1368 lines
43 KiB
C
1368 lines
43 KiB
C
/**********************************************************************************************
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*
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* raymath v1.1 - Math functions to work with Vector3, Matrix and Quaternions
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*
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* CONFIGURATION:
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*
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* #define RAYMATH_IMPLEMENTATION
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* Generates the implementation of the library into the included file.
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* If not defined, the library is in header only mode and can be included in other headers
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* or source files without problems. But only ONE file should hold the implementation.
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*
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* #define RAYMATH_EXTERN_INLINE
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* Inlines all functions code, so it runs faster. This requires lots of memory on system.
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*
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* #define RAYMATH_STANDALONE
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* Avoid raylib.h header inclusion in this file.
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* Vector3 and Matrix data types are defined internally in raymath module.
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*
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*
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* LICENSE: zlib/libpng
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*
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* Copyright (c) 2015-2017 Ramon Santamaria (@raysan5)
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*
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* This software is provided "as-is", without any express or implied warranty. In no event
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* will the authors be held liable for any damages arising from the use of this software.
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*
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* Permission is granted to anyone to use this software for any purpose, including commercial
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* applications, and to alter it and redistribute it freely, subject to the following restrictions:
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*
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* 1. The origin of this software must not be misrepresented; you must not claim that you
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* wrote the original software. If you use this software in a product, an acknowledgment
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* in the product documentation would be appreciated but is not required.
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*
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* 2. Altered source versions must be plainly marked as such, and must not be misrepresented
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* as being the original software.
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*
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* 3. This notice may not be removed or altered from any source distribution.
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*
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**********************************************************************************************/
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#ifndef RAYMATH_H
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#define RAYMATH_H
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//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line
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//#define RAYMATH_EXTERN_INLINE // NOTE: To compile functions as static inline, uncomment this line
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#ifndef RAYMATH_STANDALONE
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#include "raylib.h" // Required for structs: Vector3, Matrix
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#endif
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#ifdef __cplusplus
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#define RMEXTERN extern "C" // Functions visible from other files (no name mangling of functions in C++)
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#else
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#define RMEXTERN extern // Functions visible from other files
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#endif
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#if defined(RAYMATH_EXTERN_INLINE)
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#define RMDEF RMEXTERN inline // Functions are embeded inline (compiler generated code)
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#else
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#define RMDEF RMEXTERN
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#endif
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//----------------------------------------------------------------------------------
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// Defines and Macros
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//----------------------------------------------------------------------------------
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#ifndef PI
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#define PI 3.14159265358979323846
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#endif
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#ifndef DEG2RAD
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#define DEG2RAD (PI/180.0f)
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#endif
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#ifndef RAD2DEG
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#define RAD2DEG (180.0f/PI)
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#endif
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//----------------------------------------------------------------------------------
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// Types and Structures Definition
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//----------------------------------------------------------------------------------
