(TextFormat("%2.3f",v1.z),20,60,20,cz); + + + DrawText(TextFormat("%2.3f",v2.x),200,20,20,cx); + DrawText(TextFormat("%2.3f",v2.y),200,40,20,cy); + DrawText(TextFormat("%2.3f",v2.z),200,60,20,cz); + + EndDrawing(); + //---------------------------------------------------------------------------------- + } + + // De-Initialization + //-------------------------------------------------------------------------------------- + CloseWindow(); // Close window and OpenGL context + //-------------------------------------------------------------------------------------- + + return 0; +} diff --git a/examples/core/raymath.h b/examples/core/raymath.h deleted file mode 100644 index 398aef4ab..000000000 --- a/examples/core/raymath.h +++ /dev/null @@ -1,1466 +0,0 @@ -/********************************************************************************************** -* -* raymath v1.2 - Math functions to work with Vector3, Matrix and Quaternions -* -* CONFIGURATION: -* -* #define RAYMATH_IMPLEMENTATION -* Generates the implementation of the library into the included file. -* If not defined, the library is in header only mode and can be included in other headers -* or source files without problems. But only ONE file should hold the implementation. -* -* #define RAYMATH_HEADER_ONLY -* Define static inline functions code, so #include header suffices for use. -* This may use up lots of memory. -* -* #define RAYMATH_STANDALONE -* Avoid raylib.h header inclusion in this file. -* Vector3 and Matrix data types are defined internally in raymath module. -* -* -* LICENSE: zlib/libpng -* -* Copyright (c) 2015-2020 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. -* -**********************************************************************************************/ - -#ifndef RAYMATH_H -#define RAYMATH_H - -//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line -//#define RAYMATH_HEADER_ONLY // NOTE: To compile functions as static inline, uncomment this line - -#ifndef RAYMATH_STANDALONE - #include "raylib.h" // Required for structs: Vector3, Matrix -#endif - -#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_HEADER_ONLY) - #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_HEADER_ONLY is contradictory" -#endif - -#if defined(RAYMATH_IMPLEMENTATION) - #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED) - #define RMDEF __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll). - #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED) - #define RMDEF __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll) - #else - #define RMDEF extern inline // Provide external definition - #endif -#elif defined(RAYMATH_HEADER_ONLY) - #define RMDEF static inline // Functions may be inlined, no external out-of-line definition -#else - #if defined(__TINYC__) - #define RMDEF static inline // plain inline not supported by tinycc (See issue #435) - #else - #define RMDEF inline // Functions may be inlined or external definition used - #endif -#endif - -//---------------------------------------------------------------------------------- -// Defines and Macros -//---------------------------------------------------------------------------------- -#ifndef PI - #define PI 3.14159265358979323846 -#endif - -#ifndef DEG2RAD - #define DEG2RAD (PI/180.0f) -#endif - -#ifndef RAD2DEG - #define RAD2DEG (180.0f/PI) -#endif - -// Return float vector for Matrix -#ifndef MatrixToFloat - #define MatrixToFloat(mat) (MatrixToFloatV(mat).v) -#endif - -// Return float vector for Vector3 -#ifndef Vector3ToFloat - #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v) -#endif - -//---------------------------------------------------------------------------------- -// Types and Structures Definition -//---------------------------------------------------------------------------------- - -#if defined(RAYMATH_STANDALONE) - // Vector2 type - typedef struct Vector2 { - float x; - float y; - } Vector2; - - // Vector3 type - typedef struct Vector3 { - float x; - float y; - float z; - } Vector3; - - // Quaternion type - typedef struct Quaternion { - float x; - float y; - float z; - float w; - } Quaternion; - - // Matrix type (OpenGL style 4x4 - right handed, column major) - typedef struct Matrix { - float m0, m4, m8, m12; - float m1, m5, m9, m13; - float m2, m6, m10, m14; - float m3, m7, m11, m15; - } Matrix; -#endif - -// NOTE: Helper types to be used instead of array return types for *ToFloat functions -typedef struct float3 { float v[3]; } float3; -typedef struct float16 { float v[16]; } float16; - -#include // Required for: sinf(), cosf(), sqrtf(), tan(), fabs() - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Utils math -//---------------------------------------------------------------------------------- - -// Clamp float value -RMDEF float Clamp(float value, float min, float max) -{ - const float res = value < min ? min : value; - return res > max ? max : res; -} - -// Calculate linear interpolation between two floats -RMDEF float Lerp(float start, float end, float amount) -{ - return start + amount*(end - start); -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector2 math -//---------------------------------------------------------------------------------- - -// Vector with components value 0.0f -RMDEF Vector2 Vector2Zero(void) -{ - Vector2 result = { 0.0f, 0.0f }; - return result; -} - -// Vector with components value 1.0f -RMDEF Vector2 Vector2One(void) -{ - Vector2 result = { 1.0f, 1.0f }; - return result; -} - -// Add two vectors (v1 + v2) -RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x + v2.x, v1.y + v2.y }; - return result; -} - -// Add vector and float value -RMDEF Vector2 Vector2AddValue(Vector2 v, float add) -{ - Vector2 result = { v.x + add, v.y + add }; - return result; -} - -// Subtract two vectors (v1 - v2) -RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x - v2.x, v1.y - v2.y }; - return result; -} - -// Subtract vector by float value -RMDEF Vector2 Vector2SubtractValue(Vector2 v, float sub) -{ - Vector2 result = { v.x - sub, v.y - sub }; - return result; -} - -// Calculate vector length -RMDEF float Vector2Length(Vector2 v) -{ - float result = sqrtf((v.x*v.x) + (v.y*v.y)); - return result; -} - -// Calculate two vectors dot product -RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2) -{ - float result = (v1.x*v2.x + v1.y*v2.y); - return result; -} - -// Calculate distance between two vectors -RMDEF float Vector2Distance(Vector2 v1, Vector2 v2) -{ - float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); - return result; -} - -// Calculate angle from two vectors in X-axis -RMDEF float Vector2Angle(Vector2 v1, Vector2 v2) -{ - float result = atan2f(v2.y - v1.y, v2.x - v1.x)*(180.0f/PI); - if (result < 0) result += 360.0f; - return result; -} - -// Scale vector (multiply by value) -RMDEF Vector2 Vector2Scale(Vector2 v, float scale) -{ - Vector2 result = { v.x*scale, v.y*scale }; - return result; -} - -// Multiply vector by vector -RMDEF Vector2 Vector2Multiply(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x*v2.x, v1.y*v2.y }; - return result; -} - -// Negate vector -RMDEF Vector2 Vector2Negate(Vector2 v) -{ - Vector2 result = { -v.x, -v.y }; - return result; -} - -// Divide vector by vector -RMDEF Vector2 Vector2Divide(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x/v2.x, v1.y/v2.y }; - return result; -} - -// Normalize provided vector -RMDEF Vector2 Vector2Normalize(Vector2 v) -{ - Vector2 result = Vector2Scale(v, 1/Vector2Length(v)); - return result; -} - -// Calculate linear interpolation between two vectors -RMDEF Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount) -{ - Vector2 result = { 0 }; - - result.x = v1.x + amount*(v2.x - v1.x); - result.y = v1.y + amount*(v2.y - v1.y); - - return result; -} - -// Rotate Vector by float in Degrees. -RMDEF Vector2 Vector2Rotate(Vector2 v, float degs) -{ - float rads = degs*DEG2RAD; - Vector2 result = {v.x * cosf(rads) - v.y * sinf(rads) , v.x * sinf(rads) + v.y * cosf(rads) }; - return result; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector3 math -//---------------------------------------------------------------------------------- - -// Vector with components value 0.0f -RMDEF Vector3 Vector3Zero(void) -{ - Vector3 result = { 0.0f, 0.0f, 0.0f }; - return result; -} - -// Vector with components value 1.0f -RMDEF Vector3 Vector3One(void) -{ - Vector3 result = { 1.0f, 1.0f, 1.0f }; - return result; -} - -// Add two vectors -RMDEF Vector3 Vector3Add(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z }; - return result; -} - -// Add vector and float value -RMDEF Vector3 Vector3AddValue(Vector3 v, float add) -{ - Vector3 result = { v.x + add, v.y + add, v.z + add }; - return result; -} - -// Subtract two vectors -RMDEF Vector3 Vector3Subtract(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z }; - return result; -} - -// Subtract vector by float value -RMDEF Vector3 Vector3SubtractValue(Vector3 v, float sub) -{ - Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; - return result; -} - -// Multiply vector by scalar -RMDEF Vector3 Vector3Scale(Vector3 v, float scalar) -{ - Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar }; - return result; -} - -// Multiply vector by vector -RMDEF Vector3 Vector3Multiply(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z }; - return result; -} - -// Calculate two vectors cross product -RMDEF Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x }; - return result; -} - -// Calculate one vector perpendicular vector -RMDEF Vector3 Vector3Perpendicular(Vector3 v) -{ - Vector3 result = { 0 }; - - float min = (float) fabs(v.x); - Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; - - if (fabs(v.y) < min) - { - min = (float) fabs(v.y); - Vector3 tmp = {0.0f, 1.0f, 0.0f}; - cardinalAxis = tmp; - } - - if (fabs(v.z) < min) - { - Vector3 tmp = {0.0f, 0.0f, 1.0f}; - cardinalAxis = tmp; - } - - result = Vector3CrossProduct(v, cardinalAxis); - - return result; -} - -// Calculate vector length -RMDEF float Vector3Length(const Vector3 v) -{ - float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); - return result; -} - -// Calculate two vectors dot product -RMDEF float Vector3DotProduct(Vector3 v1, Vector3 v2) -{ - float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); - return result; -} - -// Calculate distance between two vectors -RMDEF float Vector3Distance(Vector3 v1, Vector3 v2) -{ - float dx = v2.x - v1.x; - float dy = v2.y - v1.y; - float dz = v2.z - v1.z; - float result = sqrtf(dx*dx + dy*dy + dz*dz); - return result; -} - -// Negate provided vector (invert direction) -RMDEF Vector3 Vector3Negate(Vector3 v) -{ - Vector3 result = { -v.x, -v.y, -v.z }; - return result; -} - -// Divide vector by vector -RMDEF Vector3 Vector3Divide(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z }; - return result; -} - -// Normalize provided vector -RMDEF Vector3 Vector3Normalize(Vector3 v) -{ - Vector3 result = v; - - float length, ilength; - length = Vector3Length(v); - if (length == 0.0f) length = 1.0f; - ilength = 1.0f/length; - - result.x *= ilength; - result.y *= ilength; - result.z *= ilength; - - return result; -} - -// Orthonormalize provided vectors -// Makes vectors normalized and orthogonal to each other -// Gram-Schmidt function implementation -RMDEF void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2) -{ - *v1 = Vector3Normalize(*v1); - Vector3 vn = Vector3CrossProduct(*v1, *v2); - vn = Vector3Normalize(vn); - *v2 = Vector3CrossProduct(vn, *v1); -} - -// Transforms a Vector3 by a given Matrix -RMDEF Vector3 Vector3Transform(Vector3 v, Matrix mat) -{ - Vector3 result = { 0 }; - float x = v.x; - float y = v.y; - float z = v.z; - - result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; - result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; - result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; - - return result; -} - -// Transform a vector by quaternion rotation -RMDEF Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q) -{ - Vector3 result = { 0 }; - - result.x = v.x*(q.x*q.x + q.w*q.w - q.y*q.y - q.z*q.z) + v.y*(2*q.x*q.y - 2*q.w*q.z) + v.z*(2*q.x*q.z + 2*q.w*q.y); - result.y = v.x*(2*q.w*q.z + 2*q.x*q.y) + v.y*(q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z) + v.z*(-2*q.w*q.x + 2*q.y*q.z); - result.z = v.x*(-2*q.w*q.y + 2*q.x*q.z) + v.y*(2*q.w*q.x + 2*q.y*q.z)+ v.z*(q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z); - - return result; -} - -// Calculate linear interpolation between two vectors -RMDEF Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount) -{ - Vector3 result = { 0 }; - - 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 Vector3Reflect(Vector3 v, Vector3 normal) -{ - // I is the original vector - // N is the normal of the incident plane - // R = I - (2*N*( DotProduct[ I,N] )) - - Vector3 