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raylib-src/src/raymath.h

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/**********************************************************************************************
*
* raymath v2.0 - Math functions to work with Vector2, Vector3, Matrix and Quaternions
*
* CONVENTIONS:
* - Matrix structure is defined as row-major (memory layout) but parameters naming AND all
* math operations performed by the library consider the structure as it was column-major
* It is like transposed versions of the matrices are used for all the maths
* It benefits some functions making them cache-friendly and also avoids matrix
* transpositions sometimes required by OpenGL
* Example: In memory order, row0 is [m0 m4 m8 m12] but in semantic math row0 is [m0 m1 m2 m3]
* - Functions are always self-contained, no function use another raymath function inside,
* required code is directly re-implemented inside
* - Functions input parameters are always received by value (2 unavoidable exceptions)
* - Functions use always a "result" variable for return (except C++ operators)
* - Functions are always defined inline
* - Angles are always in radians (DEG2RAD/RAD2DEG macros provided for convenience)
* - No compound literals used to make sure libray is compatible with C++
*
* 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_STATIC_INLINE
* Define static inline functions code, so #include header suffices for use.
* This may use up lots of memory.
*
* #define RAYMATH_DISABLE_CPP_OPERATORS
* Disables C++ operator overloads for raymath types.
*
* LICENSE: zlib/libpng
*
* Copyright (c) 2015-2024 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
#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_STATIC_INLINE)
#error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_STATIC_INLINE is contradictory"
#endif
// Function specifiers definition
#if defined(RAYMATH_IMPLEMENTATION)
#if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED)
#define RMAPI __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll)
#elif defined(BUILD_LIBTYPE_SHARED)
#define RMAPI __attribute__((visibility("default"))) // We are building raylib as a Unix shared library (.so/.dylib)
#elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED)
#define RMAPI __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll)
#else
#define RMAPI extern inline // Provide external definition
#endif
#elif defined(RAYMATH_STATIC_INLINE)
#define RMAPI static inline // Functions may be inlined, no external out-of-line definition
#else
#if defined(__TINYC__)
#define RMAPI static inline // plain inline not supported by tinycc (See issue #435)
#else
#define RMAPI inline // Functions may be inlined or external definition used
#endif
#endif
//----------------------------------------------------------------------------------
// Defines and Macros
//----------------------------------------------------------------------------------
#ifndef PI
#define PI 3.14159265358979323846f
#endif
#ifndef EPSILON
#define EPSILON 0.000001f
#endif
#ifndef DEG2RAD
#define DEG2RAD (PI/180.0f)
#endif
#ifndef RAD2DEG
#define RAD2DEG (180.0f/PI)
#endif
// Get float vector for Matrix
#ifndef MatrixToFloat
#define MatrixToFloat(mat) (MatrixToFloatV(mat).v)
#endif
// Get float vector for Vector3
#ifndef Vector3ToFloat
#define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v)
#endif
//----------------------------------------------------------------------------------
// Types and Structures Definition
//----------------------------------------------------------------------------------
#if !defined(RL_VECTOR2_TYPE)
// Vector2 type
typedef struct Vector2 {
float x;
float y;
} Vector2;
#define RL_VECTOR2_TYPE
#endif
#if !defined(RL_VECTOR3_TYPE)
// Vector3 type
typedef struct Vector3 {
float x;
float y;
float z;
} Vector3;
#define RL_VECTOR3_TYPE
#endif
#if !defined(RL_VECTOR4_TYPE)
// Vector4 type
typedef struct Vector4 {
float x;
float y;
float z;
float w;
} Vector4;
#define RL_VECTOR4_TYPE
#endif
#if !defined(RL_QUATERNION_TYPE)
// Quaternion type
typedef Vector4 Quaternion;
#define RL_QUATERNION_TYPE
#endif
#if !defined(RL_MATRIX_TYPE)
// Matrix type (OpenGL style 4x4 - right handed, column major)
typedef struct Matrix {
float m0, m4, m8, m12; // Matrix first row (4 components)
float m1, m5, m9, m13; // Matrix second row (4 components)
float m2, m6, m10, m14; // Matrix third row (4 components)
float m3, m7, m11, m15; // Matrix fourth row (4 components)
} Matrix;
#define RL_MATRIX_TYPE