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#if defined(RAYMATH_STANDALONE)
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// Vector2 type
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typedef struct Vector2 {
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float x;
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float y;
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} Vector2;
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// Vector3 type
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typedef struct Vector3 {
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float x;
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float y;
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float z;
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} Vector3;
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// Matrix type (OpenGL style 4x4 - right handed, column major)
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typedef struct Matrix {
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float m0, m4, m8, m12;
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float m1, m5, m9, m13;
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float m2, m6, m10, m14;
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float m3, m7, m11, m15;
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} Matrix;
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#endif
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// Quaternion type
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typedef struct Quaternion {
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float x;
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float y;
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float z;
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float w;
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} Quaternion;
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#ifndef RAYMATH_EXTERN_INLINE
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//------------------------------------------------------------------------------------
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// Functions Declaration - math utils
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//------------------------------------------------------------------------------------
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RMDEF float Clamp(float value, float min, float max); // Clamp float value
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//------------------------------------------------------------------------------------
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// Functions Declaration to work with Vector2
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//------------------------------------------------------------------------------------
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RMDEF Vector2 Vector2Zero(void); // Vector with components value 0.0f
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RMDEF Vector2 Vector2One(void); // Vector with components value 1.0f
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RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2); // Add two vectors (v1 + v2)
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RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2); // Subtract two vectors (v1 - v2)
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RMDEF float Vector2Length(Vector2 v); // Calculate vector length
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RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2); // Calculate two vectors dot product
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RMDEF float Vector2Distance(Vector2 v1, Vector2 v2); // Calculate distance between two vectors
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RMDEF float Vector2Angle(Vector2 v1, Vector2 v2); // Calculate angle between two vectors in X-axis
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RMDEF void Vector2Scale(Vector2 *v, float scale); // Scale vector (multiply by value)
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RMDEF void Vector2Negate(Vector2 *v); // Negate vector
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RMDEF void Vector2Divide(Vector2 *v, float div); // Divide vector by a float value
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RMDEF void Vector2Normalize(Vector2 *v); // Normalize provided vector
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//------------------------------------------------------------------------------------
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// Functions Declaration to work with Vector3
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//------------------------------------------------------------------------------------
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RMDEF Vector3 Vector3Zero(void); // Vector with components value 0.0f
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RMDEF Vector3 Vector3One(void); // Vector with components value 1.0f
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RMDEF Vector3 Vector3Add(Vector3 v1, Vector3 v2); // Add two vectors
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RMDEF Vector3 Vector3Multiply(Vector3 v, float scalar); // Multiply vector by scalar
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RMDEF Vector3 Vector3MultiplyV(Vector3 v1, Vector3 v2); // Multiply vector by vector
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RMDEF Vector3 Vector3Subtract(Vector3 v1, Vector3 v2); // Substract two vectors
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RMDEF Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2); // Calculate two vectors cross product
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RMDEF Vector3 Vector3Perpendicular(Vector3 v); // Calculate one vector perpendicular vector
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RMDEF float Vector3Length(const Vector3 v); // Calculate vector length
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RMDEF float Vector3DotProduct(Vector3 v1, Vector3 v2); // Calculate two vectors dot product
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RMDEF float Vector3Distance(Vector3 v1, Vector3 v2); // Calculate distance between two points
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RMDEF void Vector3Scale(Vector3 *v, float scale); // Scale provided vector
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RMDEF void Vector3Negate(Vector3 *v); // Negate provided vector (invert direction)
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RMDEF void Vector3Normalize(Vector3 *v); // Normalize provided vector