result = { 0 }; - - float dotProduct = Vector3DotProduct(v, normal); - - result.x = v.x - (2.0f*normal.x)*dotProduct; - result.y = v.y - (2.0f*normal.y)*dotProduct; - result.z = v.z - (2.0f*normal.z)*dotProduct; - - return result; -} - -// Return min value for each pair of components -RMDEF Vector3 Vector3Min(Vector3 v1, Vector3 v2) -{ - Vector3 result = { 0 }; - - result.x = fminf(v1.x, v2.x); - result.y = fminf(v1.y, v2.y); - result.z = fminf(v1.z, v2.z); - - return result; -} - -// Return max value for each pair of components -RMDEF Vector3 Vector3Max(Vector3 v1, Vector3 v2) -{ - Vector3 result = { 0 }; - - result.x = fmaxf(v1.x, v2.x); - result.y = fmaxf(v1.y, v2.y); - result.z = fmaxf(v1.z, v2.z); - - return result; -} - -// Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c) -// NOTE: Assumes P is on the plane of the triangle -RMDEF Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c) -{ - //Vector v0 = b - a, v1 = c - a, v2 = p - a; - - Vector3 v0 = Vector3Subtract(b, a); - Vector3 v1 = Vector3Subtract(c, a); - Vector3 v2 = Vector3Subtract(p, a); - float d00 = Vector3DotProduct(v0, v0); - float d01 = Vector3DotProduct(v0, v1); - float d11 = Vector3DotProduct(v1, v1); - float d20 = Vector3DotProduct(v2, v0); - float d21 = Vector3DotProduct(v2, v1); - - float denom = d00*d11 - d01*d01; - - Vector3 result = { 0 }; - - result.y = (d11*d20 - d01*d21)/denom; - result.z = (d00*d21 - d01*d20)/denom; - result.x = 1.0f - (result.z + result.y); - - return result; -} - -// Returns Vector3 as float array -RMDEF float3 Vector3ToFloatV(Vector3 v) -{ - float3 buffer = { 0 }; - - buffer.v[0] = v.x; - buffer.v[1] = v.y; - buffer.v[2] = v.z; - - return buffer; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Matrix math -//---------------------------------------------------------------------------------- - -// Compute matrix determinant -RMDEF float MatrixDeterminant(Matrix mat) -{ - // 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 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) -{ - float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15); - return result; -} - -// Transposes provided matrix -RMDEF Matrix MatrixTranspose(Matrix mat) -{ - Matrix result = { 0 }; - - result.m0 = mat.m0; - result.m1 = mat.m4; - result.m2 = mat.m8; - result.m3 = mat.m12; - result.m4 = mat.m1; - result.m5 = mat.m5; - result.m6 = mat.m9; - result.m7 = mat.m13; - result.m8 = mat.m2; - result.m9 = mat.m6; - result.m10 = mat.m10; - result.m11 = mat.m14; - result.m12 = mat.m3; - result.m13 = mat.m7; - result.m14 = mat.m11; - result.m15 = mat.m15; - - return result; -} - -// Invert provided matrix -RMDEF Matrix MatrixInvert(Matrix mat) -{ - Matrix result = { 0 }; - - // 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 = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); - - result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet; - result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet; - result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet; - result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet; - result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet; - result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet; - result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet; - result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet; - result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet; - result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet; - result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet; - result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet; - result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet; - result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet; - result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet; - result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet; - - return result; -} - -// Normalize provided matrix -RMDEF Matrix MatrixNormalize(Matrix mat) -{ - Matrix result = { 0 }; - - float det = MatrixDeterminant(mat); - - result.m0 = mat.m0/det; - result.m1 = mat.m1/det; - result.m2 = mat.m2/det; - result.m3 = mat.m3/det; - result.m4 = mat.m4/det; - result.m5 = mat.m5/det; - result.m6 = mat.m6/det; - result.m7 = mat.m7/det; - result.m8 = mat.m8/det; - result.m9 = mat.m9/det; - result.m10 = mat.m10/det; - result.m11 = mat.m11/det; - result.m12 = mat.m12/det; - result.m13 = mat.m13/det; - result.m14 = mat.m14/det; - result.m15 = mat.m15/det; - - return result; -} - -// Returns identity matrix -RMDEF Matrix MatrixIdentity(void) -{ - Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, - 0.0f, 1.0f, 0.0f, 0.0f, - 0.0f, 0.0f, 1.0f, 0.0f, - 0.0f, 0.0f, 0.0f, 1.0f }; - - 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; -} - -// Subtract two matrices (left - right) -RMDEF Matrix MatrixSubtract(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 = { 1.0f, 0.0f, 0.0f, x, - 0.0f, 1.0f, 0.0f, y, - 0.0f, 0.0f, 1.0f, z, - 0.0f, 0.0f, 0.0f, 1.0f }; - - return result; -} - -// Create rotation matrix from axis and angle -// NOTE: Angle should be provided in radians -RMDEF Matrix MatrixRotate(Vector3 axis, float angle) -{ - Matrix result = { 0 }; - - float x = axis.x, y = axis.y, z = axis.z; - - float length = sqrtf(x*x + y*y + z*z); - - if ((length != 1.0f) && (length != 0.0f)) - { - length = 1.0f/length; - x *= length; - y *= length; - z *= length; - } - - float sinres = sinf(angle); - float cosres = cosf(angle); - float t = 1.0f - cosres; - - result.m0 = x*x*t + cosres; - result.m1 = y*x*t + z*sinres; - result.m2 = z*x*t - y*sinres; - result.m3 = 0.0f; - - result.m4 = x*y*t - z*sinres; - result.m5 = y*y*t + cosres; - result.m6 = z*y*t + x*sinres; - result.m7 = 0.0f; - - result.m8 = x*z*t + y*sinres; - result.m9 = y*z*t - x*sinres; - result.m10 = z*z*t + cosres; - result.m11 = 0.0f; - - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; - - return result; -} - -// Returns xyz-rotation matrix (angles in radians) -RMDEF Matrix MatrixRotateXYZ(Vector3 ang) -{ - Matrix result = MatrixIdentity(); - - float cosz = cosf(-ang.z); - float sinz = sinf(-ang.z); - float cosy = cosf(-ang.y); - float siny = sinf(-ang.y); - float cosx = cosf(-ang.x); - float sinx = sinf(-ang.x); - - result.m0 = cosz * cosy; - result.m4 = (cosz * siny * sinx) - (sinz * cosx); - result.m8 = (cosz * siny * cosx) + (sinz * sinx); - - result.m1 = sinz * cosy; - result.m5 = (sinz * siny * sinx) + (cosz * cosx); - result.m9 = (sinz * siny * cosx) - (cosz * sinx); - - result.m2 = -siny; - result.m6 = cosy * sinx; - result.m10= cosy * cosx; - - return result; -} - -// Returns x-rotation matrix (angle in radians) -RMDEF Matrix MatrixRotateX(float angle) -{ - Matrix result = MatrixIdentity(); - - float cosres = cosf(angle); - float sinres = sinf(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 = cosf(angle); - float sinres = sinf(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, 0.0f, 0.0f, 0.0f, - 0.0f, y, 0.0f, 0.0f, - 0.0f, 0.0f, z, 0.0f, - 0.0f, 0.0f, 0.0f, 1.0f }; - - return result; -} - -// Returns two matrix multiplication -// NOTE: When multiplying matrices... the order matters! -RMDEF Matrix MatrixMultiply(Matrix left, Matrix right) -{ - Matrix result = { 0 }; - - result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12; - result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13; - result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14; - result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15; - result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12; - result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13; - result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14; - result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15; - result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12; - result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13; - result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14; - result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15; - result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12; - result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13; - result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14; - result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15; - - return result; -} - -// Returns perspective projection matrix -RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far) -{ - Matrix result = { 0 }; - - float rl = (float)(right - left); - float tb = (float)(top - bottom); - float fn = (float)(far - near); - - result.m0 = ((float) near*2.0f)/rl; - result.m1 = 0.0f; - result.m2 = 0.0f; - result.m3 = 0.0f; - - result.m4 = 0.0f; - result.m5 = ((float) near*2.0f)/tb; - result.m6 = 0.0f; - result.m7 = 0.0f; - - result.m8 = ((float)right + (float)left)/rl; - result.m9 = ((float)top + (float)bottom)/tb; - result.m10 = -((float)far + (float)near)/fn; - result.m11 = -1.0f; - - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = -((float)far*(float)near*2.0f)/fn; - result.m15 = 0.0f; - - return result; -} - -// Returns perspective projection matrix -// NOTE: Angle should be provided in radians -RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far) -{ - double top = near*tan(fovy*0.5); - double right = top*aspect; - Matrix result = MatrixFrustum(-right, right, -top, top, near, far); - - return result; -} - -// Returns orthographic projection matrix -RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far) -{ - Matrix result = { 0 }; - - float rl = (float)(right - left); - float tb = (float)(top - bottom); - float fn = (float)(far - near); - - result.m0 = 2.0f/rl; - result.m1 = 0.0f; - result.m2 = 0.0f; - result.m3 = 0.0f; - result.m4 = 0.0f; - result.m5 = 2.0f/tb; - result.m6 = 0.0f; - result.m7 = 0.0f; - result.m8 = 0.0f; - result.m9 = 0.0f; - result.m10 = -2.0f/fn; - result.m11 = 0.0f; - result.m12 = -((float)left + (float)right)/rl; - result.m13 = -((float)top + (float)bottom)/tb; - result.m14 = -((float)far + (float)near)/fn; - result.m15 = 1.0f; - - return result; -} - -// Returns camera look-at matrix (view matrix) -RMDEF Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up) -{ - Matrix result = { 0 }; - - Vector3 z = Vector3Subtract(eye, target); - z = Vector3Normalize(z); - Vector3 x = Vector3CrossProduct(up, z); - x = Vector3Normalize(x); - Vector3 y = Vector3CrossProduct(z, x); - y = Vector3Normalize(y); - - result.m0 = x.x; - result.m1 = x.y; - result.m2 = x.z; - result.m3 = 0.0f; - result.m4 = y.x; - result.m5 = y.y; - result.m6 = y.z; - result.m7 = 0.0f; - result.m8 = z.x; - result.m9 = z.y; - result.m10 = z.z; - result.m11 = 0.0f; - result.m12 = eye.x; - result.m13 = eye.y; - result.m14 = eye.z; - result.m15 = 1.0f; - - result = MatrixInvert(result); - - return result; -} - -// Returns float array of matrix data -RMDEF float16 MatrixToFloatV(Matrix mat) -{ - float16 buffer = { 0 }; - - buffer.v[0] = mat.m0; - buffer.v[1] = mat.m1; - buffer.v[2] = mat.m2; - buffer.v[3] = mat.m3; - buffer.v[4] = mat.m4; - buffer.v[5] = mat.m5; - buffer.v[6] = mat.m6; - buffer.v[7] = mat.m7; - buffer.v[8] = mat.m8; - buffer.v[9] = mat.m9; - buffer.v[10] = mat.m10; - buffer.v[11] = mat.m11; - buffer.v[12] = mat.m12; - buffer.v[13] = mat.m13; - buffer.v[14] = mat.m14; - buffer.v[15] = mat.m15; - - return buffer; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Quaternion math -//---------------------------------------------------------------------------------- - -// Add two quaternions -RMDEF Quaternion QuaternionAdd(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w}; - return result; -} - -// Add quaternion and float value -RMDEF Quaternion QuaternionAddValue(Quaternion q, float add) -{ - Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add}; - return result; -} - -// Subtract two quaternions -RMDEF Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w}; - return result; -} - -// Subtract quaternion and float value -RMDEF Quaternion QuaternionSubtractValue(Quaternion q, float sub) -{ - Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub}; - return result; -} - -// Returns identity quaternion -RMDEF Quaternion QuaternionIdentity(void) -{ - Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; - return result; -} - -// Computes the length of a quaternion -RMDEF float QuaternionLength(Quaternion q) -{ - float result = (float)sqrt(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); - return result; -} - -// Normalize provided quaternion -RMDEF Quaternion QuaternionNormalize(Quaternion q) -{ - Quaternion result = { 0 }; - - float length, ilength; - length = QuaternionLength(q); - if (length == 0.0f) length = 1.0f; - ilength = 1.0f/length; - - result.x = q.x*ilength; - result.y = q.y*ilength; - result.z = q.z*ilength; - result.w = q.w*ilength; - - return result; -} - -// Invert provided quaternion -RMDEF Quaternion QuaternionInvert(Quaternion