#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 <math.h> // Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), floor(), fminf(), fmaxf(), fabsf()
//----------------------------------------------------------------------------------
// Module Functions Definition - Utils math
//----------------------------------------------------------------------------------
// Clamp float value
RMAPI float Clamp(float value, float min, float max)
{
float result = (value < min)? min : value;
if (result > max) result = max;
return result;
}
// Calculate linear interpolation between two floats
RMAPI float Lerp(float start, float end, float amount)
{
float result = start + amount*(end - start);
return result;
}
// Normalize input value within input range
RMAPI float Normalize(float value, float start, float end)
{
float result = (value - start)/(end - start);
return result;
}
// Remap input value within input range to output range
RMAPI float Remap(float value, float inputStart, float inputEnd, float outputStart, float outputEnd)
{
float result = (value - inputStart)/(inputEnd - inputStart)*(outputEnd - outputStart) + outputStart;
return result;
}
// Wrap input value from min to max
RMAPI float Wrap(float value, float min, float max)
{
float result = value - (max - min)*floorf((value - min)/(max - min));
return result;
}
// Check whether two given floats are almost equal
RMAPI int FloatEquals(float x, float y)
{
#if !defined(EPSILON)
#define EPSILON 0.000001f
#endif
int result = (fabsf(x - y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(x), fabsf(y))));
return result;
}
//----------------------------------------------------------------------------------
// Module Functions Definition - Vector2 math
//----------------------------------------------------------------------------------
// Vector with components value 0.0f
RMAPI Vector2 Vector2Zero(void)
{
Vector2 result = { 0.0f, 0.0f };
return result;
}
// Vector with components value 1.0f
RMAPI Vector2 Vector2One(void)
{
Vector2 result = { 1.0f, 1.0f };
return result;
}
// Add two vectors (v1 + v2)
RMAPI Vector2 Vector2Add(Vector2 v1, Vector2 v2)
{
Vector2 result = { v1.x + v2.x, v1.y + v2.y };
return result;
}
// Add vector and float value
RMAPI Vector2 Vector2AddValue(Vector2 v, float add)
{
Vector2 result = { v.x + add, v.y + add };
return result;
}
// Subtract two vectors (v1 - v2)
RMAPI Vector2 Vector2Subtract(Vector2 v1, Vector2 v2)
{
Vector2 result = { v1.x - v2.x, v1.y - v2.y };
return result;
}
// Subtract vector by float value
RMAPI Vector2 Vector2SubtractValue(Vector2 v, float sub)
{
Vector2 result = { v.x - sub, v.y - sub };
return result;
}
// Calculate vector length
RMAPI float Vector2Length(Vector2 v)
{
float result = sqrtf((v.x*v.x) + (v.y*v.y));
return result;
}
// Calculate vector square length
RMAPI float Vector2LengthSqr(Vector2 v)
{
float result = (v.x*v.x) + (v.y*v.y);
return result;
}
// Calculate two vectors dot product
RMAPI float Vector2DotProduct(Vector2 v1, Vector2 v2)
{
float result = (v1.x*v2.x + v1.y*v2.y);
return result;
}
// Calculate two vectors cross product
RMAPI float Vector2CrossProduct(Vector2 v1, Vector2 v2)
{
float result = (v1.x*v2.y - v1.y*v2.x);
return result;
}
// Calculate distance between two vectors
RMAPI 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 square distance between two vectors
RMAPI float Vector2DistanceSqr(Vector2 v1, Vector2 v2)
{
float result = ((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
return result;
}
// Calculate the signed angle from v1 to v2, relative to the origin (0, 0)
// NOTE: Coordinate system convention: positive X right, positive Y down,
// positive angles appear clockwise, and negative angles appear counterclockwise
RMAPI float Vector2Angle(Vector2 v1, Vector2 v2)
{
float result = 0.0f;
float dot = v1.x*v2.x + v1.y*v2.y;
float det = v1.x*v2.y - v1.y*v2.x;
result = atan2f(det, dot);
return result;
}
// Calculate angle defined by a two vectors line
// NOTE: Parameters need to be normalized
// Current implementation should be aligned with glm::angle
RMAPI float Vector2LineAngle(Vector2 start, Vector2 end)
{
float result = 0.0f;
// TODO(10/9/2023): Currently angles move clockwise, determine if this is wanted behavior
result = -atan2f(end.y - start.y, end.x - start.x);
return result;
}
// Scale vector (multiply by value)
RMAPI Vector2 Vector2Scale(Vector2 v, float scale)
{
Vector2 result = { v.x*scale, v.y*scale };
return result;
}
// Multiply vector by vector
RMAPI Vector2 Vector2Multiply(Vector2 v1, Vector2 v2)
{
Vector2 result = { v1.x*v2.x, v1.y*v2.y };