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RMDEF void Vector3Transform(Vector3 *v, Matrix mat); // Transforms a Vector3 by a given Matrix
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RMDEF Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount); // Calculate linear interpolation between two vectors
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RMDEF Vector3 Vector3Reflect(Vector3 vector, Vector3 normal); // Calculate reflected vector to normal
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RMDEF Vector3 Vector3Min(Vector3 vec1, Vector3 vec2); // Return min value for each pair of components
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RMDEF Vector3 Vector3Max(Vector3 vec1, Vector3 vec2); // Return max value for each pair of components
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RMDEF Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c); // Barycenter coords for p in triangle abc
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RMDEF float *Vector3ToFloat(Vector3 vec); // Returns Vector3 as float array
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//------------------------------------------------------------------------------------
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// Functions Declaration to work with Matrix
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//------------------------------------------------------------------------------------
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RMDEF float MatrixDeterminant(Matrix mat); // Compute matrix determinant
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RMDEF float MatrixTrace(Matrix mat); // Returns the trace of the matrix (sum of the values along the diagonal)
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RMDEF void MatrixTranspose(Matrix *mat); // Transposes provided matrix
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RMDEF void MatrixInvert(Matrix *mat); // Invert provided matrix
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RMDEF void MatrixNormalize(Matrix *mat); // Normalize provided matrix
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RMDEF Matrix MatrixIdentity(void); // Returns identity matrix
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RMDEF Matrix MatrixAdd(Matrix left, Matrix right); // Add two matrices
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RMDEF Matrix MatrixSubstract(Matrix left, Matrix right); // Substract two matrices (left - right)
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RMDEF Matrix MatrixTranslate(float x, float y, float z); // Returns translation matrix
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RMDEF Matrix MatrixRotate(Vector3 axis, float angle); // Returns rotation matrix for an angle around an specified axis (angle in radians)
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RMDEF Matrix MatrixRotateX(float angle); // Returns x-rotation matrix (angle in radians)
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RMDEF Matrix MatrixRotateY(float angle); // Returns y-rotation matrix (angle in radians)
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RMDEF Matrix MatrixRotateZ(float angle); // Returns z-rotation matrix (angle in radians)
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RMDEF Matrix MatrixScale(float x, float y, float z); // Returns scaling matrix
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RMDEF Matrix MatrixMultiply(Matrix left, Matrix right); // Returns two matrix multiplication
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RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far); // Returns perspective projection matrix
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RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far); // Returns perspective projection matrix
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RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far); // Returns orthographic projection matrix
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RMDEF Matrix MatrixLookAt(Vector3 position, Vector3 target, Vector3 up); // Returns camera look-at matrix (view matrix)
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RMDEF float *MatrixToFloat(Matrix mat); // Returns float array of Matrix data
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//------------------------------------------------------------------------------------
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// Functions Declaration to work with Quaternions
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//------------------------------------------------------------------------------------
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RMDEF Quaternion QuaternionIdentity(void); // Returns identity quaternion
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RMDEF float QuaternionLength(Quaternion quat); // Compute the length of a quaternion
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RMDEF void QuaternionNormalize(Quaternion *q); // Normalize provided quaternion
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RMDEF void QuaternionInvert(Quaternion *quat); // Invert provided quaternion
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RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2); // Calculate two quaternion multiplication
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RMDEF Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount); // Calculate linear interpolation between two quaternions
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RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount); // Calculates spherical linear interpolation between two quaternions
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RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount); // Calculate slerp-optimized interpolation between two quaternions
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RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to); // Calculate quaternion based on the rotation from one vector to another
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RMDEF Quaternion QuaternionFromMatrix(Matrix matrix); // Returns a quaternion for a given rotation matrix
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RMDEF Matrix QuaternionToMatrix(Quaternion q); // Returns a matrix for a given quaternion
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RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle); // Returns rotation quaternion for an angle and axis
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RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle); // Returns the rotation angle and axis for a given quaternion