q) -{ - Quaternion result = q; - float length = QuaternionLength(q); - float lengthSq = length*length; - - if (lengthSq != 0.0) - { - float i = 1.0f/lengthSq; - - result.x *= -i; - result.y *= -i; - result.z *= -i; - result.w *= i; - } - - return result; -} - -// Calculate two quaternion multiplication -RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2) -{ - Quaternion result = { 0 }; - - 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; -} - -// Scale quaternion by float value -RMDEF Quaternion QuaternionScale(Quaternion q, float mul) -{ - Quaternion result = { 0 }; - - float qax = q.x, qay = q.y, qaz = q.z, qaw = q.w; - - result.x = qax * mul + qaw * mul + qay * mul - qaz * mul; - result.y = qay * mul + qaw * mul + qaz * mul - qax * mul; - result.z = qaz * mul + qaw * mul + qax * mul - qay * mul; - result.w = qaw * mul - qax * mul - qay * mul - qaz * mul; - - return result; -} - -// Divide two quaternions -RMDEF Quaternion QuaternionDivide(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x / q2.x, q1.y / q2.y, q1.z / q2.z, q1.w / q2.w}; - return result; -} - -// Calculate linear interpolation between two quaternions -RMDEF Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = { 0 }; - - result.x = q1.x + amount*(q2.x - q1.x); - result.y = q1.y + amount*(q2.y - q1.y); - result.z = q1.z + amount*(q2.z - q1.z); - result.w = q1.w + amount*(q2.w - q1.w); - - return result; -} - -// Calculate slerp-optimized interpolation between two quaternions -RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = QuaternionLerp(q1, q2, amount); - result = QuaternionNormalize(result); - - return result; -} - -// Calculates spherical linear interpolation between two quaternions -RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = { 0 }; - - 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 if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount); - else - { - float halfTheta = acosf(cosHalfTheta); - float sinHalfTheta = sqrtf(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 = sinf((1 - amount)*halfTheta)/sinHalfTheta; - float ratioB = sinf(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; -} - -// Calculate quaternion based on the rotation from one vector to another -RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) -{ - Quaternion result = { 0 }; - - float cos2Theta = Vector3DotProduct(from, to); - Vector3 cross = Vector3CrossProduct(from, to); - - result.x = cross.x; - result.y = cross.y; - result.z = cross.y; - result.w = 1.0f + cos2Theta; // NOTE: Added QuaternioIdentity() - - // Normalize to essentially nlerp the original and identity to 0.5 - result = QuaternionNormalize(result); - - // Above lines are equivalent to: - //Quaternion result = QuaternionNlerp(q, QuaternionIdentity(), 0.5f); - - return result; -} - -// Returns a quaternion for a given rotation matrix -RMDEF Quaternion QuaternionFromMatrix(Matrix mat) -{ - Quaternion result = { 0 }; - - float trace = MatrixTrace(mat); - - if (trace > 0.0f) - { - float s = sqrtf(trace + 1)*2.0f; - float invS = 1.0f/s; - - result.w = s*0.25f; - result.x = (mat.m6 - mat.m9)*invS; - result.y = (mat.m8 - mat.m2)*invS; - result.z = (mat.m1 - mat.m4)*invS; - } - else - { - float m00 = mat.m0, m11 = mat.m5, m22 = mat.m10; - - if (m00 > m11 && m00 > m22) - { - float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m6 - mat.m9)*invS; - result.x = s*0.25f; - result.y = (mat.m4 + mat.m1)*invS; - result.z = (mat.m8 + mat.m2)*invS; - } - else if (m11 > m22) - { - float s = sqrtf(1.0f + m11 - m00 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m8 - mat.m2)*invS; - result.x = (mat.m4 + mat.m1)*invS; - result.y = s*0.25f; - result.z = (mat.m9 + mat.m6)*invS; - } - else - { - float s = sqrtf(1.0f + m22 - m00 - m11)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m1 - mat.m4)*invS; - result.x = (mat.m8 + mat.m2)*invS; - result.y = (mat.m9 + mat.m6)*invS; - result.z = s*0.25f; - } - } - - return result; -} - -// Returns a matrix for a given quaternion -RMDEF Matrix QuaternionToMatrix(Quaternion q) -{ - Matrix result = { 0 }; - - 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 length = QuaternionLength(q); - float lengthSquared = length*length; - - float xx = x*x2/lengthSquared; - float xy = x*y2/lengthSquared; - float xz = x*z2/lengthSquared; - - float yy = y*y2/lengthSquared; - float yz = y*z2/lengthSquared; - float zz = z*z2/lengthSquared; - - float wx = w*x2/lengthSquared; - float wy = w*y2/lengthSquared; - float wz = w*z2/lengthSquared; - - result.m0 = 1.0f - (yy + zz); - result.m1 = xy - wz; - result.m2 = xz + wy; - result.m3 = 0.0f; - result.m4 = xy + wz; - result.m5 = 1.0f - (xx + zz); - result.m6 = yz - wx; - result.m7 = 0.0f; - result.m8 = xz - wy; - result.m9 = yz + wx; - result.m10 = 1.0f - (xx + yy); - result.m11 = 0.0f; - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; - - return result; -} - -// Returns rotation quaternion for an angle and axis -// NOTE: angle must be provided in radians -RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle) -{ - Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; - - if (Vector3Length(axis) != 0.0f) - - angle *= 0.5f; - - axis = Vector3Normalize(axis); - - float sinres = sinf(angle); - float cosres = cosf(angle); - - result.x = axis.x*sinres; - result.y = axis.y*sinres; - result.z = axis.z*sinres; - result.w = cosres; - - result = QuaternionNormalize(result); - - return result; -} - -// Returns the rotation angle and axis for a given quaternion -RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle) -{ - if (fabs(q.w) > 1.0f) q = QuaternionNormalize(q); - - Vector3 resAxis = { 0.0f, 0.0f, 0.0f }; - float resAngle = 2.0f*acosf(q.w); - float den = sqrtf(1.0f - 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 = 1.0f; - } - - *outAxis = resAxis; - *outAngle = resAngle; -} - -// Returns he quaternion equivalent to Euler angles -RMDEF Quaternion QuaternionFromEuler(float roll, float pitch, float yaw) -{ - Quaternion q = { 0 }; - - float x0 = cosf(roll*0.5f); - float x1 = sinf(roll*0.5f); - float y0 = cosf(pitch*0.5f); - float y1 = sinf(pitch*0.5f); - float z0 = cosf(yaw*0.5f); - float z1 = sinf(yaw*0.5f); - - q.x = x1*y0*z0 - x0*y1*z1; - q.y = x0*y1*z0 + x1*y0*z1; - q.z = x0*y0*z1 - x1*y1*z0; - q.w = x0*y0*z0 + x1*y1*z1; - - return q; -} - -// Return the Euler angles equivalent to quaternion (roll, pitch, yaw) -// NOTE: Angles are returned in a Vector3 struct in degrees -RMDEF Vector3 QuaternionToEuler(Quaternion q) -{ - Vector3 result = { 0 }; - - // roll (x-axis rotation) - float x0 = 2.0f*(q.w*q.x + q.y*q.z); - float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y); - result.x = atan2f(x0, x1)*RAD2DEG; - - // pitch (y-axis rotation) - float y0 = 2.0f*(q.w*q.y - q.z*q.x); - y0 = y0 > 1.0f ? 1.0f : y0; - y0 = y0 < -1.0f ? -1.0f : y0; - result.y = asinf(y0)*RAD2DEG; - - // yaw (z-axis rotation) - float z0 = 2.0f*(q.w*q.z + q.x*q.y); - float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z); - result.z = atan2f(z0, z1)*RAD2DEG; - - return result; -} - -// Transform a quaternion given a transformation matrix -RMDEF Quaternion QuaternionTransform(Quaternion q, Matrix mat) -{ - Quaternion result = { 0 }; - - result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w; - result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w; - result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w; - result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w; - - return result; -} - -#endif // RAYMATH_H diff --git a/examples/models/raymath.h b/examples/models/raymath.h deleted file mode 100644 index 398aef4ab..000000000 --- a/examples/models/raymath.h +++ /dev/null @@ -1,1466 +0,0 @@ -/********************************************************************************************** -* -* raymath v1.2 - Math functions to work with Vector3, Matrix and Quaternions -* -* CONFIGURATION: -* -* #define RAYMATH_IMPLEMENTATION -* Generates the implementation of the library into the included file. -* If not defined, the library is in header only mode and can be included in other headers -* or source files without problems. But only ONE file should hold the implementation. -* -* #define RAYMATH_HEADER_ONLY -* Define static inline functions code, so #include header suffices for use. -* This may use up lots of memory. -* -* #define RAYMATH_STANDALONE -* Avoid raylib.h header inclusion in this file. -* Vector3 and Matrix data types are defined internally in raymath module. -* -* -* LICENSE: zlib/libpng -* -* Copyright (c) 2015-2020 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. -* -**********************************************************************************************/ - -#ifndef RAYMATH_H -#define RAYMATH_H - -//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line -//#define RAYMATH_HEADER_ONLY // NOTE: To compile functions as static inline, uncomment this line - -#ifndef RAYMATH_STANDALONE - #include "raylib.h" // Required for structs: Vector3, Matrix -#endif - -#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_HEADER_ONLY) - #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_HEADER_ONLY is contradictory" -#endif - -#if defined(RAYMATH_IMPLEMENTATION) - #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED) - #define RMDEF __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll). - #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED) - #define RMDEF __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll) - #else - #define RMDEF extern inline // Provide external definition - #endif -#elif defined(RAYMATH_HEADER_ONLY) - #define RMDEF static inline // Functions may be inlined, no external out-of-line definition -#else - #if defined(__TINYC__) - #define RMDEF static inline // plain inline not supported by tinycc (See issue #435) - #else - #define RMDEF inline // Functions may be inlined or external definition used - #endif -#endif - -//---------------------------------------------------------------------------------- -// Defines and Macros -//---------------------------------------------------------------------------------- -#ifndef PI - #define PI 3.14159265358979323846 -#endif - -#ifndef DEG2RAD - #define DEG2RAD (PI/180.0f) -#endif - -#ifndef RAD2DEG - #define RAD2DEG (180.0f/PI) -#endif - -// Return float vector for Matrix -#ifndef MatrixToFloat - #define MatrixToFloat(mat) (MatrixToFloatV(mat).v) -#endif - -// Return float vector for Vector3 -#ifndef Vector3ToFloat - #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v) -#endif - -//---------------------------------------------------------------------------------- -// Types and Structures Definition -//---------------------------------------------------------------------------------- - -#if defined(RAYMATH_STANDALONE) - // Vector2 type - typedef struct Vector2 { - float x; - float y; - } Vector2; - - // Vector3 type - typedef struct Vector3 { - float x; - float y; - float z; - } Vector3; - - // Quaternion type - typedef struct Quaternion { - float x; - float y; - float z; - float w; - } Quaternion; - - // Matrix type (OpenGL style 4x4 - right handed, column major) - typedef struct Matrix { - float m0, m4, m8, m12; - float m1, m5, m9, m13; - float m2, m6, m10, m14; - float m3, m7, m11, m15; - } Matrix; -#endif - -// NOTE: Helper types to be used instead of array return types for *ToFloat functions -typedef struct float3 { float v[3]; } float3; -typedef struct float16 { float v[16]; } float16; - -#include // Required for: sinf(), cosf(), sqrtf(), tan(), fabs() - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Utils math -//---------------------------------------------------------------------------------- - -// Clamp float value -RMDEF float Clamp(float value, float min, float max) -{ - const float res = value < min ? min : value; - return res > max ? max : res; -} - -// Calculate linear interpolation between two floats -RMDEF float Lerp(float start, float end, float amount) -{ - return start + amount*(end - start); -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector2 math -//---------------------------------------------------------------------------------- - -// Vector with components value 0.0f -RMDEF Vector2 Vector2Zero(void) -{ - Vector2 result = { 0.0f, 0.0f }; - return result; -} - -// Vector with components value 1.0f -RMDEF Vector2 Vector2One(void) -{ - Vector2 result = { 1.0f, 1.0f }; - return result; -} - -// Add two vectors (v1 + v2) -RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x + v2.x, v1.y + v2.y }; - return result; -} - -// Add vector and float value -RMDEF Vector2 Vector2AddValue(Vector2 v, float add) -{ - Vector2 result = { v.x + add, v.y + add }; - return result; -} - -// Subtract two vectors (v1 - v2) -RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x - v2.x, v1.y - v2.y }; - return result; -} - -// Subtract