return result;
}
// Negate vector
RMAPI Vector2 Vector2Negate(Vector2 v)
{
Vector2 result = { -v.x, -v.y };
return result;
}
// Divide vector by vector
RMAPI Vector2 Vector2Divide(Vector2 v1, Vector2 v2)
{
Vector2 result = { v1.x/v2.x, v1.y/v2.y };
return result;
}
// Normalize provided vector
RMAPI Vector2 Vector2Normalize(Vector2 v)
{
Vector2 result = { 0 };
float length = sqrtf((v.x*v.x) + (v.y*v.y));
if (length > 0)
{
float ilength = 1.0f/length;
result.x = v.x*ilength;
result.y = v.y*ilength;
}
return result;
}
// Transforms a Vector2 by a given Matrix
RMAPI Vector2 Vector2Transform(Vector2 v, Matrix mat)
{
Vector2 result = { 0 };
float x = v.x;
float y = v.y;
float z = 0;
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;
return result;
}
// Calculate linear interpolation between two vectors
RMAPI 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;
}
// Calculate reflected vector to normal
RMAPI Vector2 Vector2Reflect(Vector2 v, Vector2 normal)
{
Vector2 result = { 0 };
float dotProduct = (v.x*normal.x + v.y*normal.y); // Dot product
result.x = v.x - (2.0f*normal.x)*dotProduct;
result.y = v.y - (2.0f*normal.y)*dotProduct;
return result;
}
// Get min value for each pair of components
RMAPI Vector2 Vector2Min(Vector2 v1, Vector2 v2)
{
Vector2 result = { 0 };
result.x = fminf(v1.x, v2.x);
result.y = fminf(v1.y, v2.y);
return result;
}
// Get max value for each pair of components
RMAPI Vector2 Vector2Max(Vector2 v1, Vector2 v2)
{
Vector2 result = { 0 };
result.x = fmaxf(v1.x, v2.x);
result.y = fmaxf(v1.y, v2.y);
return result;
}
// Rotate vector by angle
RMAPI Vector2 Vector2Rotate(Vector2 v, float angle)
{
Vector2 result = { 0 };
float cosres = cosf(angle);
float sinres = sinf(angle);
result.x = v.x*cosres - v.y*sinres;
result.y = v.x*sinres + v.y*cosres;
return result;
}
// Move Vector towards target
RMAPI Vector2 Vector2MoveTowards(Vector2 v, Vector2 target, float maxDistance)
{
Vector2 result = { 0 };
float dx = target.x - v.x;
float dy = target.y - v.y;
float value = (dx*dx) + (dy*dy);
if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target;
float dist = sqrtf(value);
result.x = v.x + dx/dist*maxDistance;
result.y = v.y + dy/dist*maxDistance;
return result;
}
// Invert the given vector
RMAPI Vector2 Vector2Invert(Vector2 v)
{
Vector2 result = { 1.0f/v.x, 1.0f/v.y };
return result;
}
// Clamp the components of the vector between
// min and max values specified by the given vectors
RMAPI Vector2 Vector2Clamp(Vector2 v, Vector2 min, Vector2 max)
{
Vector2 result = { 0 };
result.x = fminf(max.x, fmaxf(min.x, v.x));
result.y = fminf(max.y, fmaxf(min.y, v.y));
return result;
}
// Clamp the magnitude of the vector between two min and max values
RMAPI Vector2 Vector2ClampValue(Vector2 v, float min, float max)
{
Vector2 result = v;
float length = (v.x*v.x) + (v.y*v.y);
if (length > 0.0f)
{
length = sqrtf(length);
float scale = 1; // By default, 1 as the neutral element.
if (length < min)
{
scale = min/length;
}
else if (length > max)
{
scale = max/length;
}
result.x = v.x*scale;
result.y = v.y*scale;
}
return result;
}
// Check whether two given vectors are almost equal
RMAPI int Vector2Equals(Vector2 p, Vector2 q)
{
#if !defined(EPSILON)
#define EPSILON 0.000001f
#endif
int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y)))));
return result;
}
// Compute the direction of a refracted ray
// v: normalized direction of the incoming ray
// n: normalized normal vector of the interface of two optical media
// r: ratio of the refractive index of the medium from where the ray comes
// to the refractive index of the medium on the other side of the surface
RMAPI Vector2 Vector2Refract(Vector2 v, Vector2 n, float r)
{
Vector2 result = { 0 };
float dot = v.x*n.x + v.y*n.y;
float d = 1.0f - r*r*(1.0f - dot*dot);
if (d >= 0.0f)
{
d = sqrtf(d);
v.x = r*v.x - (r*dot + d)*n.x;
v.y = r*v.y - (r*dot + d)*n.y;
result = v;
}
return result;
}
//----------------------------------------------------------------------------------
// Module Functions Definition - Vector3 math
//----------------------------------------------------------------------------------
// Vector with components value 0.0f
RMAPI Vector3 Vector3Zero(void)
{
Vector3 result = { 0.0f, 0.0f, 0.0f };
return result;
}
// Vector with components value 1.0f
RMAPI Vector3 Vector3One(void)
{
Vector3 result = { 1.0f, 1.0f, 1.0f };
return result;
}
// Add two vectors
RMAPI 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
RMAPI Vector3 Vector3AddValue(Vector3 v, float add)
{