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RMDEF Quaternion QuaternionFromEuler(float roll, float pitch, float yaw); // Returns he quaternion equivalent to Euler angles
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RMDEF Vector3 QuaternionToEuler(Quaternion q); // Return the Euler angles equivalent to quaternion (roll, pitch, yaw)
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RMDEF void QuaternionTransform(Quaternion *q, Matrix mat); // Transform a quaternion given a transformation matrix
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#endif // notdef RAYMATH_EXTERN_INLINE
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#endif // RAYMATH_H
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//////////////////////////////////////////////////////////////////// end of header file
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#if defined(RAYMATH_IMPLEMENTATION) || defined(RAYMATH_EXTERN_INLINE)
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#include <math.h> // Required for: sinf(), cosf(), tan(), fabs()
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//----------------------------------------------------------------------------------
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// Module Functions Definition - Utils math
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//----------------------------------------------------------------------------------
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// Clamp float value
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RMDEF float Clamp(float value, float min, float max)
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{
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const float res = value < min ? min : value;
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return res > max ? max : res;
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}
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//----------------------------------------------------------------------------------
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// Module Functions Definition - Vector2 math
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//----------------------------------------------------------------------------------
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// Vector with components value 0.0f
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RMDEF Vector2 Vector2Zero(void) { return (Vector2){ 0.0f, 0.0f }; }
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// Vector with components value 1.0f
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RMDEF Vector2 Vector2One(void) { return (Vector2){ 1.0f, 1.0f }; }
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// Add two vectors (v1 + v2)
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RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2)
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{
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return (Vector2){ v1.x + v2.x, v1.y + v2.y };
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}
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// Subtract two vectors (v1 - v2)
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RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2)
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{
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return (Vector2){ v1.x - v2.x, v1.y - v2.y };
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}
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// Calculate vector length
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RMDEF float Vector2Length(Vector2 v)
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{
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return sqrtf((v.x*v.x) + (v.y*v.y));
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}
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// Calculate two vectors dot product
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RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2)
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{
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return (v1.x*v2.x + v1.y*v2.y);
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}
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// Calculate distance between two vectors
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RMDEF float Vector2Distance(Vector2 v1, Vector2 v2)
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{
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return sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
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}
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// Calculate angle from two vectors in X-axis
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RMDEF float Vector2Angle(Vector2 v1, Vector2 v2)
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{
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float angle = atan2f(v2.y - v1.y, v2.x - v1.x)*(180.0f/PI);
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if (angle < 0) angle += 360.0f;
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return angle;
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}
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// Scale vector (multiply by value)
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RMDEF void Vector2Scale(Vector2 *v, float scale)
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{
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v->x *= scale;
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v->y *= scale;
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}
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// Negate vector
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RMDEF void Vector2Negate(Vector2 *v)
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{
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v->x = -v->x;
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v->y = -v->y;
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}
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// Divide vector by a float value
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RMDEF void Vector2Divide(Vector2 *v, float div)
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{
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*v = (Vector2){v->x/div, v->y/div};
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}
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// Normalize provided vector
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RMDEF void Vector2Normalize(Vector2 *v)
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{
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Vector2Divide(v, Vector2Length(*v));