vector by float value -RMDEF Vector2 Vector2SubtractValue(Vector2 v, float sub) -{ - Vector2 result = { v.x - sub, v.y - sub }; - return result; -} - -// Calculate vector length -RMDEF float Vector2Length(Vector2 v) -{ - float result = sqrtf((v.x*v.x) + (v.y*v.y)); - return result; -} - -// Calculate two vectors dot product -RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2) -{ - float result = (v1.x*v2.x + v1.y*v2.y); - return result; -} - -// Calculate distance between two vectors -RMDEF float Vector2Distance(Vector2 v1, Vector2 v2) -{ - float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); - return result; -} - -// Calculate angle from two vectors in X-axis -RMDEF float Vector2Angle(Vector2 v1, Vector2 v2) -{ - float result = atan2f(v2.y - v1.y, v2.x - v1.x)*(180.0f/PI); - if (result < 0) result += 360.0f; - return result; -} - -// Scale vector (multiply by value) -RMDEF Vector2 Vector2Scale(Vector2 v, float scale) -{ - Vector2 result = { v.x*scale, v.y*scale }; - return result; -} - -// Multiply vector by vector -RMDEF Vector2 Vector2Multiply(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x*v2.x, v1.y*v2.y }; - return result; -} - -// Negate vector -RMDEF Vector2 Vector2Negate(Vector2 v) -{ - Vector2 result = { -v.x, -v.y }; - return result; -} - -// Divide vector by vector -RMDEF Vector2 Vector2Divide(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x/v2.x, v1.y/v2.y }; - return result; -} - -// Normalize provided vector -RMDEF Vector2 Vector2Normalize(Vector2 v) -{ - Vector2 result = Vector2Scale(v, 1/Vector2Length(v)); - return result; -} - -// Calculate linear interpolation between two vectors -RMDEF Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount) -{ - Vector2 result = { 0 }; - - result.x = v1.x + amount*(v2.x - v1.x); - result.y = v1.y + amount*(v2.y - v1.y); - - return result; -} - -// Rotate Vector by float in Degrees. -RMDEF Vector2 Vector2Rotate(Vector2 v, float degs) -{ - float rads = degs*DEG2RAD; - Vector2 result = {v.x * cosf(rads) - v.y * sinf(rads) , v.x * sinf(rads) + v.y * cosf(rads) }; - return result; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector3 math -//---------------------------------------------------------------------------------- - -// Vector with components value 0.0f -RMDEF Vector3 Vector3Zero(void) -{ - Vector3 result = { 0.0f, 0.0f, 0.0f }; - return result; -} - -// Vector with components value 1.0f -RMDEF Vector3 Vector3One(void) -{ - Vector3 result = { 1.0f, 1.0f, 1.0f }; - return result; -} - -// Add two vectors -RMDEF Vector3 Vector3Add(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z }; - return result; -} - -// Add vector and float value -RMDEF Vector3 Vector3AddValue(Vector3 v, float add) -{ - Vector3 result = { v.x + add, v.y + add, v.z + add }; - return result; -} - -// Subtract two vectors -RMDEF Vector3 Vector3Subtract(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z }; - return result; -} - -// Subtract vector by float value -RMDEF Vector3 Vector3SubtractValue(Vector3 v, float sub) -{ - Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; - return result; -} - -// Multiply vector by scalar -RMDEF Vector3 Vector3Scale(Vector3 v, float scalar) -{ - Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar }; - return result; -} - -// Multiply vector by vector -RMDEF Vector3 Vector3Multiply(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z }; - return result; -} - -// Calculate two vectors cross product -RMDEF Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x }; - return result; -} - -// Calculate one vector perpendicular vector -RMDEF Vector3 Vector3Perpendicular(Vector3 v) -{ - Vector3 result = { 0 }; - - float min = (float) fabs(v.x); - Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; - - if (fabs(v.y) < min) - { - min = (float) fabs(v.y); - Vector3 tmp = {0.0f, 1.0f, 0.0f}; - cardinalAxis = tmp; - } - - if (fabs(v.z) < min) - { - Vector3 tmp = {0.0f, 0.0f, 1.0f}; - cardinalAxis = tmp; - } - - result = Vector3CrossProduct(v, cardinalAxis); - - return result; -} - -// Calculate vector length -RMDEF float Vector3Length(const Vector3 v) -{ - float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); - return result; -} - -// Calculate two vectors dot product -RMDEF float Vector3DotProduct(Vector3 v1, Vector3 v2) -{ - float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); - return result; -} - -// Calculate distance between two vectors -RMDEF float Vector3Distance(Vector3 v1, Vector3 v2) -{ - float dx = v2.x - v1.x; - float dy = v2.y - v1.y; - float dz = v2.z - v1.z; - float result = sqrtf(dx*dx + dy*dy + dz*dz); - return result; -} - -// Negate provided vector (invert direction) -RMDEF Vector3 Vector3Negate(Vector3 v) -{ - Vector3 result = { -v.x, -v.y, -v.z }; - return result; -} - -// Divide vector by vector -RMDEF Vector3 Vector3Divide(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z }; - return result; -} - -// Normalize provided vector -RMDEF Vector3 Vector3Normalize(Vector3 v) -{ - Vector3 result = v; - - float length, ilength; - length = Vector3Length(v); - if (length == 0.0f) length = 1.0f; - ilength = 1.0f/length; - - result.x *= ilength; - result.y *= ilength; - result.z *= ilength; - - return result; -} - -// Orthonormalize provided vectors -// Makes vectors normalized and orthogonal to each other -// Gram-Schmidt function implementation -RMDEF void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2) -{ - *v1 = Vector3Normalize(*v1); - Vector3 vn = Vector3CrossProduct(*v1, *v2); - vn = Vector3Normalize(vn); - *v2 = Vector3CrossProduct(vn, *v1); -} - -// Transforms a Vector3 by a given Matrix -RMDEF Vector3 Vector3Transform(Vector3 v, Matrix mat) -{ - Vector3 result = { 0 }; - float x = v.x; - float y = v.y; - float z = v.z; - - result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; - result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; - result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; - - return result; -} - -// Transform a vector by quaternion rotation -RMDEF Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q) -{ - Vector3 result = { 0 }; - - result.x = v.x*(q.x*q.x + q.w*q.w - q.y*q.y - q.z*q.z) + v.y*(2*q.x*q.y - 2*q.w*q.z) + v.z*(2*q.x*q.z + 2*q.w*q.y); - result.y = v.x*(2*q.w*q.z + 2*q.x*q.y) + v.y*(q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z) + v.z*(-2*q.w*q.x + 2*q.y*q.z); - result.z = v.x*(-2*q.w*q.y + 2*q.x*q.z) + v.y*(2*q.w*q.x + 2*q.y*q.z)+ v.z*(q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z); - - return result; -} - -// Calculate linear interpolation between two vectors -RMDEF Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount) -{ - Vector3 result = { 0 }; - - 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 Vector3Reflect(Vector3 v, Vector3 normal) -{ - // I is the original vector - // N is the normal of the incident plane - // R = I - (2*N*( DotProduct[ I,N] )) - - Vector3 result = { 0 }; - - float dotProduct = Vector3DotProduct(v, normal); - - result.x = v.x - (2.0f*normal.x)*dotProduct; - result.y = v.y - (2.0f*normal.y)*dotProduct; - result.z = v.z - (2.0f*normal.z)*dotProduct; - - return result; -} - -// Return min value for each pair of components -RMDEF Vector3 Vector3Min(Vector3 v1, Vector3 v2) -{ - Vector3 result = { 0 }; - - result.x = fminf(v1.x, v2.x); - result.y = fminf(v1.y, v2.y); - result.z = fminf(v1.z, v2.z); - - return result; -} - -// Return max value for each pair of components -RMDEF Vector3 Vector3Max(Vector3 v1, Vector3 v2) -{ - Vector3 result = { 0 }; - - result.x = fmaxf(v1.x, v2.x); - result.y = fmaxf(v1.y, v2.y); - result.z = fmaxf(v1.z, v2.z); - - return result; -} - -// Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c) -// NOTE: Assumes P is on the plane of the triangle -RMDEF Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c) -{ - //Vector v0 = b - a, v1 = c - a, v2 = p - a; - - Vector3 v0 = Vector3Subtract(b, a); - Vector3 v1 = Vector3Subtract(c, a); - Vector3 v2 = Vector3Subtract(p, a); - float d00 = Vector3DotProduct(v0, v0); - float d01 = Vector3DotProduct(v0, v1); - float d11 = Vector3DotProduct(v1, v1); - float d20 = Vector3DotProduct(v2, v0); - float d21 = Vector3DotProduct(v2, v1); - - float denom = d00*d11 - d01*d01; - - Vector3 result = { 0 }; - - result.y = (d11*d20 - d01*d21)/denom; - result.z = (d00*d21 - d01*d20)/denom; - result.x = 1.0f - (result.z + result.y); - - return result; -} - -// Returns Vector3 as float array -RMDEF float3 Vector3ToFloatV(Vector3 v) -{ - float3 buffer = { 0 }; - - buffer.v[0] = v.x; - buffer.v[1] = v.y; - buffer.v[2] = v.z; - - return buffer; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Matrix math -//---------------------------------------------------------------------------------- - -// Compute matrix determinant -RMDEF float MatrixDeterminant(Matrix mat) -{ - // 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 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) -{ - float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15); - return result; -} - -// Transposes provided matrix -RMDEF Matrix MatrixTranspose(Matrix mat) -{ - Matrix result = { 0 }; - - result.m0 = mat.m0; - result.m1 = mat.m4; - result.m2 = mat.m8; - result.m3 = mat.m12; - result.m4 = mat.m1; - result.m5 = mat.m5; - result.m6 = mat.m9; - result.m7 = mat.m13; - result.m8 = mat.m2; - result.m9 = mat.m6; - result.m10 = mat.m10; - result.m11 = mat.m14; - result.m12 = mat.m3; - result.m13 = mat.m7; - result.m14 = mat.m11; - result.m15 = mat.m15; - - return result; -} - -// Invert provided matrix -RMDEF Matrix MatrixInvert(Matrix mat) -{ - Matrix result = { 0 }; - - // 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 = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); - - result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet; - result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet; - result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet; - result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet; - result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet; - result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet; - result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet; - result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet; - result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet; - result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet; - result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet; - result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet; - result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet; - result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet; - result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet; - result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet; - - return result; -} - -// Normalize provided matrix -RMDEF Matrix MatrixNormalize(Matrix mat) -{ - Matrix result = { 0 }; - - float det = MatrixDeterminant(mat); - - result.m0 = mat.m0/det; - result.m1 = mat.m1/det; - result.m2 = mat.m2/det; - result.m3 = mat.m3/det; - result.m4 = mat.m4/det; - result.m5 = mat.m5/det; - result.m6 = mat.m6/det; - result.m7 = mat.m7/det; - result.m8 = mat.m8/det; - result.m9 = mat.m9/det; - result.m10 = mat.m10/det; - result.m11 = mat.m11/det; - result.m12 = mat.m12/det; - result.m13 = mat.m13/det; - result.m14 = mat.m14/det; - result.m15 = mat.m15/det; - - return result; -} - -// Returns identity matrix -RMDEF Matrix MatrixIdentity(void) -{ - Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, - 0.0f, 1.0f, 0.0f, 0.0f, - 0.0f, 0.0f, 1.0f, 0.0f, - 0.0f, 0.0f, 0.0f, 1.0f }; - - 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; -} - -// Subtract two matrices (left - right) -RMDEF Matrix MatrixSubtract(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 = { 1.0f, 0.0f, 0.0f, x, - 0.0f, 1.0f, 0.0f, y, - 0.0f, 0.0f, 1.0f, z, - 0.0f, 0.0f, 0.0f, 1.0f }; - - return result; -} - -// Create rotation matrix from axis and angle -// NOTE: Angle should be provided in radians -RMDEF Matrix MatrixRotate(Vector3 axis, float angle) -{ - Matrix result = { 0 }; - - float x = axis.x, y = axis.y, z = axis.z; - - float length = sqrtf(x*x + y*y + z*z); - - if ((length != 1.0f) && (length != 0.0f)) - { - length = 1.0f/length; - x *= length; - y *= length; - z *= length; - } - - float sinres = sinf(angle); - float cosres = cosf(angle); - float t = 1.0f - cosres; - - result.m0 = x*x*t + cosres; - result.m1 = y*x*t + z*sinres; - result.m2 = z*x*t - y*sinres; - result.m3 = 0.0f; - - result.m4 = x*y*t - z*sinres; - result.m5 = y*y*t + cosres; - result.m6 = z*y*t + x*sinres; - result.m7 = 0.0f; - - result.m8 = x*z*t + y*sinres; - result.m9 = y*z*t - x*sinres; - result.m10 = z*z*t + cosres; - result.m11 = 0.0f; - - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; - - return result; -} - -// Returns