Vector3 result = { v.x + add, v.y + add, v.z + add };
return result;
}
// Subtract two vectors
RMAPI 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
RMAPI Vector3 Vector3SubtractValue(Vector3 v, float sub)
{
Vector3 result = { v.x - sub, v.y - sub, v.z - sub };
return result;
}
// Multiply vector by scalar
RMAPI Vector3 Vector3Scale(Vector3 v, float scalar)
{
Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar };
return result;
}
// Multiply vector by vector
RMAPI 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
RMAPI 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
RMAPI Vector3 Vector3Perpendicular(Vector3 v)
{
Vector3 result = { 0 };
float min = fabsf(v.x);
Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f};
if (fabsf(v.y) < min)
{
min = fabsf(v.y);
Vector3 tmp = {0.0f, 1.0f, 0.0f};
cardinalAxis = tmp;
}
if (fabsf(v.z) < min)
{
Vector3 tmp = {0.0f, 0.0f, 1.0f};
cardinalAxis = tmp;
}
// Cross product between vectors
result.x = v.y*cardinalAxis.z - v.z*cardinalAxis.y;
result.y = v.z*cardinalAxis.x - v.x*cardinalAxis.z;
result.z = v.x*cardinalAxis.y - v.y*cardinalAxis.x;
return result;
}
// Calculate vector length
RMAPI float Vector3Length(const Vector3 v)
{
float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
return result;
}
// Calculate vector square length
RMAPI float Vector3LengthSqr(const Vector3 v)
{
float result = v.x*v.x + v.y*v.y + v.z*v.z;
return result;
}
// Calculate two vectors dot product
RMAPI 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
RMAPI float Vector3Distance(Vector3 v1, Vector3 v2)
{
float result = 0.0f;
float dx = v2.x - v1.x;
float dy = v2.y - v1.y;
float dz = v2.z - v1.z;
result = sqrtf(dx*dx + dy*dy + dz*dz);
return result;
}
// Calculate square distance between two vectors
RMAPI float Vector3DistanceSqr(Vector3 v1, Vector3 v2)
{
float result = 0.0f;
float dx = v2.x - v1.x;
float dy = v2.y - v1.y;
float dz = v2.z - v1.z;
result = dx*dx + dy*dy + dz*dz;
return result;
}
// Calculate angle between two vectors
RMAPI float Vector3Angle(Vector3 v1, Vector3 v2)
{
float result = 0.0f;
Vector3 cross = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x };
float len = sqrtf(cross.x*cross.x + cross.y*cross.y + cross.z*cross.z);
float dot = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
result = atan2f(len, dot);
return result;
}
// Negate provided vector (invert direction)
RMAPI Vector3 Vector3Negate(Vector3 v)
{
Vector3 result = { -v.x, -v.y, -v.z };
return result;
}
// Divide vector by vector
RMAPI 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
RMAPI Vector3 Vector3Normalize(Vector3 v)
{
Vector3 result = v;
float length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
if (length != 0.0f)
{
float ilength = 1.0f/length;
result.x *= ilength;
result.y *= ilength;
result.z *= ilength;
}
return result;
}
//Calculate the projection of the vector v1 on to v2
RMAPI Vector3 Vector3Project(Vector3 v1, Vector3 v2)
{
Vector3 result = { 0 };
float v1dv2 = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
float v2dv2 = (v2.x*v2.x + v2.y*v2.y + v2.z*v2.z);
float mag = v1dv2/v2dv2;
result.x = v2.x*mag;
result.y = v2.y*mag;
result.z = v2.z*mag;
return result;
}
//Calculate the rejection of the vector v1 on to v2
RMAPI Vector3 Vector3Reject(Vector3 v1, Vector3 v2)
{
Vector3 result = { 0 };
float v1dv2 = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
float v2dv2 = (v2.x*v2.x + v2.y*v2.y + v2.z*v2.z);
float mag = v1dv2/v2dv2;
result.x = v1.x - (v2.x*mag);
result.y = v1.y - (v2.y*mag);
result.z = v1.z - (v2.z*mag);
return result;
}
// Orthonormalize provided vectors
// Makes vectors normalized and orthogonal to each other
// Gram-Schmidt function implementation
RMAPI void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2)
{
float length = 0.0f;
float ilength = 0.0f;
// Vector3Normalize(*v1);
Vector3 v = *v1;
length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
if (length == 0.0f) length = 1.0f;
ilength = 1.0f/length;
v1->x *= ilength;
v1->y *= ilength;
v1->z *= ilength;
// Vector3CrossProduct(*v1, *v2)
Vector3 vn1 = { v1->y*v2->z - v1->z*v2->y, v1->z*v2->x - v1->x*v2->z, v1->x*v2->y - v1->y*v2->x };
// Vector3Normalize(vn1);
v = vn1;
length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
if (length == 0.0f) length = 1.0f;
ilength = 1.0f/length;
vn1.x *= ilength;
vn1.y *= ilength;
vn1.z *= ilength;
// Vector3CrossProduct(vn1, *v1)
Vector3 vn2 = { vn1.y*v1->z - vn1.z*v1->y, vn1.z*v1->x - vn1.x*v1->z, vn1.x*v1->y - vn1.y*v1->x };
*v2 = vn2;
}
// Transforms a Vector3 by a given Matrix