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}
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//----------------------------------------------------------------------------------
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// Module Functions Definition - Vector3 math
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//----------------------------------------------------------------------------------
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// Vector with components value 0.0f
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RMDEF Vector3 Vector3Zero(void) { return (Vector3){ 0.0f, 0.0f, 0.0f }; }
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// Vector with components value 1.0f
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RMDEF Vector3 Vector3One(void) { return (Vector3){ 1.0f, 1.0f, 1.0f }; }
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// Add two vectors
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RMDEF Vector3 Vector3Add(Vector3 v1, Vector3 v2)
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{
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return (Vector3){ v1.x + v2.x, v1.y + v2.y, v1.z + v2.z };
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}
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// Substract two vectors
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RMDEF Vector3 Vector3Subtract(Vector3 v1, Vector3 v2)
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{
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return (Vector3){ v1.x - v2.x, v1.y - v2.y, v1.z - v2.z };
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}
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// Multiply vector by scalar
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RMDEF Vector3 Vector3Multiply(Vector3 v, float scalar)
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{
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v.x *= scalar;
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v.y *= scalar;
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v.z *= scalar;
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return v;
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}
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// Multiply vector by vector
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RMDEF Vector3 Vector3MultiplyV(Vector3 v1, Vector3 v2)
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{
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Vector3 result;
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result.x = v1.x * v2.x;
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result.y = v1.y * v2.y;
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result.z = v1.z * v2.z;
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return result;
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}
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// Calculate two vectors cross product
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RMDEF Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2)
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{
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Vector3 result;
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result.x = v1.y*v2.z - v1.z*v2.y;
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result.y = v1.z*v2.x - v1.x*v2.z;
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result.z = v1.x*v2.y - v1.y*v2.x;
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return result;
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}
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// Calculate one vector perpendicular vector
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RMDEF Vector3 Vector3Perpendicular(Vector3 v)
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{
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Vector3 result;
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float min = fabsf(v.x);
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Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f};
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if (fabsf(v.y) < min)
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{
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min = fabsf(v.y);
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cardinalAxis = (Vector3){0.0f, 1.0f, 0.0f};
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}
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if (fabsf(v.z) < min)
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{
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cardinalAxis = (Vector3){0.0f, 0.0f, 1.0f};
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}
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result = Vector3CrossProduct(v, cardinalAxis);
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return result;
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}
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// Calculate vector length
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RMDEF float Vector3Length(const Vector3 v)
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{
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return sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
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}
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// Calculate two vectors dot product
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RMDEF float Vector3DotProduct(Vector3 v1, Vector3 v2)
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{
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return (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
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}
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// Calculate distance between two vectors
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RMDEF float Vector3Distance(Vector3 v1, Vector3 v2)
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{
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float dx = v2.x - v1.x;
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float dy = v2.y - v1.y;
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float dz = v2.z - v1.z;
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return sqrtf(dx*dx + dy*dy + dz*dz);
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}
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// Scale provided vector
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RMDEF void Vector3Scale(Vector3 *v, float scale)
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{
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v->x *= scale;