xyz-rotation matrix (angles in radians) -RMDEF Matrix MatrixRotateXYZ(Vector3 ang) -{ - Matrix result = MatrixIdentity(); - - float cosz = cosf(-ang.z); - float sinz = sinf(-ang.z); - float cosy = cosf(-ang.y); - float siny = sinf(-ang.y); - float cosx = cosf(-ang.x); - float sinx = sinf(-ang.x); - - result.m0 = cosz * cosy; - result.m4 = (cosz * siny * sinx) - (sinz * cosx); - result.m8 = (cosz * siny * cosx) + (sinz * sinx); - - result.m1 = sinz * cosy; - result.m5 = (sinz * siny * sinx) + (cosz * cosx); - result.m9 = (sinz * siny * cosx) - (cosz * sinx); - - result.m2 = -siny; - result.m6 = cosy * sinx; - result.m10= cosy * cosx; - - return result; -} - -// Returns x-rotation matrix (angle in radians) -RMDEF Matrix MatrixRotateX(float angle) -{ - Matrix result = MatrixIdentity(); - - float cosres = cosf(angle); - float sinres = sinf(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 = cosf(angle); - float sinres = sinf(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, 0.0f, 0.0f, 0.0f, - 0.0f, y, 0.0f, 0.0f, - 0.0f, 0.0f, z, 0.0f, - 0.0f, 0.0f, 0.0f, 1.0f }; - - return result; -} - -// Returns two matrix multiplication -// NOTE: When multiplying matrices... the order matters! -RMDEF Matrix MatrixMultiply(Matrix left, Matrix right) -{ - Matrix result = { 0 }; - - result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12; - result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13; - result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14; - result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15; - result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12; - result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13; - result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14; - result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15; - result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12; - result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13; - result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14; - result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15; - result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12; - result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13; - result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14; - result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15; - - return result; -} - -// Returns perspective projection matrix -RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far) -{ - Matrix result = { 0 }; - - float rl = (float)(right - left); - float tb = (float)(top - bottom); - float fn = (float)(far - near); - - result.m0 = ((float) near*2.0f)/rl; - result.m1 = 0.0f; - result.m2 = 0.0f; - result.m3 = 0.0f; - - result.m4 = 0.0f; - result.m5 = ((float) near*2.0f)/tb; - result.m6 = 0.0f; - result.m7 = 0.0f; - - result.m8 = ((float)right + (float)left)/rl; - result.m9 = ((float)top + (float)bottom)/tb; - result.m10 = -((float)far + (float)near)/fn; - result.m11 = -1.0f; - - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = -((float)far*(float)near*2.0f)/fn; - result.m15 = 0.0f; - - return result; -} - -// Returns perspective projection matrix -// NOTE: Angle should be provided in radians -RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far) -{ - double top = near*tan(fovy*0.5); - double right = top*aspect; - Matrix result = MatrixFrustum(-right, right, -top, top, near, far); - - return result; -} - -// Returns orthographic projection matrix -RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far) -{ - Matrix result = { 0 }; - - float rl = (float)(right - left); - float tb = (float)(top - bottom); - float fn = (float)(far - near); - - result.m0 = 2.0f/rl; - result.m1 = 0.0f; - result.m2 = 0.0f; - result.m3 = 0.0f; - result.m4 = 0.0f; - result.m5 = 2.0f/tb; - result.m6 = 0.0f; - result.m7 = 0.0f; - result.m8 = 0.0f; - result.m9 = 0.0f; - result.m10 = -2.0f/fn; - result.m11 = 0.0f; - result.m12 = -((float)left + (float)right)/rl; - result.m13 = -((float)top + (float)bottom)/tb; - result.m14 = -((float)far + (float)near)/fn; - result.m15 = 1.0f; - - return result; -} - -// Returns camera look-at matrix (view matrix) -RMDEF Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up) -{ - Matrix result = { 0 }; - - Vector3 z = Vector3Subtract(eye, target); - z = Vector3Normalize(z); - Vector3 x = Vector3CrossProduct(up, z); - x = Vector3Normalize(x); - Vector3 y = Vector3CrossProduct(z, x); - y = Vector3Normalize(y); - - result.m0 = x.x; - result.m1 = x.y; - result.m2 = x.z; - result.m3 = 0.0f; - result.m4 = y.x; - result.m5 = y.y; - result.m6 = y.z; - result.m7 = 0.0f; - result.m8 = z.x; - result.m9 = z.y; - result.m10 = z.z; - result.m11 = 0.0f; - result.m12 = eye.x; - result.m13 = eye.y; - result.m14 = eye.z; - result.m15 = 1.0f; - - result = MatrixInvert(result); - - return result; -} - -// Returns float array of matrix data -RMDEF float16 MatrixToFloatV(Matrix mat) -{ - float16 buffer = { 0 }; - - buffer.v[0] = mat.m0; - buffer.v[1] = mat.m1; - buffer.v[2] = mat.m2; - buffer.v[3] = mat.m3; - buffer.v[4] = mat.m4; - buffer.v[5] = mat.m5; - buffer.v[6] = mat.m6; - buffer.v[7] = mat.m7; - buffer.v[8] = mat.m8; - buffer.v[9] = mat.m9; - buffer.v[10] = mat.m10; - buffer.v[11] = mat.m11; - buffer.v[12] = mat.m12; - buffer.v[13] = mat.m13; - buffer.v[14] = mat.m14; - buffer.v[15] = mat.m15; - - return buffer; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Quaternion math -//---------------------------------------------------------------------------------- - -// Add two quaternions -RMDEF Quaternion QuaternionAdd(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w}; - return result; -} - -// Add quaternion and float value -RMDEF Quaternion QuaternionAddValue(Quaternion q, float add) -{ - Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add}; - return result; -} - -// Subtract two quaternions -RMDEF Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w}; - return result; -} - -// Subtract quaternion and float value -RMDEF Quaternion QuaternionSubtractValue(Quaternion q, float sub) -{ - Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub}; - return result; -} - -// Returns identity quaternion -RMDEF Quaternion QuaternionIdentity(void) -{ - Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; - return result; -} - -// Computes the length of a quaternion -RMDEF float QuaternionLength(Quaternion q) -{ - float result = (float)sqrt(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); - return result; -} - -// Normalize provided quaternion -RMDEF Quaternion QuaternionNormalize(Quaternion q) -{ - Quaternion result = { 0 }; - - float length, ilength; - length = QuaternionLength(q); - if (length == 0.0f) length = 1.0f; - ilength = 1.0f/length; - - result.x = q.x*ilength; - result.y = q.y*ilength; - result.z = q.z*ilength; - result.w = q.w*ilength; - - return result; -} - -// Invert provided quaternion -RMDEF Quaternion QuaternionInvert(Quaternion q) -{ - Quaternion result = q; - float length = QuaternionLength(q); - float lengthSq = length*length; - - if (lengthSq != 0.0) - { - float i = 1.0f/lengthSq; - - result.x *= -i; - result.y *= -i; - result.z *= -i; - result.w *= i; - } - - return result; -} - -// Calculate two quaternion multiplication -RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2) -{ - Quaternion result = { 0 }; - - 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; -} - -// Scale quaternion by float value -RMDEF Quaternion QuaternionScale(Quaternion q, float mul) -{ - Quaternion result = { 0 }; - - float qax = q.x, qay = q.y, qaz = q.z, qaw = q.w; - - result.x = qax * mul + qaw * mul + qay * mul - qaz * mul; - result.y = qay * mul + qaw * mul + qaz * mul - qax * mul; - result.z = qaz * mul + qaw * mul + qax * mul - qay * mul; - result.w = qaw * mul - qax * mul - qay * mul - qaz * mul; - - return result; -} - -// Divide two quaternions -RMDEF Quaternion QuaternionDivide(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x / q2.x, q1.y / q2.y, q1.z / q2.z, q1.w / q2.w}; - return result; -} - -// Calculate linear interpolation between two quaternions -RMDEF Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = { 0 }; - - result.x = q1.x + amount*(q2.x - q1.x); - result.y = q1.y + amount*(q2.y - q1.y); - result.z = q1.z + amount*(q2.z - q1.z); - result.w = q1.w + amount*(q2.w - q1.w); - - return result; -} - -// Calculate slerp-optimized interpolation between two quaternions -RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = QuaternionLerp(q1, q2, amount); - result = QuaternionNormalize(result); - - return result; -} - -// Calculates spherical linear interpolation between two quaternions -RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = { 0 }; - - 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 if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount); - else - { - float halfTheta = acosf(cosHalfTheta); - float sinHalfTheta = sqrtf(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 = sinf((1 - amount)*halfTheta)/sinHalfTheta; - float ratioB = sinf(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; -} - -// Calculate quaternion based on the rotation from one vector to another -RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) -{ - Quaternion result = { 0 }; - - float cos2Theta = Vector3DotProduct(from, to); - Vector3 cross = Vector3CrossProduct(from, to); - - result.x = cross.x; - result.y = cross.y; - result.z = cross.y; - result.w = 1.0f + cos2Theta; // NOTE: Added QuaternioIdentity() - - // Normalize to essentially nlerp the original and identity to 0.5 - result = QuaternionNormalize(result); - - // Above lines are equivalent to: - //Quaternion result = QuaternionNlerp(q, QuaternionIdentity(), 0.5f); - - return result; -} - -// Returns a quaternion for a given rotation matrix -RMDEF Quaternion QuaternionFromMatrix(Matrix mat) -{ - Quaternion result = { 0 }; - - float trace = MatrixTrace(mat); - - if (trace > 0.0f) - { - float s = sqrtf(trace + 1)*2.0f; - float invS = 1.0f/s; - - result.w = s*0.25f; - result.x = (mat.m6 - mat.m9)*invS; - result.y = (mat.m8 - mat.m2)*invS; - result.z = (mat.m1 - mat.m4)*invS; - } - else - { - float m00 = mat.m0, m11 = mat.m5, m22 = mat.m10; - - if (m00 > m11 && m00 > m22) - { - float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m6 - mat.m9)*invS; - result.x = s*0.25f; - result.y = (mat.m4 + mat.m1)*invS; - result.z = (mat.m8 + mat.m2)*invS; - } - else if (m11 > m22) - { - float s = sqrtf(1.0f + m11 - m00 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m8 - mat.m2)*invS; - result.x = (mat.m4 + mat.m1)*invS; - result.y = s*0.25f; - result.z = (mat.m9 + mat.m6)*invS; - } - else - { - float s = sqrtf(1.0f + m22 - m00 - m11)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m1 - mat.m4)*invS; - result.x = (mat.m8 + mat.m2)*invS; - result.y = (mat.m9 + mat.m6)*invS; - result.z = s*0.25f; - } - } - - return result; -} - -// Returns a matrix for a given quaternion -RMDEF Matrix QuaternionToMatrix(Quaternion q) -{ - Matrix result = { 0 }; - - 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 length = QuaternionLength(q); - float lengthSquared = length*length; - - float xx = x*x2/lengthSquared; - float xy = x*y2/lengthSquared; - float xz = x*z2/lengthSquared; - - float yy = y*y2/lengthSquared; - float yz = y*z2/lengthSquared; - float zz = z*z2/lengthSquared; - - float wx = w*x2/lengthSquared; - float wy = w*y2/lengthSquared; - float wz = w*z2/lengthSquared; - - result.m0 = 1.0f - (yy + zz); - result.m1 = xy - wz; - result.m2 = xz + wy; - result.m3 = 0.0f; - result.m4 = xy + wz; - result.m5 = 1.0f - (xx + zz); - result.m6 = yz - wx; - result.m7 = 0.0f; - result.m8 = xz - wy; - result.m9 = yz + wx; - result.m10 = 1.0f - (xx + yy); - result.m11 = 0.0f; - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; - - return result; -} - -// Returns rotation quaternion for an angle and axis -// NOTE: angle must be provided in radians -RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle) -{ - Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; - - if (Vector3Length(axis) != 0.0f) - - angle *= 0.5f; - - axis = Vector3Normalize(axis); - - float sinres = sinf(angle); - float cosres = cosf(angle); - - result.x = axis.x*sinres; - result.y = axis.y*sinres; - result.z = axis.z*sinres; - result.w = cosres; - - result = QuaternionNormalize(result); - - return result; -} - -// Returns the rotation angle and axis for a given quaternion -RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle) -{ - if (fabs(q.w) > 1.0f) q = QuaternionNormalize(q); - - Vector3 resAxis = { 0.0f, 0.0f, 0.0f }; - float resAngle = 2.0f*acosf(q.w); - float den = sqrtf(1.0f - 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 = 1.0f; - } - - *outAxis = resAxis; - *outAngle = resAngle; -} - -// Returns he quaternion equivalent to Euler angles -RMDEF Quaternion QuaternionFromEuler(float roll, float pitch, float yaw) -{ - Quaternion q = { 0 }; - - float x0 = cosf(roll*0.5f); - float x1 = sinf(roll*0.5f); - float y0 = cosf(pitch*0.5f); - float y1 = sinf(pitch*0.5f); - float z0 = cosf(yaw*0.5f); - float z1 = sinf(yaw*0.5f); - - q.x = x1*y0*z0 - x0*y1*z1; - q.y = x0*y1*z0 + x1*y0*z1; - q.z = x0*y0*z1 - x1*y1*z0; - q.w = x0*y0*z0 + x1*y1*z1; - - return q; -} - -// Return the Euler angles equivalent to quaternion (roll, pitch, yaw) -// NOTE: Angles are returned in a Vector3 struct in degrees -RMDEF Vector3 QuaternionToEuler(Quaternion q) -{ - Vector3 result = { 0 }; - - // roll (x-axis rotation) - float x0 = 2.0f*(q.w*q.x + q.y*q.z); - float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y); - result.x = atan2f(x0, x1)*RAD2DEG; - - // pitch (y-axis rotation) - float y0 = 2.0f*(q.w*q.y - q.z*q.x); - y0 = y0 > 1.0f ? 