RMAPI 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
RMAPI 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;
}
// Rotates a vector around an axis
RMAPI Vector3 Vector3RotateByAxisAngle(Vector3 v, Vector3 axis, float angle)
{
// Using Euler-Rodrigues Formula
// Ref.: https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Rodrigues_formula
Vector3 result = v;
// Vector3Normalize(axis);
float length = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
if (length == 0.0f) length = 1.0f;
float ilength = 1.0f/length;
axis.x *= ilength;
axis.y *= ilength;
axis.z *= ilength;
angle /= 2.0f;
float a = sinf(angle);
float b = axis.x*a;
float c = axis.y*a;
float d = axis.z*a;
a = cosf(angle);
Vector3 w = { b, c, d };
// Vector3CrossProduct(w, v)
Vector3 wv = { w.y*v.z - w.z*v.y, w.z*v.x - w.x*v.z, w.x*v.y - w.y*v.x };
// Vector3CrossProduct(w, wv)
Vector3 wwv = { w.y*wv.z - w.z*wv.y, w.z*wv.x - w.x*wv.z, w.x*wv.y - w.y*wv.x };
// Vector3Scale(wv, 2*a)
a *= 2;
wv.x *= a;
wv.y *= a;
wv.z *= a;
// Vector3Scale(wwv, 2)
wwv.x *= 2;
wwv.y *= 2;
wwv.z *= 2;
result.x += wv.x;
result.y += wv.y;
result.z += wv.z;
result.x += wwv.x;
result.y += wwv.y;
result.z += wwv.z;
return result;
}
// Move Vector towards target
RMAPI Vector3 Vector3MoveTowards(Vector3 v, Vector3 target, float maxDistance)
{
Vector3 result = { 0 };
float dx = target.x - v.x;
float dy = target.y - v.y;
float dz = target.z - v.z;
float value = (dx*dx) + (dy*dy) + (dz*dz);
if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target;
float dist = sqrtf(value);
result.x = v.x + dx/dist*maxDistance;
result.y = v.y + dy/dist*maxDistance;
result.z = v.z + dz/dist*maxDistance;
return result;
}
// Calculate linear interpolation between two vectors
RMAPI 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 cubic hermite interpolation between two vectors and their tangents
// as described in the GLTF 2.0 specification: https://registry.khronos.org/glTF/specs/2.0/glTF-2.0.html#interpolation-cubic
RMAPI Vector3 Vector3CubicHermite(Vector3 v1, Vector3 tangent1, Vector3 v2, Vector3 tangent2, float amount)
{
Vector3 result = { 0 };
float amountPow2 = amount*amount;
float amountPow3 = amount*amount*amount;
result.x = (2*amountPow3 - 3*amountPow2 + 1)*v1.x + (amountPow3 - 2*amountPow2 + amount)*tangent1.x + (-2*amountPow3 + 3*amountPow2)*v2.x + (amountPow3 - amountPow2)*tangent2.x;
result.y = (2*amountPow3 - 3*amountPow2 + 1)*v1.y + (amountPow3 - 2*amountPow2 + amount)*tangent1.y + (-2*amountPow3 + 3*amountPow2)*v2.y + (amountPow3 - amountPow2)*tangent2.y;
result.z = (2*amountPow3 - 3*amountPow2 + 1)*v1.z + (amountPow3 - 2*amountPow2 + amount)*tangent1.z + (-2*amountPow3 + 3*amountPow2)*v2.z + (amountPow3 - amountPow2)*tangent2.z;
return result;
}
// Calculate reflected vector to normal
RMAPI Vector3 Vector3Reflect(Vector3 v, Vector3 normal)
{
Vector3 result = { 0 };
// I is the original vector
// N is the normal of the incident plane
// R = I - (2*N*(DotProduct[I, N]))
float dotProduct = (v.x*normal.x + v.y*normal.y + v.z*normal.z);
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;
}
// Get min value for each pair of components
RMAPI 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;
}
// Get max value for each pair of components
RMAPI 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
RMAPI Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c)
{
Vector3 result = { 0 };
Vector3 v0 = { b.x - a.x, b.y - a.y, b.z - a.z }; // Vector3Subtract(b, a)
Vector3 v1 = { c.x - a.x, c.y - a.y, c.z - a.z }; // Vector3Subtract(c, a)
Vector3 v2 = { p.x - a.x, p.y - a.y, p.z - a.z }; // Vector3Subtract(p, a)
float d00 = (v0.x*v0.x + v0.y*v0.y + v0.z*v0.z); // Vector3DotProduct(v0, v0)
float d01 = (v0.x*v1.x + v0.y*v1.y + v0.z*v1.z); // Vector3DotProduct(v0, v1)
float d11 = (v1.x*v1.x + v1.y*v1.y + v1.z*v1.z); // Vector3DotProduct(v1, v1)
float d20 = (v2.x*v0.x + v2.y*v0.y + v2.z*v0.z); // Vector3DotProduct(v2, v0)
float d21 = (v2.x*v1.x + v2.y*v1.y + v2.z*v1.z); // Vector3DotProduct(v2, v1)
float denom = d00*d11 - d01*d01;
result.y = (d11*d20 - d01*d21)/denom;
result.z = (d00*d21 - d01*d20)/denom;
result.x = 1.0f - (result.z + result.y);
return result;
}
// Projects a Vector3 from screen space into object space
// NOTE: We are avoiding calling other raymath functions despite available
RMAPI Vector3 Vector3Unproject(Vector3 source, Matrix projection, Matrix view)
{
Vector3 result = { 0 };
// Calculate unprojected matrix (multiply view matrix by projection matrix) and invert it
Matrix matViewProj = { // MatrixMultiply(view, projection);