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v->y *= scale;
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v->z *= scale;
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}
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// Negate provided vector (invert direction)
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RMDEF void Vector3Negate(Vector3 *v)
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{
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v->x = -v->x;
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v->y = -v->y;
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v->z = -v->z;
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}
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// Normalize provided vector
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RMDEF void Vector3Normalize(Vector3 *v)
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{
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float length, ilength;
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length = Vector3Length(*v);
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if (length == 0.0f) length = 1.0f;
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ilength = 1.0f/length;
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v->x *= ilength;
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v->y *= ilength;
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v->z *= ilength;
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}
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// Transforms a Vector3 by a given Matrix
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RMDEF void Vector3Transform(Vector3 *v, Matrix mat)
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{
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float x = v->x;
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float y = v->y;
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float z = v->z;
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v->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12;
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v->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13;
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v->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14;
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};
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// Calculate linear interpolation between two vectors
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RMDEF Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount)
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{
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Vector3 result;
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result.x = v1.x + amount*(v2.x - v1.x);
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result.y = v1.y + amount*(v2.y - v1.y);
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result.z = v1.z + amount*(v2.z - v1.z);
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return result;
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}
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// Calculate reflected vector to normal
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RMDEF Vector3 Vector3Reflect(Vector3 vector, Vector3 normal)
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{
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// I is the original vector
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// N is the normal of the incident plane
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// R = I - (2*N*( DotProduct[ I,N] ))
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Vector3 result;
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float dotProduct = Vector3DotProduct(vector, normal);
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result.x = vector.x - (2.0f*normal.x)*dotProduct;
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|
result.y = vector.y - (2.0f*normal.y)*dotProduct;
|
|
result.z = vector.z - (2.0f*normal.z)*dotProduct;
|
|
|
|
return result;
|
|
}
|
|
|
|
// Return min value for each pair of components
|
|
RMDEF Vector3 Vector3Min(Vector3 vec1, Vector3 vec2)
|
|
{
|
|
Vector3 result;
|
|
|
|
result.x = fminf(vec1.x, vec2.x);
|
|
result.y = fminf(vec1.y, vec2.y);
|
|
result.z = fminf(vec1.z, vec2.z);
|
|
|
|
return result;
|
|
}
|
|
|
|
// Return max value for each pair of components
|
|
RMDEF Vector3 Vector3Max(Vector3 vec1, Vector3 vec2)
|
|
{
|
|
Vector3 result;
|
|
|
|
result.x = fmaxf(vec1.x, vec2.x);
|
|
result.y = fmaxf(vec1.y, vec2.y);
|
|
result.z = fmaxf(vec1.z, vec2.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;
|
|
|
|
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 float *Vector3ToFloat(Vector3 vec)
|
|
{
|
|
static float buffer[3];
|
|
|
|
buffer[0] = vec.x;
|
|
buffer[1] = vec.y;
|
|
buffer[2] = vec.z;
|
|
|
|
return buffer;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// Module Functions Definition - Matrix math
|
|
//----------------------------------------------------------------------------------
|
|
|
|
// Compute matrix determinant
|
|
RMDEF float MatrixDeterminant(Matrix mat)
|
|
{
|
|
float result;
|
|
|
|
// Cache the matrix values (speed optimization)
|
|
float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
|
|
float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
|
|
float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
|
|
float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15;
|
|
|
|
result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 +
|
|
a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 +
|
|
a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 +
|
|
a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 +
|
|
a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 +
|
|
a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33;
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns the trace of the matrix (sum of the values along the diagonal)
|
|
RMDEF float MatrixTrace(Matrix mat)
|
|
{
|
|
return (mat.m0 + mat.m5 + mat.m10 + mat.m15);
|
|
}
|
|
|
|
// Transposes provided matrix
|
|
RMDEF void MatrixTranspose(Matrix *mat)
|
|
{
|
|
Matrix temp;
|
|
|
|
temp.m0 = mat->m0;
|
|
temp.m1 = mat->m4;
|
|
temp.m2 = mat->m8;
|
|
temp.m3 = mat->m12;
|
|
temp.m4 = mat->m1;
|
|
temp.m5 = mat->m5;
|
|
temp.m6 = mat->m9;
|
|
temp.m7 = mat->m13;
|
|
temp.m8 = mat->m2;
|
|
temp.m9 = mat->m6;
|
|
temp.m10 = mat->m10;
|
|
temp.m11 = mat->m14;
|
|
temp.m12 = mat->m3;
|
|
temp.m13 = mat->m7;
|
|
temp.m14 = mat->m11;
|
|
temp.m15 = mat->m15;
|
|
|
|
*mat = temp;
|
|
}
|
|
|
|
// Invert provided matrix
|
|
RMDEF void MatrixInvert(Matrix *mat)
|
|
{
|
|
Matrix temp;
|
|
|
|