1.0f : y0; - y0 = y0 < -1.0f ? -1.0f : y0; - result.y = asinf(y0)*RAD2DEG; - - // yaw (z-axis rotation) - float z0 = 2.0f*(q.w*q.z + q.x*q.y); - float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z); - result.z = atan2f(z0, z1)*RAD2DEG; - - return result; -} - -// Transform a quaternion given a transformation matrix -RMDEF Quaternion QuaternionTransform(Quaternion q, Matrix mat) -{ - Quaternion result = { 0 }; - - result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w; - result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w; - result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w; - result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w; - - return result; -} - -#endif // RAYMATH_H diff --git a/examples/shaders/raymath.h b/examples/shaders/raymath.h deleted file mode 100644 index 398aef4ab..000000000 --- a/examples/shaders/raymath.h +++ /dev/null @@ -1,1466 +0,0 @@ -/********************************************************************************************** -* -* raymath v1.2 - Math functions to work with Vector3, Matrix and Quaternions -* -* CONFIGURATION: -* -* #define RAYMATH_IMPLEMENTATION -* Generates the implementation of the library into the included file. -* If not defined, the library is in header only mode and can be included in other headers -* or source files without problems. But only ONE file should hold the implementation. -* -* #define RAYMATH_HEADER_ONLY -* Define static inline functions code, so #include header suffices for use. -* This may use up lots of memory. -* -* #define RAYMATH_STANDALONE -* Avoid raylib.h header inclusion in this file. -* Vector3 and Matrix data types are defined internally in raymath module. -* -* -* LICENSE: zlib/libpng -* -* Copyright (c) 2015-2020 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. -* -**********************************************************************************************/ - -#ifndef RAYMATH_H -#define RAYMATH_H - -//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line -//#define RAYMATH_HEADER_ONLY // NOTE: To compile functions as static inline, uncomment this line - -#ifndef RAYMATH_STANDALONE - #include "raylib.h" // Required for structs: Vector3, Matrix -#endif - -#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_HEADER_ONLY) - #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_HEADER_ONLY is contradictory" -#endif - -#if defined(RAYMATH_IMPLEMENTATION) - #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED) - #define RMDEF __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll). - #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED) - #define RMDEF __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll) - #else - #define RMDEF extern inline // Provide external definition - #endif -#elif defined(RAYMATH_HEADER_ONLY) - #define RMDEF static inline // Functions may be inlined, no external out-of-line definition -#else - #if defined(__TINYC__) - #define RMDEF static inline // plain inline not supported by tinycc (See issue #435) - #else - #define RMDEF inline // Functions may be inlined or external definition used - #endif -#endif - -//---------------------------------------------------------------------------------- -// Defines and Macros -//---------------------------------------------------------------------------------- -#ifndef PI - #define PI 3.14159265358979323846 -#endif - -#ifndef DEG2RAD - #define DEG2RAD (PI/180.0f) -#endif - -#ifndef RAD2DEG - #define RAD2DEG (180.0f/PI) -#endif - -// Return float vector for Matrix -#ifndef MatrixToFloat - #define MatrixToFloat(mat) (MatrixToFloatV(mat).v) -#endif - -// Return float vector for Vector3 -#ifndef Vector3ToFloat - #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v) -#endif - -//---------------------------------------------------------------------------------- -// Types and Structures Definition -//---------------------------------------------------------------------------------- - -#if defined(RAYMATH_STANDALONE) - // Vector2 type - typedef struct Vector2 { - float x; - float y; - } Vector2; - - // Vector3 type - typedef struct Vector3 { - float x; - float y; - float z; - } Vector3; - - // Quaternion type - typedef struct Quaternion { - float x; - float y; - float z; - float w; - } Quaternion; - - // Matrix type (OpenGL style 4x4 - right handed, column major) - typedef struct Matrix { - float m0, m4, m8, m12; - float m1, m5, m9, m13; - float m2, m6, m10, m14; - float m3, m7, m11, m15; - } Matrix; -#endif - -// NOTE: Helper types to be used instead of array return types for *ToFloat functions -typedef struct float3 { float v[3]; } float3; -typedef struct float16 { float v[16]; } float16; - -#include // Required for: sinf(), cosf(), sqrtf(), tan(), fabs() - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Utils math -//---------------------------------------------------------------------------------- - -// Clamp float value -RMDEF float Clamp(float value, float min, float max) -{ - const float res = value < min ? min : value; - return res > max ? max : res; -} - -// Calculate linear interpolation between two floats -RMDEF float Lerp(float start, float end, float amount) -{ - return start + amount*(end - start); -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector2 math -//---------------------------------------------------------------------------------- - -// Vector with components value 0.0f -RMDEF Vector2 Vector2Zero(void) -{ - Vector2 result = { 0.0f, 0.0f }; - return result; -} - -// Vector with components value 1.0f -RMDEF Vector2 Vector2One(void) -{ - Vector2 result = { 1.0f, 1.0f }; - return result; -} - -// Add two vectors (v1 + v2) -RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x + v2.x, v1.y + v2.y }; - return result; -} - -// Add vector and float value -RMDEF Vector2 Vector2AddValue(Vector2 v, float add) -{ - Vector2 result = { v.x + add, v.y + add }; - return result; -} - -// Subtract two vectors (v1 - v2) -RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x - v2.x, v1.y - v2.y }; - return result; -} - -// Subtract vector by float value -RMDEF Vector2 Vector2SubtractValue(Vector2 v, float sub) -{ - Vector2 result = { v.x - sub, v.y - sub }; - return result; -} - -// Calculate vector length -RMDEF float Vector2Length(Vector2 v) -{ - float result = sqrtf((v.x*v.x) + (v.y*v.y)); - return result; -} - -// Calculate two vectors dot product -RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2) -{ - float result = (v1.x*v2.x + v1.y*v2.y); - return result; -} - -// Calculate distance between two vectors -RMDEF float Vector2Distance(Vector2 v1, Vector2 v2) -{ - float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); - return result; -} - -// Calculate angle from two vectors in X-axis -RMDEF float Vector2Angle(Vector2 v1, Vector2 v2) -{ - float result = atan2f(v2.y - v1.y, v2.x - v1.x)*(180.0f/PI); - if (result < 0) result += 360.0f; - return result; -} - -// Scale vector (multiply by value) -RMDEF Vector2 Vector2Scale(Vector2 v, float scale) -{ - Vector2 result = { v.x*scale, v.y*scale }; - return result; -} - -// Multiply vector by vector -RMDEF Vector2 Vector2Multiply(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x*v2.x, v1.y*v2.y }; - return result; -} - -// Negate vector -RMDEF Vector2 Vector2Negate(Vector2 v) -{ - Vector2 result = { -v.x, -v.y }; - return result; -} - -// Divide vector by vector -RMDEF Vector2 Vector2Divide(Vector2 v1, Vector2 v2) -{ - Vector2 result = { v1.x/v2.x, v1.y/v2.y }; - return result; -} - -// Normalize provided vector -RMDEF Vector2 Vector2Normalize(Vector2 v) -{ - Vector2 result = Vector2Scale(v, 1/Vector2Length(v)); - return result; -} - -// Calculate linear interpolation between two vectors -RMDEF Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount) -{ - Vector2 result = { 0 }; - - result.x = v1.x + amount*(v2.x - v1.x); - result.y = v1.y + amount*(v2.y - v1.y); - - return result; -} - -// Rotate Vector by float in Degrees. -RMDEF Vector2 Vector2Rotate(Vector2 v, float degs) -{ - float rads = degs*DEG2RAD; - Vector2 result = {v.x * cosf(rads) - v.y * sinf(rads) , v.x * sinf(rads) + v.y * cosf(rads) }; - return result; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Vector3 math -//---------------------------------------------------------------------------------- - -// Vector with components value 0.0f -RMDEF Vector3 Vector3Zero(void) -{ - Vector3 result = { 0.0f, 0.0f, 0.0f }; - return result; -} - -// Vector with components value 1.0f -RMDEF Vector3 Vector3One(void) -{ - Vector3 result = { 1.0f, 1.0f, 1.0f }; - return result; -} - -// Add two vectors -RMDEF Vector3 Vector3Add(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z }; - return result; -} - -// Add vector and float value -RMDEF Vector3 Vector3AddValue(Vector3 v, float add) -{ - Vector3 result = { v.x + add, v.y + add, v.z + add }; - return result; -} - -// Subtract two vectors -RMDEF Vector3 Vector3Subtract(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z }; - return result; -} - -// Subtract vector by float value -RMDEF Vector3 Vector3SubtractValue(Vector3 v, float sub) -{ - Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; - return result; -} - -// Multiply vector by scalar -RMDEF Vector3 Vector3Scale(Vector3 v, float scalar) -{ - Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar }; - return result; -} - -// Multiply vector by vector -RMDEF Vector3 Vector3Multiply(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z }; - return result; -} - -// Calculate two vectors cross product -RMDEF Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x }; - return result; -} - -// Calculate one vector perpendicular vector -RMDEF Vector3 Vector3Perpendicular(Vector3 v) -{ - Vector3 result = { 0 }; - - float min = (float) fabs(v.x); - Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; - - if (fabs(v.y) < min) - { - min = (float) fabs(v.y); - Vector3 tmp = {0.0f, 1.0f, 0.0f}; - cardinalAxis = tmp; - } - - if (fabs(v.z) < min) - { - Vector3 tmp = {0.0f, 0.0f, 1.0f}; - cardinalAxis = tmp; - } - - result = Vector3CrossProduct(v, cardinalAxis); - - return result; -} - -// Calculate vector length -RMDEF float Vector3Length(const Vector3 v) -{ - float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); - return result; -} - -// Calculate two vectors dot product -RMDEF float Vector3DotProduct(Vector3 v1, Vector3 v2) -{ - float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); - return result; -} - -// Calculate distance between two vectors -RMDEF float Vector3Distance(Vector3 v1, Vector3 v2) -{ - float dx = v2.x - v1.x; - float dy = v2.y - v1.y; - float dz = v2.z - v1.z; - float result = sqrtf(dx*dx + dy*dy + dz*dz); - return result; -} - -// Negate provided vector (invert direction) -RMDEF Vector3 Vector3Negate(Vector3 v) -{ - Vector3 result = { -v.x, -v.y, -v.z }; - return result; -} - -// Divide vector by vector -RMDEF Vector3 Vector3Divide(Vector3 v1, Vector3 v2) -{ - Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z }; - return result; -} - -// Normalize provided vector -RMDEF Vector3 Vector3Normalize(Vector3 v) -{ - Vector3 result = v; - - float length, ilength; - length = Vector3Length(v); - if (length == 0.0f) length = 1.0f; - ilength = 1.0f/length; - - result.x *= ilength; - result.y *= ilength; - result.z *= ilength; - - return result; -} - -// Orthonormalize provided vectors -// Makes vectors normalized and orthogonal to each other -// Gram-Schmidt function implementation -RMDEF void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2) -{ - *v1 = Vector3Normalize(*v1); - Vector3 vn = Vector3CrossProduct(*v1, *v2); - vn = Vector3Normalize(vn); - *v2 = Vector3CrossProduct(vn, *v1); -} - -// Transforms a Vector3 by a given Matrix -RMDEF Vector3 Vector3Transform(Vector3 v, Matrix mat) -{ - Vector3 result = { 0 }; - float x = v.x; - float y = v.y; - float z = v.z; - - result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; - result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; - result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; - - return