view.m0*projection.m0 + view.m1*projection.m4 + view.m2*projection.m8 + view.m3*projection.m12,
view.m0*projection.m1 + view.m1*projection.m5 + view.m2*projection.m9 + view.m3*projection.m13,
view.m0*projection.m2 + view.m1*projection.m6 + view.m2*projection.m10 + view.m3*projection.m14,
view.m0*projection.m3 + view.m1*projection.m7 + view.m2*projection.m11 + view.m3*projection.m15,
view.m4*projection.m0 + view.m5*projection.m4 + view.m6*projection.m8 + view.m7*projection.m12,
view.m4*projection.m1 + view.m5*projection.m5 + view.m6*projection.m9 + view.m7*projection.m13,
view.m4*projection.m2 + view.m5*projection.m6 + view.m6*projection.m10 + view.m7*projection.m14,
view.m4*projection.m3 + view.m5*projection.m7 + view.m6*projection.m11 + view.m7*projection.m15,
view.m8*projection.m0 + view.m9*projection.m4 + view.m10*projection.m8 + view.m11*projection.m12,
view.m8*projection.m1 + view.m9*projection.m5 + view.m10*projection.m9 + view.m11*projection.m13,
view.m8*projection.m2 + view.m9*projection.m6 + view.m10*projection.m10 + view.m11*projection.m14,
view.m8*projection.m3 + view.m9*projection.m7 + view.m10*projection.m11 + view.m11*projection.m15,
view.m12*projection.m0 + view.m13*projection.m4 + view.m14*projection.m8 + view.m15*projection.m12,
view.m12*projection.m1 + view.m13*projection.m5 + view.m14*projection.m9 + view.m15*projection.m13,
view.m12*projection.m2 + view.m13*projection.m6 + view.m14*projection.m10 + view.m15*projection.m14,
view.m12*projection.m3 + view.m13*projection.m7 + view.m14*projection.m11 + view.m15*projection.m15 };
// Calculate inverted matrix -> MatrixInvert(matViewProj);
// Cache the matrix values (speed optimization)
float a00 = matViewProj.m0, a01 = matViewProj.m1, a02 = matViewProj.m2, a03 = matViewProj.m3;
float a10 = matViewProj.m4, a11 = matViewProj.m5, a12 = matViewProj.m6, a13 = matViewProj.m7;
float a20 = matViewProj.m8, a21 = matViewProj.m9, a22 = matViewProj.m10, a23 = matViewProj.m11;
float a30 = matViewProj.m12, a31 = matViewProj.m13, a32 = matViewProj.m14, a33 = matViewProj.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);
Matrix matViewProjInv = {
(a11*b11 - a12*b10 + a13*b09)*invDet,
(-a01*b11 + a02*b10 - a03*b09)*invDet,
(a31*b05 - a32*b04 + a33*b03)*invDet,
(-a21*b05 + a22*b04 - a23*b03)*invDet,
(-a10*b11 + a12*b08 - a13*b07)*invDet,
(a00*b11 - a02*b08 + a03*b07)*invDet,
(-a30*b05 + a32*b02 - a33*b01)*invDet,
(a20*b05 - a22*b02 + a23*b01)*invDet,
(a10*b10 - a11*b08 + a13*b06)*invDet,
(-a00*b10 + a01*b08 - a03*b06)*invDet,
(a30*b04 - a31*b02 + a33*b00)*invDet,
(-a20*b04 + a21*b02 - a23*b00)*invDet,
(-a10*b09 + a11*b07 - a12*b06)*invDet,
(a00*b09 - a01*b07 + a02*b06)*invDet,
(-a30*b03 + a31*b01 - a32*b00)*invDet,
(a20*b03 - a21*b01 + a22*b00)*invDet };
// Create quaternion from source point
Quaternion quat = { source.x, source.y, source.z, 1.0f };
// Multiply quat point by unprojecte matrix
Quaternion qtransformed = { // QuaternionTransform(quat, matViewProjInv)
matViewProjInv.m0*quat.x + matViewProjInv.m4*quat.y + matViewProjInv.m8*quat.z + matViewProjInv.m12*quat.w,
matViewProjInv.m1*quat.x + matViewProjInv.m5*quat.y + matViewProjInv.m9*quat.z + matViewProjInv.m13*quat.w,
matViewProjInv.m2*quat.x + matViewProjInv.m6*quat.y + matViewProjInv.m10*quat.z + matViewProjInv.m14*quat.w,
matViewProjInv.m3*quat.x + matViewProjInv.m7*quat.y + matViewProjInv.m11*quat.z + matViewProjInv.m15*quat.w };
// Normalized world points in vectors
result.x = qtransformed.x/qtransformed.w;
result.y = qtransformed.y/qtransformed.w;
result.z = qtransformed.z/qtransformed.w;
return result;
}
// Get Vector3 as float array
RMAPI float3 Vector3ToFloatV(Vector3 v)
{
float3 buffer = { 0 };
buffer.v[0] = v.x;
buffer.v[1] = v.y;
buffer.v[2] = v.z;
return buffer;
}
// Invert the given vector
RMAPI Vector3 Vector3Invert(Vector3 v)
{
Vector3 result = { 1.0f/v.x, 1.0f/v.y, 1.0f/v.z };
return result;
}
// Clamp the components of the vector between
// min and max values specified by the given vectors
RMAPI Vector3 Vector3Clamp(Vector3 v, Vector3 min, Vector3 max)
{
Vector3 result = { 0 };
result.x = fminf(max.x, fmaxf(min.x, v.x));
result.y = fminf(max.y, fmaxf(min.y, v.y));
result.z = fminf(max.z, fmaxf(min.z, v.z));
return result;
}
// Clamp the magnitude of the vector between two values
RMAPI Vector3 Vector3ClampValue(Vector3 v, float min, float max)
{
Vector3 result = v;
float length = (v.x*v.x) + (v.y*v.y) + (v.z*v.z);
if (length > 0.0f)
{
length = sqrtf(length);
float scale = 1; // By default, 1 as the neutral element.