// Cache the matrix values (speed optimization)
|
|
float a00 = mat->m0, a01 = mat->m1, a02 = mat->m2, a03 = mat->m3;
|
|
float a10 = mat->m4, a11 = mat->m5, a12 = mat->m6, a13 = mat->m7;
|
|
float a20 = mat->m8, a21 = mat->m9, a22 = mat->m10, a23 = mat->m11;
|
|
float a30 = mat->m12, a31 = mat->m13, a32 = mat->m14, a33 = mat->m15;
|
|
|
|
float b00 = a00*a11 - a01*a10;
|
|
float b01 = a00*a12 - a02*a10;
|
|
float b02 = a00*a13 - a03*a10;
|
|
float b03 = a01*a12 - a02*a11;
|
|
float b04 = a01*a13 - a03*a11;
|
|
float b05 = a02*a13 - a03*a12;
|
|
float b06 = a20*a31 - a21*a30;
|
|
float b07 = a20*a32 - a22*a30;
|
|
float b08 = a20*a33 - a23*a30;
|
|
float b09 = a21*a32 - a22*a31;
|
|
float b10 = a21*a33 - a23*a31;
|
|
float b11 = a22*a33 - a23*a32;
|
|
|
|
// Calculate the invert determinant (inlined to avoid double-caching)
|
|
float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
|
|
|
|
temp.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet;
|
|
temp.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet;
|
|
temp.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet;
|
|
temp.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet;
|
|
temp.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet;
|
|
temp.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet;
|
|
temp.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet;
|
|
temp.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet;
|
|
temp.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet;
|
|
temp.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet;
|
|
temp.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet;
|
|
temp.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet;
|
|
temp.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet;
|
|
temp.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet;
|
|
temp.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet;
|
|
temp.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet;
|
|
|
|
*mat = temp;
|
|
}
|
|
|
|
// Normalize provided matrix
|
|
RMDEF void MatrixNormalize(Matrix *mat)
|
|
{
|
|
float det = MatrixDeterminant(*mat);
|
|
|
|
mat->m0 /= det;
|
|
mat->m1 /= det;
|
|
mat->m2 /= det;
|
|
mat->m3 /= det;
|
|
mat->m4 /= det;
|
|
mat->m5 /= det;
|
|
mat->m6 /= det;
|
|
mat->m7 /= det;
|
|
mat->m8 /= det;
|
|
mat->m9 /= det;
|
|
mat->m10 /= det;
|
|
mat->m11 /= det;
|
|
mat->m12 /= det;
|
|
mat->m13 /= det;
|
|
mat->m14 /= det;
|
|
mat->m15 /= det;
|
|
}
|
|
|
|
// Returns identity matrix
|
|
RMDEF Matrix MatrixIdentity(void)
|
|
{
|
|
Matrix result = { 1.0f, 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;
|
|
}
|
|
|
|
// Substract two matrices (left - right)
|
|
RMDEF Matrix MatrixSubstract(Matrix left, Matrix right)
|
|
{
|
|
Matrix result = MatrixIdentity();
|
|
|
|
result.m0 = left.m0 - right.m0;
|
|
result.m1 = left.m1 - right.m1;
|
|
result.m2 = left.m2 - right.m2;
|
|
result.m3 = left.m3 - right.m3;
|
|
result.m4 = left.m4 - right.m4;
|
|
result.m5 = left.m5 - right.m5;
|
|
result.m6 = left.m6 - right.m6;
|
|
result.m7 = left.m7 - right.m7;
|
|
result.m8 = left.m8 - right.m8;
|
|
result.m9 = left.m9 - right.m9;
|
|
result.m10 = left.m10 - right.m10;
|
|
result.m11 = left.m11 - right.m11;
|
|
result.m12 = left.m12 - right.m12;
|
|
result.m13 = left.m13 - right.m13;
|
|
result.m14 = left.m14 - right.m14;
|
|
result.m15 = left.m15 - right.m15;
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns translation matrix
|
|
RMDEF Matrix MatrixTranslate(float x, float y, float z)
|
|
{
|
|
Matrix result = { 1.0f, 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;
|
|
|
|
Matrix mat = MatrixIdentity();
|
|
|
|
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;
|
|
|
|
// Cache some matrix values (speed optimization)
|
|
float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
|
|
float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
|
|
float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
|
|
|
|
// Construct the elements of the rotation matrix
|
|
float b00 = x*x*t + cosres, b01 = y*x*t + z*sinres, b02 = z*x*t - y*sinres;
|
|
float b10 = x*y*t - z*sinres, b11 = y*y*t + cosres, b12 = z*y*t + x*sinres;
|
|
float b20 = x*z*t + y*sinres, b21 = y*z*t - x*sinres, b22 = z*z*t + cosres;
|
|
|
|
// Perform rotation-specific matrix multiplication
|
|
result.m0 = a00*b00 + a10*b01 + a20*b02;
|
|
result.m1 = a01*b00 + a11*b01 + a21*b02;
|
|
result.m2 = a02*b00 + a12*b01 + a22*b02;
|
|
result.m3 = a03*b00 + a13*b01 + a23*b02;
|
|
result.m4 = a00*b10 + a10*b11 + a20*b12;
|
|
result.m5 = a01*b10 + a11*b11 + a21*b12;
|
|
result.m6 = a02*b10 + a12*b11 + a22*b12;
|
|
result.m7 = a03*b10 + a13*b11 + a23*b12;
|
|
result.m8 = a00*b20 + a10*b21 + a20*b22;
|
|
result.m9 = a01*b20 + a11*b21 + a21*b22;
|
|
result.m10 = a02*b20 + a12*b21 + a22*b22;
|
|
result.m11 = a03*b20 + a13*b21 + a23*b22;
|
|
result.m12 = mat.m12;
|
|
result.m13 = mat.m13;
|
|
result.m14 = mat.m14;
|
|
result.m15 = mat.m15;
|
|
|
|
return result;
|
|
}
|
|
|
|
// 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;
|
|
|
|
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;
|
|
|
|
float rl = (right - left);
|
|
float tb = (top - bottom);
|
|
float fn = (far - near);
|
|
|
|
result.m0 = (near*2.0f)/rl;
|
|
result.m1 = 0.0f;
|
|
result.m2 = 0.0f;
|
|
result.m3 = 0.0f;
|
|
|
|
result.m4 = 0.0f;
|
|
result.m5 = (near*2.0f)/tb;
|
|
result.m6 = 0.0f;
|
|
result.m7 = 0.0f;
|
|
|
|
result.m8 = (right + left)/rl;
|
|
result.m9 = (top + bottom)/tb;
|
|
result.m10 = -(far + near)/fn;
|
|
result.m11 = -1.0f;
|
|
|
|
result.m12 = 0.0f;
|
|
result.m13 = 0.0f;
|
|
result.m14 = -(far*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;
|
|
|
|
return MatrixFrustum(-right, right, -top, top, near, far);
|
|
}
|
|
|
|
// Returns orthographic projection matrix
|
|
RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far)
|
|
{
|
|
Matrix result;
|
|
|
|
float rl = (right - left);
|
|
float tb = (top - bottom);
|
|
float fn = (far - near);
|
|
|
|
result.m0 = 2.0f/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 = -(left + right)/rl;
|
|
result.m13 = -(top + bottom)/tb;
|
|
result.m14 = -(far + 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;
|
|
|
|
Vector3 z = Vector3Subtract(eye, target);
|
|
Vector3Normalize(&z);
|
|
Vector3 x = Vector3CrossProduct(up, z);
|
|
Vector3Normalize(&x);
|
|
Vector3 y = Vector3CrossProduct(z, x);
|
|
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;
|
|
|
|
MatrixInvert(&result);
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns float array of matrix data
|
|
RMDEF float *MatrixToFloat(Matrix mat)
|
|
{
|
|
static float buffer[16];
|
|
|
|
buffer[0] = mat.m0;
|
|
buffer[1] = mat.m1;
|
|
buffer[2] = mat.m2;
|
|
buffer[3] = mat.m3;
|
|
buffer[4] = mat.m4;
|
|
buffer[5] = mat.m5;