result; -} - -// Transform a vector by quaternion rotation -RMDEF Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q) -{ - Vector3 result = { 0 }; - - result.x = v.x*(q.x*q.x + q.w*q.w - q.y*q.y - q.z*q.z) + v.y*(2*q.x*q.y - 2*q.w*q.z) + v.z*(2*q.x*q.z + 2*q.w*q.y); - result.y = v.x*(2*q.w*q.z + 2*q.x*q.y) + v.y*(q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z) + v.z*(-2*q.w*q.x + 2*q.y*q.z); - result.z = v.x*(-2*q.w*q.y + 2*q.x*q.z) + v.y*(2*q.w*q.x + 2*q.y*q.z)+ v.z*(q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z); - - return result; -} - -// Calculate linear interpolation between two vectors -RMDEF Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount) -{ - Vector3 result = { 0 }; - - 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 Vector3Reflect(Vector3 v, Vector3 normal) -{ - // I is the original vector - // N is the normal of the incident plane - // R = I - (2*N*( DotProduct[ I,N] )) - - Vector3 result = { 0 }; - - float dotProduct = Vector3DotProduct(v, normal); - - result.x = v.x - (2.0f*normal.x)*dotProduct; - result.y = v.y - (2.0f*normal.y)*dotProduct; - result.z = v.z - (2.0f*normal.z)*dotProduct; - - return result; -} - -// Return min value for each pair of components -RMDEF Vector3 Vector3Min(Vector3 v1, Vector3 v2) -{ - Vector3 result = { 0 }; - - result.x = fminf(v1.x, v2.x); - result.y = fminf(v1.y, v2.y); - result.z = fminf(v1.z, v2.z); - - return result; -} - -// Return max value for each pair of components -RMDEF Vector3 Vector3Max(Vector3 v1, Vector3 v2) -{ - Vector3 result = { 0 }; - - result.x = fmaxf(v1.x, v2.x); - result.y = fmaxf(v1.y, v2.y); - result.z = fmaxf(v1.z, v2.z); - - return result; -} - -// Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c) -// NOTE: Assumes P is on the plane of the triangle -RMDEF Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c) -{ - //Vector v0 = b - a, v1 = c - a, v2 = p - a; - - Vector3 v0 = Vector3Subtract(b, a); - Vector3 v1 = Vector3Subtract(c, a); - Vector3 v2 = Vector3Subtract(p, a); - float d00 = Vector3DotProduct(v0, v0); - float d01 = Vector3DotProduct(v0, v1); - float d11 = Vector3DotProduct(v1, v1); - float d20 = Vector3DotProduct(v2, v0); - float d21 = Vector3DotProduct(v2, v1); - - float denom = d00*d11 - d01*d01; - - Vector3 result = { 0 }; - - result.y = (d11*d20 - d01*d21)/denom; - result.z = (d00*d21 - d01*d20)/denom; - result.x = 1.0f - (result.z + result.y); - - return result; -} - -// Returns Vector3 as float array -RMDEF float3 Vector3ToFloatV(Vector3 v) -{ - float3 buffer = { 0 }; - - buffer.v[0] = v.x; - buffer.v[1] = v.y; - buffer.v[2] = v.z; - - return buffer; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Matrix math -//---------------------------------------------------------------------------------- - -// Compute matrix determinant -RMDEF float MatrixDeterminant(Matrix mat) -{ - // 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 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) -{ - float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15); - return result; -} - -// Transposes provided matrix -RMDEF Matrix MatrixTranspose(Matrix mat) -{ - Matrix result = { 0 }; - - result.m0 = mat.m0; - result.m1 = mat.m4; - result.m2 = mat.m8; - result.m3 = mat.m12; - result.m4 = mat.m1; - result.m5 = mat.m5; - result.m6 = mat.m9; - result.m7 = mat.m13; - result.m8 = mat.m2; - result.m9 = mat.m6; - result.m10 = mat.m10; - result.m11 = mat.m14; - result.m12 = mat.m3; - result.m13 = mat.m7; - result.m14 = mat.m11; - result.m15 = mat.m15; - - return result; -} - -// Invert provided matrix -RMDEF Matrix MatrixInvert(Matrix mat) -{ - Matrix result = { 0 }; - - // 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 = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); - - result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet; - result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet; - result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet; - result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet; - result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet; - result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet; - result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet; - result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet; - result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet; - result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet; - result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet; - result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet; - result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet; - result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet; - result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet; - result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet; - - return result; -} - -// Normalize provided matrix -RMDEF Matrix MatrixNormalize(Matrix mat) -{ - Matrix result = { 0 }; - - float det = MatrixDeterminant(mat); - - result.m0 = mat.m0/det; - result.m1 = mat.m1/det; - result.m2 = mat.m2/det; - result.m3 = mat.m3/det; - result.m4 = mat.m4/det; - result.m5 = mat.m5/det; - result.m6 = mat.m6/det; - result.m7 = mat.m7/det; - result.m8 = mat.m8/det; - result.m9 = mat.m9/det; - result.m10 = mat.m10/det; - result.m11 = mat.m11/det; - result.m12 = mat.m12/det; - result.m13 = mat.m13/det; - result.m14 = mat.m14/det; - result.m15 = mat.m15/det; - - return result; -} - -// Returns identity matrix -RMDEF Matrix MatrixIdentity(void) -{ - Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, - 0.0f, 1.0f, 0.0f, 0.0f, - 0.0f, 0.0f, 1.0f, 0.0f, - 0.0f, 0.0f, 0.0f, 1.0f }; - - 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; -} - -// Subtract two matrices (left - right) -RMDEF Matrix MatrixSubtract(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 = { 1.0f, 0.0f, 0.0f, x, - 0.0f, 1.0f, 0.0f, y, - 0.0f, 0.0f, 1.0f, z, - 0.0f, 0.0f, 0.0f, 1.0f }; - - return result; -} - -// Create rotation matrix from axis and angle -// NOTE: Angle should be provided in radians -RMDEF Matrix MatrixRotate(Vector3 axis, float angle) -{ - Matrix result = { 0 }; - - float x = axis.x, y = axis.y, z = axis.z; - - float length = sqrtf(x*x + y*y + z*z); - - if ((length != 1.0f) && (length != 0.0f)) - { - length = 1.0f/length; - x *= length; - y *= length; - z *= length; - } - - float sinres = sinf(angle); - float cosres = cosf(angle); - float t = 1.0f - cosres; - - result.m0 = x*x*t + cosres; - result.m1 = y*x*t + z*sinres; - result.m2 = z*x*t - y*sinres; - result.m3 = 0.0f; - - result.m4 = x*y*t - z*sinres; - result.m5 = y*y*t + cosres; - result.m6 = z*y*t + x*sinres; - result.m7 = 0.0f; - - result.m8 = x*z*t + y*sinres; - result.m9 = y*z*t - x*sinres; - result.m10 = z*z*t + cosres; - result.m11 = 0.0f; - - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; - - return result; -} - -// Returns xyz-rotation matrix (angles in radians) -RMDEF Matrix MatrixRotateXYZ(Vector3 ang) -{ - Matrix result = MatrixIdentity(); - - float cosz = cosf(-ang.z); - float sinz = sinf(-ang.z); - float cosy = cosf(-ang.y); - float siny = sinf(-ang.y); - float cosx = cosf(-ang.x); - float sinx = sinf(-ang.x); - - result.m0 = cosz * cosy; - result.m4 = (cosz * siny * sinx) - (sinz * cosx); - result.m8 = (cosz * siny * cosx) + (sinz * sinx); - - result.m1 = sinz * cosy; - result.m5 = (sinz * siny * sinx) + (cosz * cosx); - result.m9 = (sinz * siny * cosx) - (cosz * sinx); - - result.m2 = -siny; - result.m6 = cosy * sinx; - result.m10= cosy * cosx; - - return result; -} - -// Returns x-rotation matrix (angle in radians) -RMDEF Matrix MatrixRotateX(float angle) -{ - Matrix result = MatrixIdentity(); - - float cosres = cosf(angle); - float sinres = sinf(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 = cosf(angle); - float sinres = sinf(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, 0.0f, 0.0f, 0.0f, - 0.0f, y, 0.0f, 0.0f, - 0.0f, 0.0f, z, 0.0f, - 0.0f, 0.0f, 0.0f, 1.0f }; - - return result; -} - -// Returns two matrix multiplication -// NOTE: When multiplying matrices... the order matters! -RMDEF Matrix MatrixMultiply(Matrix left, Matrix right) -{ - Matrix result = { 0 }; - - result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12; - result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13; - result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14; - result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15; - result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12; - result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13; - result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14; - result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15; - result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12; - result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13; - result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14; - result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15; - result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12; - result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13; - result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14; - result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15; - - return result; -} - -// Returns perspective projection matrix -RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far) -{ - Matrix result = { 0 }; - - float rl = (float)(right - left); - float tb = (float)(top - bottom); - float fn = (float)(far - near); - - result.m0 = ((float) near*2.0f)/rl; - result.m1 = 0.0f; - result.m2 = 0.0f; - result.m3 = 0.0f; - - result.m4 = 0.0f; - result.m5 = ((float) near*2.0f)/tb; - result.m6 = 0.0f; - result.m7 = 0.0f; - - result.m8 = ((float)right + (float)left)/rl; - result.m9 = ((float)top + (float)bottom)/tb; - result.m10 = -((float)far + (float)near)/fn; - result.m11 = -1.0f; - - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = -((float)far*(float)near*2.0f)/fn; - result.m15 = 0.0f; - - return result; -} - -// Returns perspective projection matrix -// NOTE: Angle should be provided in radians -RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far) -{ - double top = near*tan(fovy*0.5); - double right = top*aspect; - Matrix result = MatrixFrustum(-right, right, -top, top, near, far); - - return result; -} - -// Returns orthographic projection matrix -RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far) -{ - Matrix result = { 0 }; - - float rl = (float)(right - left); - float tb = (float)(top - bottom); - float fn = (float)(far - near); - - result.m0 = 2.0f/rl; - result.m1 = 0.0f; - result.m2 = 0.0f; - result.m3 = 0.0f; - result.m4 = 0.0f; - result.m5 = 2.0f/tb; - result.m6 = 0.0f; - result.m7 = 0.0f; - result.m8 = 0.0f; - result.m9 = 0.0f; - result.m10 = -2.0f/fn; - result.m11 = 0.0f; - result.m12 = -((float)left + (float)right)/rl; - result.m13 = -((float)top + (float)bottom)/tb; - result.m14 = -((float)far + (float)near)/fn; - result.m15 = 1.0f; - - return result; -} - -// Returns camera look-at matrix (view matrix) -RMDEF Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up) -{ - Matrix result = { 0 }; - - Vector3 z = Vector3Subtract(eye, target); - z = Vector3Normalize(z); - Vector3 x = Vector3CrossProduct(up, z); - x = Vector3Normalize(x); - Vector3 y = Vector3CrossProduct(z, x); - y = Vector3Normalize(y); - - result.m0 = x.x; - result.m1 = x.y; - result.m2 = x.z; - result.m3 = 0.0f; - result.m4 = y.x; - result.m5 = y.y; - result.m6 = y.z; - result.m7 = 0.0f; - result.m8 = z.x; - result.m9 = z.y; - result.m10 = z.z; - result.m11 = 0.0f; - result.m12 = eye.x; - result.m13 = eye.y; - result.m14 = eye.z; - result.m15 = 1.0f; - - result = MatrixInvert(result); - - return result; -} - -// Returns float array of matrix data -RMDEF float16 MatrixToFloatV(Matrix mat) -{ - float16 buffer = { 0 }; - - buffer.v[0] = mat.m0; - buffer.v[1] = mat.m1; - buffer.v[2] = mat.m2; - buffer.v[3] = mat.m3; - buffer.v[4] = mat.m4; - buffer.v[5] = mat.m5; - buffer.v[6] = mat.m6; - buffer.v[7] = mat.m7; - buffer.v[8] = mat.m8; - buffer.v[9] = mat.m9; - buffer.v[10] = mat.m10; - buffer.v[11] = mat.m11; - buffer.v[12] = mat.m12; - buffer.v[13] = mat.m13; - buffer.v[14] = mat.m14; - buffer.v[15] = mat.m15; - - return buffer; -} - -//---------------------------------------------------------------------------------- -// Module Functions Definition - Quaternion math -//---------------------------------------------------------------------------------- - -// Add two quaternions -RMDEF Quaternion QuaternionAdd(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w}; - return result; -} - -// Add quaternion and float value -RMDEF Quaternion QuaternionAddValue(Quaternion q, float add) -{ - Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add}; - return