if (length < min)
{
scale = min/length;
}
else if (length > max)
{
scale = max/length;
}
result.x = v.x*scale;
result.y = v.y*scale;
result.z = v.z*scale;
}
return result;
}
// Check whether two given vectors are almost equal
RMAPI int Vector3Equals(Vector3 p, Vector3 q)
{
#if !defined(EPSILON)
#define EPSILON 0.000001f
#endif
int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z)))));
return result;
}
// Compute the direction of a refracted ray
// v: normalized direction of the incoming ray
// n: normalized normal vector of the interface of two optical media
// r: ratio of the refractive index of the medium from where the ray comes
// to the refractive index of the medium on the other side of the surface
RMAPI Vector3 Vector3Refract(Vector3 v, Vector3 n, float r)
{
Vector3 result = { 0 };
float dot = v.x*n.x + v.y*n.y + v.z*n.z;
float d = 1.0f - r*r*(1.0f - dot*dot);
if (d >= 0.0f)
{
d = sqrtf(d);
v.x = r*v.x - (r*dot + d)*n.x;
v.y = r*v.y - (r*dot + d)*n.y;
v.z = r*v.z - (r*dot + d)*n.z;
result = v;
}
return result;
}
//----------------------------------------------------------------------------------
// Module Functions Definition - Vector4 math
//----------------------------------------------------------------------------------
RMAPI Vector4 Vector4Zero(void)
{
Vector4 result = { 0.0f, 0.0f, 0.0f, 0.0f };
return result;
}
RMAPI Vector4 Vector4One(void)
{
Vector4 result = { 1.0f, 1.0f, 1.0f, 1.0f };
return result;
}
RMAPI Vector4 Vector4Add(Vector4 v1, Vector4 v2)
{
Vector4 result = {
v1.x + v2.x,
v1.y + v2.y,
v1.z + v2.z,
v1.w + v2.w
};
return result;
}
RMAPI Vector4 Vector4AddValue(Vector4 v, float add)
{
Vector4 result = {
v.x + add,
v.y + add,
v.z + add,
v.w + add
};
return result;
}
RMAPI Vector4 Vector4Subtract(Vector4 v1, Vector4 v2)
{
Vector4 result = {
v1.x - v2.x,
v1.y - v2.y,
v1.z - v2.z,
v1.w - v2.w
};
return result;
}
RMAPI Vector4 Vector4SubtractValue(Vector4 v, float add)
{
Vector4 result = {
v.x - add,
v.y - add,
v.z - add,
v.w - add
};
return result;
}
RMAPI float Vector4Length(Vector4 v)
{
float result = sqrtf((v.x*v.x) + (v.y*v.y) + (v.z*v.z) + (v.w*v.w));
return result;
}
RMAPI float Vector4LengthSqr(Vector4 v)
{
float result = (v.x*v.x) + (v.y*v.y) + (v.z*v.z) + (v.w*v.w);
return result;
}
RMAPI float Vector4DotProduct(Vector4 v1, Vector4 v2)
{
float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z + v1.w*v2.w);
return result;
}
// Calculate distance between two vectors
RMAPI float Vector4Distance(Vector4 v1, Vector4 v2)
{
float result = sqrtf(
(v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y) +
(v1.z - v2.z)*(v1.z - v2.z) + (v1.w - v2.w)*(v1.w - v2.w));
return result;
}
// Calculate square distance between two vectors
RMAPI float Vector4DistanceSqr(Vector4 v1, Vector4 v2)
{
float result =
(v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y) +
(v1.z - v2.z)*(v1.z - v2.z) + (v1.w - v2.w)*(v1.w - v2.w);
return result;
}
RMAPI Vector4 Vector4Scale(Vector4 v, float scale)
{
Vector4 result = { v.x*scale, v.y*scale, v.z*scale, v.w*scale };
return result;
}
// Multiply vector by vector
RMAPI Vector4 Vector4Multiply(Vector4 v1, Vector4 v2)
{
Vector4 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z, v1.w*v2.w };
return result;
}
// Negate vector
RMAPI Vector4 Vector4Negate(Vector4 v)
{
Vector4 result = { -v.x, -v.y, -v.z, -v.w };
return result;
}
// Divide vector by vector
RMAPI Vector4 Vector4Divide(Vector4 v1, Vector4 v2)
{
Vector4 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z, v1.w/v2.w };
return result;
}
// Normalize provided vector
RMAPI Vector4 Vector4Normalize(Vector4 v)
{
Vector4 result = { 0 };
float length = sqrtf((v.x*v.x) + (v.y*v.y) + (v.z*v.z) + (v.w*v.w));
if (length > 0)
{
float ilength = 1.0f/length;
result.x = v.x*ilength;
result.y = v.y*ilength;
result.z = v.z*ilength;
result.w = v.w*ilength;
}
return result;
}
// Get min value for each pair of components
RMAPI Vector4 Vector4Min(Vector4 v1, Vector4 v2)
{
Vector4 result = { 0 };
result.x = fminf(v1.x, v2.x);
result.y = fminf(v1.y, v2.y);
result.z = fminf(v1.z, v2.z);
result.w = fminf(v1.w, v2.w);
return result;
}
// Get max value for each pair of components
RMAPI Vector4 Vector4Max(Vector4 v1, Vector4 v2)
{
Vector4 result = { 0 };
result.x = fmaxf(v1.x, v2.x);
result.y = fmaxf(v1.y, v2.y);
result.z = fmaxf(v1.z, v2.z);
result.w = fmaxf(v1.w, v2.w);
return result;
}
// Calculate linear interpolation between two vectors
RMAPI Vector4 Vector4Lerp(Vector4 v1, Vector4 v2, float amount)
{
Vector4 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);
result.w = v1.w + amount*(v2.w - v1.w);
return result;
}
// Move Vector towards target
RMAPI Vector4 Vector4MoveTowards(Vector4 v, Vector4 target, float maxDistance)
{
Vector4 result = { 0 };
float dx = target.x - v.x;
float dy = target.y - v.y;
float dz = target.z - v.z;
float dw = target.w - v.w;
float value = (dx*dx) + (dy*dy) + (dz*dz) + (dw*dw);
if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target;
float dist = sqrtf(value);
result.x = v.x + dx/dist*maxDistance;
result.y = v.y + dy/dist*maxDistance;
result.z = v.z + dz/dist*maxDistance;
result.w = v.w + dw/dist*maxDistance;
return result;
}
// Invert the given vector
RMAPI Vector4 Vector4Invert(Vector4 v)
{
Vector4 result = { 1.0f/v.x, 1.0f/v.y, 1.0f/v.z, 1.0f/v.w };
return result;
}
// Check whether two given vectors are almost equal
RMAPI int Vector4Equals(Vector4 p, Vector4 q)
{
#if !defined(EPSILON)
#define EPSILON 0.000001f
#endif
int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) &&
((fabsf(p.w - q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))));
return result;
}
//----------------------------------------------------------------------------------
// Module Functions Definition - Matrix math
//----------------------------------------------------------------------------------
// Compute matrix determinant
RMAPI float MatrixDeterminant(Matrix mat)
{
float result = 0.0f;
// 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;
}
// Get the trace of the matrix (sum of the values along the diagonal)
RMAPI float MatrixTrace(Matrix mat)
{
float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15);
return result;
}
// Transposes provided matrix
RMAPI 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
RMAPI 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;
}
// Get identity matrix
RMAPI 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
RMAPI Matrix MatrixAdd(Matrix left, Matrix right)
{
Matrix result = { 0 };
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)
RMAPI Matrix MatrixSubtract(Matrix left, Matrix right)
{
Matrix result = { 0 };
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;
}
// Get two matrix multiplication
// NOTE: When multiplying matrices... the order matters!