|
|
buffer[6] = mat.m6;
|
|
buffer[7] = mat.m7;
|
|
buffer[8] = mat.m8;
|
|
buffer[9] = mat.m9;
|
|
buffer[10] = mat.m10;
|
|
buffer[11] = mat.m11;
|
|
buffer[12] = mat.m12;
|
|
buffer[13] = mat.m13;
|
|
buffer[14] = mat.m14;
|
|
buffer[15] = mat.m15;
|
|
|
|
return buffer;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// Module Functions Definition - Quaternion math
|
|
//----------------------------------------------------------------------------------
|
|
|
|
// Returns identity quaternion
|
|
RMDEF Quaternion QuaternionIdentity(void)
|
|
{
|
|
return (Quaternion){ 0.0f, 0.0f, 0.0f, 1.0f };
|
|
}
|
|
|
|
// Computes the length of a quaternion
|
|
RMDEF float QuaternionLength(Quaternion quat)
|
|
{
|
|
return sqrt(quat.x*quat.x + quat.y*quat.y + quat.z*quat.z + quat.w*quat.w);
|
|
}
|
|
|
|
// Normalize provided quaternion
|
|
RMDEF void QuaternionNormalize(Quaternion *q)
|
|
{
|
|
float length, ilength;
|
|
|
|
length = QuaternionLength(*q);
|
|
|
|
if (length == 0.0f) length = 1.0f;
|
|
|
|
ilength = 1.0f/length;
|
|
|
|
q->x *= ilength;
|
|
q->y *= ilength;
|
|
q->z *= ilength;
|
|
q->w *= ilength;
|
|
}
|
|
|
|
// Invert provided quaternion
|
|
RMDEF void QuaternionInvert(Quaternion *quat)
|
|
{
|
|
float length = QuaternionLength(*quat);
|
|
float lengthSq = length*length;
|
|
|
|
if (lengthSq != 0.0)
|
|
{
|
|
float i = 1.0f/lengthSq;
|
|
|
|
quat->x *= -i;
|
|
quat->y *= -i;
|
|
quat->z *= -i;
|
|
quat->w *= i;
|
|
}
|
|
}
|
|
|
|
// Calculate two quaternion multiplication
|
|
RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2)
|
|
{
|
|
Quaternion result;
|
|
|
|
float qax = q1.x, qay = q1.y, qaz = q1.z, qaw = q1.w;
|
|
float qbx = q2.x, qby = q2.y, qbz = q2.z, qbw = q2.w;
|
|
|
|
result.x = qax*qbw + qaw*qbx + qay*qbz - qaz*qby;
|
|
result.y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz;
|
|
result.z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx;
|
|
result.w = qaw*qbw - qax*qbx - qay*qby - qaz*qbz;
|
|
|
|
return result;
|
|
}
|
|
|
|
// Calculate linear interpolation between two quaternions
|
|
RMDEF Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount)
|
|
{
|
|
Quaternion result;
|
|
|
|
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;
|
|
}
|
|
|
|
// Calculates spherical linear interpolation between two quaternions
|
|
RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
|
|
{
|
|
Quaternion result;
|
|
|
|
float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w;
|
|
|
|
if (fabs(cosHalfTheta) >= 1.0f) result = q1;
|
|
else if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount);
|
|
else
|
|
{
|
|
float halfTheta = acos(cosHalfTheta);
|
|
float sinHalfTheta = sqrt(1.0f - cosHalfTheta*cosHalfTheta);
|
|
|
|
if (fabs(sinHalfTheta) < 0.001f)
|
|
{
|
|
result.x = (q1.x*0.5f + q2.x*0.5f);
|
|
result.y = (q1.y*0.5f + q2.y*0.5f);
|
|
result.z = (q1.z*0.5f + q2.z*0.5f);
|
|
result.w = (q1.w*0.5f + q2.w*0.5f);
|
|
}
|
|
else
|
|
{
|
|
float ratioA = 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 slerp-optimized interpolation between two quaternions
|
|
RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount)
|
|
{
|
|
Quaternion result = QuaternionLerp(q1, q2, amount);
|
|
QuaternionNormalize(&result);
|
|
|
|
return result;
|
|
}
|
|
|
|
// Calculate quaternion based on the rotation from one vector to another
|
|
RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to)
|
|
{
|
|
Quaternion q = { 0 };
|
|
|
|
float cos2Theta = Vector3DotProduct(from, to);
|
|
Vector3 cross = Vector3CrossProduct(from, to);
|
|
|
|
q.x = cross.x;
|
|
q.y = cross.y;
|
|
q.z = cross.y;
|
|
q.w = 1.0f + cos2Theta; // NOTE: Added QuaternioIdentity()
|
|
|
|
// Normalize to essentially nlerp the original and identity to 0.5
|
|
QuaternionNormalize(&q);
|
|
|
|
// Above lines are equivalent to:
|
|
//Quaternion result = QuaternionNlerp(q, QuaternionIdentity(), 0.5f);
|
|
|
|
return q;
|
|
}
|
|
|
|
// Returns a quaternion for a given rotation matrix
|
|
RMDEF Quaternion QuaternionFromMatrix(Matrix matrix)
|
|
{
|
|
Quaternion result;
|
|
|
|
float trace = MatrixTrace(matrix);
|
|
|
|
if (trace > 0.0f)
|
|
{
|
|
float s = (float)sqrt(trace + 1)*2.0f;
|
|
float invS = 1.0f/s;
|
|
|
|
result.w = s*0.25f;
|
|
result.x = (matrix.m6 - matrix.m9)*invS;
|
|
result.y = (matrix.m8 - matrix.m2)*invS;
|
|
result.z = (matrix.m1 - matrix.m4)*invS;
|
|
}
|
|
else
|
|
{
|
|
float m00 = matrix.m0, m11 = matrix.m5, m22 = matrix.m10;
|
|
|
|
if (m00 > m11 && m00 > m22)
|
|
{
|
|
float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f;
|
|
float invS = 1.0f/s;
|
|
|
|
result.w = (matrix.m6 - matrix.m9)*invS;
|
|
result.x = s*0.25f;
|
|
result.y = (matrix.m4 + matrix.m1)*invS;
|
|
result.z = (matrix.m8 + matrix.m2)*invS;
|
|
}
|
|
else if (m11 > m22)
|
|
{
|
|
float s = (float)sqrt(1.0f + m11 - m00 - m22)*2.0f;
|
|
float invS = 1.0f/s;
|
|
|
|
result.w = (matrix.m8 - matrix.m2)*invS;
|
|
result.x = (matrix.m4 + matrix.m1)*invS;
|
|
result.y = s*0.25f;
|
|
result.z = (matrix.m9 + matrix.m6)*invS;
|
|
}
|
|
else
|
|
{
|
|
float s = (float)sqrt(1.0f + m22 - m00 - m11)*2.0f;
|
|
float invS = 1.0f/s;
|
|
|
|
result.w = (matrix.m1 - matrix.m4)*invS;
|
|
result.x = (matrix.m8 + matrix.m2)*invS;
|
|
result.y = (matrix.m9 + matrix.m6)*invS;
|
|
result.z = s*0.25f;
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
// Returns a matrix for a given quaternion
|
|
RMDEF Matrix QuaternionToMatrix(Quaternion q)
|
|
{
|
|
Matrix result;
|
|
|
|
float x = q.x, y = q.y, z = q.z, w = q.w;
|
|
|
|
float x2 = x + x;
|
|
float y2 = y + y;
|
|
float z2 = z + z;
|
|
|
|
float 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;
|
|
|
|
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;
|
|
|
|
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) QuaternionNormalize(&q);
|
|
|
|
Vector3 resAxis = { 0.0f, 0.0f, 0.0f };
|
|
float resAngle = 0.0f;
|
|
|
|
resAngle = 2.0f*(float)acos(q.w);
|
|
float den = (float)sqrt(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 v = { 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);
|
|
v.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;
|
|
v.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);
|
|
v.z = atan2f(z0, z1)*RAD2DEG;
|
|
|
|
return v;
|
|
}
|
|
|
|
// Transform a quaternion given a transformation matrix
|
|
RMDEF void QuaternionTransform(Quaternion *q, Matrix mat)
|
|
{
|
|
float x = q->x;
|
|
float y = q->y;
|
|
float z = q->z;
|
|
float w = q->w;
|
|
|
|
q->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12*w;
|
|
q->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13*w;
|
|
q->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14*w;
|
|
q->w = mat.m3*x + mat.m7*y + mat.m11*z + mat.m15*w;
|
|
}
|
|
|
|
#endif // RAYMATH_IMPLEMENTATION
|