result; -} - -// Subtract two quaternions -RMDEF Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w}; - return result; -} - -// Subtract quaternion and float value -RMDEF Quaternion QuaternionSubtractValue(Quaternion q, float sub) -{ - Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub}; - return result; -} - -// Returns identity quaternion -RMDEF Quaternion QuaternionIdentity(void) -{ - Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; - return result; -} - -// Computes the length of a quaternion -RMDEF float QuaternionLength(Quaternion q) -{ - float result = (float)sqrt(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); - return result; -} - -// Normalize provided quaternion -RMDEF Quaternion QuaternionNormalize(Quaternion q) -{ - Quaternion result = { 0 }; - - float length, ilength; - length = QuaternionLength(q); - if (length == 0.0f) length = 1.0f; - ilength = 1.0f/length; - - result.x = q.x*ilength; - result.y = q.y*ilength; - result.z = q.z*ilength; - result.w = q.w*ilength; - - return result; -} - -// Invert provided quaternion -RMDEF Quaternion QuaternionInvert(Quaternion q) -{ - Quaternion result = q; - float length = QuaternionLength(q); - float lengthSq = length*length; - - if (lengthSq != 0.0) - { - float i = 1.0f/lengthSq; - - result.x *= -i; - result.y *= -i; - result.z *= -i; - result.w *= i; - } - - return result; -} - -// Calculate two quaternion multiplication -RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2) -{ - Quaternion result = { 0 }; - - 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; -} - -// Scale quaternion by float value -RMDEF Quaternion QuaternionScale(Quaternion q, float mul) -{ - Quaternion result = { 0 }; - - float qax = q.x, qay = q.y, qaz = q.z, qaw = q.w; - - result.x = qax * mul + qaw * mul + qay * mul - qaz * mul; - result.y = qay * mul + qaw * mul + qaz * mul - qax * mul; - result.z = qaz * mul + qaw * mul + qax * mul - qay * mul; - result.w = qaw * mul - qax * mul - qay * mul - qaz * mul; - - return result; -} - -// Divide two quaternions -RMDEF Quaternion QuaternionDivide(Quaternion q1, Quaternion q2) -{ - Quaternion result = {q1.x / q2.x, q1.y / q2.y, q1.z / q2.z, q1.w / q2.w}; - return result; -} - -// Calculate linear interpolation between two quaternions -RMDEF Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = { 0 }; - - result.x = q1.x + amount*(q2.x - q1.x); - result.y = q1.y + amount*(q2.y - q1.y); - result.z = q1.z + amount*(q2.z - q1.z); - result.w = q1.w + amount*(q2.w - q1.w); - - return result; -} - -// Calculate slerp-optimized interpolation between two quaternions -RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = QuaternionLerp(q1, q2, amount); - result = QuaternionNormalize(result); - - return result; -} - -// Calculates spherical linear interpolation between two quaternions -RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount) -{ - Quaternion result = { 0 }; - - 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 if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount); - else - { - float halfTheta = acosf(cosHalfTheta); - float sinHalfTheta = sqrtf(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 = sinf((1 - amount)*halfTheta)/sinHalfTheta; - float ratioB = sinf(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; -} - -// Calculate quaternion based on the rotation from one vector to another -RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) -{ - Quaternion result = { 0 }; - - float cos2Theta = Vector3DotProduct(from, to); - Vector3 cross = Vector3CrossProduct(from, to); - - result.x = cross.x; - result.y = cross.y; - result.z = cross.y; - result.w = 1.0f + cos2Theta; // NOTE: Added QuaternioIdentity() - - // Normalize to essentially nlerp the original and identity to 0.5 - result = QuaternionNormalize(result); - - // Above lines are equivalent to: - //Quaternion result = QuaternionNlerp(q, QuaternionIdentity(), 0.5f); - - return result; -} - -// Returns a quaternion for a given rotation matrix -RMDEF Quaternion QuaternionFromMatrix(Matrix mat) -{ - Quaternion result = { 0 }; - - float trace = MatrixTrace(mat); - - if (trace > 0.0f) - { - float s = sqrtf(trace + 1)*2.0f; - float invS = 1.0f/s; - - result.w = s*0.25f; - result.x = (mat.m6 - mat.m9)*invS; - result.y = (mat.m8 - mat.m2)*invS; - result.z = (mat.m1 - mat.m4)*invS; - } - else - { - float m00 = mat.m0, m11 = mat.m5, m22 = mat.m10; - - if (m00 > m11 && m00 > m22) - { - float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m6 - mat.m9)*invS; - result.x = s*0.25f; - result.y = (mat.m4 + mat.m1)*invS; - result.z = (mat.m8 + mat.m2)*invS; - } - else if (m11 > m22) - { - float s = sqrtf(1.0f + m11 - m00 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m8 - mat.m2)*invS; - result.x = (mat.m4 + mat.m1)*invS; - result.y = s*0.25f; - result.z = (mat.m9 + mat.m6)*invS; - } - else - { - float s = sqrtf(1.0f + m22 - m00 - m11)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m1 - mat.m4)*invS; - result.x = (mat.m8 + mat.m2)*invS; - result.y = (mat.m9 + mat.m6)*invS; - result.z = s*0.25f; - } - } - - return result; -} - -// Returns a matrix for a given quaternion -RMDEF Matrix QuaternionToMatrix(Quaternion q) -{ - Matrix result = { 0 }; - - 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 length = QuaternionLength(q); - float lengthSquared = length*length; - - float xx = x*x2/lengthSquared; - float xy = x*y2/lengthSquared; - float xz = x*z2/lengthSquared; - - float yy = y*y2/lengthSquared; - float yz = y*z2/lengthSquared; - float zz = z*z2/lengthSquared; - - float wx = w*x2/lengthSquared; - float wy = w*y2/lengthSquared; - float wz = w*z2/lengthSquared; - - result.m0 = 1.0f - (yy + zz); - result.m1 = xy - wz; - result.m2 = xz + wy; - result.m3 = 0.0f; - result.m4 = xy + wz; - result.m5 = 1.0f - (xx + zz); - result.m6 = yz - wx; - result.m7 = 0.0f; - result.m8 = xz - wy; - result.m9 = yz + wx; - result.m10 = 1.0f - (xx + yy); - result.m11 = 0.0f; - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; - - return result; -} - -// Returns rotation quaternion for an angle and axis -// NOTE: angle must be provided in radians -RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle) -{ - Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; - - if (Vector3Length(axis) != 0.0f) - - angle *= 0.5f; - - axis = Vector3Normalize(axis); - - float sinres = sinf(angle); - float cosres = cosf(angle); - - result.x = axis.x*sinres; - result.y = axis.y*sinres; - result.z = axis.z*sinres; - result.w = cosres; - - result = QuaternionNormalize(result); - - return result; -} - -// Returns the rotation angle and axis for a given quaternion -RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle) -{ - if (fabs(q.w) > 1.0f) q = QuaternionNormalize(q); - - Vector3 resAxis = { 0.0f, 0.0f, 0.0f }; - float resAngle = 2.0f*acosf(q.w); - float den = sqrtf(1.0f - 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 = 1.0f; - } - - *outAxis = resAxis; - *outAngle = resAngle; -} - -// Returns he quaternion equivalent to Euler angles -RMDEF Quaternion QuaternionFromEuler(float roll, float pitch, float yaw) -{ - Quaternion q = { 0 }; - - float x0 = cosf(roll*0.5f); - float x1 = sinf(roll*0.5f); - float y0 = cosf(pitch*0.5f); - float y1 = sinf(pitch*0.5f); - float z0 = cosf(yaw*0.5f); - float z1 = sinf(yaw*0.5f); - - q.x = x1*y0*z0 - x0*y1*z1; - q.y = x0*y1*z0 + x1*y0*z1; - q.z = x0*y0*z1 - x1*y1*z0; - q.w = x0*y0*z0 + x1*y1*z1; - - return q; -} - -// Return the Euler angles equivalent to quaternion (roll, pitch, yaw) -// NOTE: Angles are returned in a Vector3 struct in degrees -RMDEF Vector3 QuaternionToEuler(Quaternion q) -{ - Vector3 result = { 0 }; - - // roll (x-axis rotation) - float x0 = 2.0f*(q.w*q.x + q.y*q.z); - float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y); - result.x = atan2f(x0, x1)*RAD2DEG; - - // pitch (y-axis rotation) - float y0 = 2.0f*(q.w*q.y - q.z*q.x); - y0 = y0 > 1.0f ? 1.0f : y0; - y0 = y0 < -1.0f ? -1.0f : y0; - result.y = asinf(y0)*RAD2DEG; - - // yaw (z-axis rotation) - float z0 = 2.0f*(q.w*q.z + q.x*q.y); - float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z); - result.z = atan2f(z0, z1)*RAD2DEG; - - return result; -} - -// Transform a quaternion given a transformation matrix -RMDEF Quaternion QuaternionTransform(Quaternion q, Matrix mat) -{ - Quaternion result = { 0 }; - - result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w; - result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w; - result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w; - result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w; - - return result; -} - -#endif // RAYMATH_H diff --git a/src/raymath.h b/src/raymath.h index b51573e72..893b7cf45 100644 --- a/src/raymath.h +++ b/src/raymath.h @@ -78,6 +78,8 @@ #define PI 3.14159265358979323846 #endif + + #ifndef DEG2RAD #define DEG2RAD (PI/180.0f) #endif @@ -926,6 +928,8 @@ RMDEF Matrix MatrixRotateZ(float angle) return result; } + + // Returns scaling matrix RMDEF Matrix MatrixScale(float x, float y, float z) { @@ -963,6 +967,17 @@ RMDEF Matrix MatrixMultiply(Matrix left, Matrix right) return result; } +// TODO suboptimal should be able to create this matrix in one go +// this is an aditional 3 matrix multiplies! +RMDEF Matrix MatrixRotateZYX(Vector3 v) +{ + Matrix result = MatrixRotateZ(v.z); + result = MatrixMultiply(result, MatrixRotateY(v.y)); + result = MatrixMultiply(result, MatrixRotateX(v.x)); + + return result; +} + // Returns perspective projection matrix RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far) { @@ -1297,105 +1312,53 @@ RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) } // Returns a quaternion for a given rotation matrix -RMDEF Quaternion QuaternionFromMatrix(Matrix mat) -{ - Quaternion result = { 0 }; - - float trace = MatrixTrace(mat); - - if (trace > 0.0f) - { - float s = sqrtf(trace + 1)*2.0f; - float invS = 1.0f/s; - - result.w = s*0.25f; - result.x = (mat.m6 - mat.m9)*invS; - result.y = (mat.m8 - mat.m2)*invS; - result.z = (mat.m1 - mat.m4)*invS; - } - else - { - float m00 = mat.m0, m11 = mat.m5, m22 = mat.m10; - - if (m00 > m11 && m00 > m22) - { - float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m6 - mat.m9)*invS; - result.x = s*0.25f; - result.y = (mat.m4 + mat.m1)*invS; - result.z = (mat.m8 + mat.m2)*invS; - } - else if (m11 > m22) - { - float s = sqrtf(1.0f + m11 - m00 - m22)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m8 - mat.m2)*invS; - result.x = (mat.m4 + mat.m1)*invS; - result.y = s*0.25f; - result.z = (mat.m9 + mat.m6)*invS; - } - else - { - float s = sqrtf(1.0f + m22 - m00 - m11)*2.0f; - float invS = 1.0f/s; - - result.w = (mat.m1 - mat.m4)*invS; - result.x = (mat.m8 + mat.m2)*invS; - result.y = (mat.m9 + mat.m6)*invS; - result.z = s*0.25f; - } - } - - return result; +RMDEF Quaternion QuaternionFromMatrix(Matrix m) +{ + Quaternion q; + if ( m.m0 > m.m5 && m.m0 > m.m10 ) { + float s = sqrt( 1.0 + m.m0 - m.m5 - m.m10 ) * 2; + q.x = 0.25 * s; + q.y = (m.m4 + m.m1 ) / s; + q.z = (m.m2 + m.m8 ) / s; + q.w = (m.m9 - m.m6 ) / s; + } else if ( m.m5 > m.m10 ) { + float s = sqrt( 1.0 + m.m5 - m.m0 - m.m10 ) * 2; + q.x = (m.m4 + m.m1 ) / s; + q.y = 0.25 * s; + q.z = (m.m9 + m.m6 ) / s; + q.w = (m.m2 - m.m8 ) / s; + } else { + float s = sqrt( 1.0 + m.m10 - m.m0 - m.m5 ) * 2; + q.x = (m.m2 + m.m8 ) / s; + q.y = (m.m9 + m.m6 ) / s; + q.z = 0.25 * s; + q.w = (m.m4 - m.m1 ) / s; + } + return q; } // Returns a matrix for a given quaternion RMDEF Matrix QuaternionToMatrix(Quaternion q) { - Matrix result = { 0 }; - - 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 length = QuaternionLength(q); - float lengthSquared = length*length; - - float xx = x*x2/lengthSquared; - float xy = x*y2/lengthSquared; - float xz = x*z2/lengthSquared; - - float yy = y*y2/lengthSquared; - float yz = y*z2/lengthSquared; - float zz = z*z2/lengthSquared; - - float wx = w*x2/lengthSquared; - float wy = w*y2/lengthSquared; - float wz = w*z2/lengthSquared; + Matrix m = MatrixIdentity(); + float a2=2*(q.x*q.x), b2=2*(q.y*q.y), c2=2*(q.z*q.z); //, d2=2*(q.w*q.w); + + float ab=2*(q.x*q.y), ac=2*(q.x*q.z), bc=2*(q.y*q.z); + float ad=2*(q.x*q.w), bd=2*(q.y*q.w), cd=2*(q.z*q.w); - result.m0 = 1.0f - (yy + zz); - result.m1 = xy - wz; - result.m2 = xz + wy; - result.m3 = 0.0f; - result.m4 = xy + wz; - result.m5 = 1.0f - (xx + zz); - result.m6 = yz - wx; - result.m7 = 0.0f; - result.m8 = xz - wy; - result.m9 = yz + wx; - result.m10 = 1.0f - (xx + yy); - result.m11 = 0.0f; - result.m12 = 0.0f; - result.m13 = 0.0f; - result.m14 = 0.0f; - result.m15 = 1.0f; + m.m0 = 1 - b2 - c2; + m.m1 = ab - cd; + m.m2 = ac + bd; + + m.m4 = ab + cd; + m.m5 = 1 - a2 - c2; + m.m6 = bc - ad; + + m.m8 = ac - bd; + m.m9 = bc + ad; + m.m10 = 1 - a2 - b2; - return result; + return m; } // Returns rotation quaternion for an angle and axis