RMAPI 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;
}
// Get translation matrix
RMAPI 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
RMAPI Matrix MatrixRotate(Vector3 axis, float angle)
{
Matrix result = { 0 };
float x = axis.x, y = axis.y, z = axis.z;
float lengthSquared = x*x + y*y + z*z;
if ((lengthSquared != 1.0f) && (lengthSquared != 0.0f))
{
float ilength = 1.0f/sqrtf(lengthSquared);
x *= ilength;
y *= ilength;
z *= ilength;
}
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;
}
// Get x-rotation matrix
// NOTE: Angle must be provided in radians
RMAPI Matrix MatrixRotateX(float angle)
{
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 }; // MatrixIdentity()
float cosres = cosf(angle);
float sinres = sinf(angle);
result.m5 = cosres;
result.m6 = sinres;
result.m9 = -sinres;
result.m10 = cosres;
return result;
}
// Get y-rotation matrix
// NOTE: Angle must be provided in radians
RMAPI Matrix MatrixRotateY(float angle)
{
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 }; // MatrixIdentity()
float cosres = cosf(angle);
float sinres = sinf(angle);
result.m0 = cosres;
result.m2 = -sinres;
result.m8 = sinres;
result.m10 = cosres;
return result;
}
// Get z-rotation matrix
// NOTE: Angle must be provided in radians
RMAPI Matrix MatrixRotateZ(float angle)
{
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 }; // MatrixIdentity()
float cosres = cosf(angle);
float sinres = sinf(angle);
result.m0 = cosres;
result.m1 = sinres;
result.m4 = -sinres;
result.m5 = cosres;
return result;
}
// Get xyz-rotation matrix
// NOTE: Angle must be provided in radians
RMAPI Matrix MatrixRotateXYZ(Vector3 angle)
{
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 }; // MatrixIdentity()
float cosz = cosf(-angle.z);
float sinz = sinf(-angle.z);
float cosy = cosf(-angle.y);
float siny = sinf(-angle.y);
float cosx = cosf(-angle.x);
float sinx = sinf(-angle.x);
result.m0 = cosz*cosy;
result.m1 = (cosz*siny*sinx) - (sinz*cosx);
result.m2 = (cosz*siny*cosx) + (sinz*sinx);
result.m4 = sinz*cosy;
result.m5 = (sinz*siny*sinx) + (cosz*cosx);
result.m6 = (sinz*siny*cosx) - (cosz*sinx);
result.m8 = -siny;
result.m9 = cosy*sinx;
result.m10= cosy*cosx;
return result;
}
// Get zyx-rotation matrix
// NOTE: Angle must be provided in radians
RMAPI Matrix MatrixRotateZYX(Vector3 angle)
{
Matrix result = { 0 };
float cz = cosf(angle.z);
float sz = sinf(angle.z);
float cy = cosf(angle.y);
float sy = sinf(angle.y);
float cx = cosf(angle.x);
float sx = sinf(angle.x);
result.m0 = cz*cy;
result.m4 = cz*sy*sx - cx*sz;
result.m8 = sz*sx + cz*cx*sy;
result.m12 = 0;
result.m1 = cy*sz;
result.m5 = cz*cx + sz*sy*sx;
result.m9 = cx*sz*sy - cz*sx;
result.m13 = 0;
result.m2 = -sy;
result.m6 = cy*sx;
result.m10 = cy*cx;
result.m14 = 0;
result.m3 = 0;
result.m7 = 0;
result.m11 = 0;
result.m15 = 1;
return result;
}
// Get scaling matrix
RMAPI 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;
}
// Get perspective projection matrix
RMAPI Matrix MatrixFrustum(double left, double right, double bottom, double top, double nearPlane, double farPlane)
{
Matrix result = { 0 };
float rl = (float)(right - left);
float tb = (float)(top - bottom);
float fn = (float)(farPlane - nearPlane);
result.m0 = ((float)nearPlane*2.0f)/rl;
result.m1 = 0.0f;
result.m2 = 0.0f;
result.m3 = 0.0f;
result.m4 = 0.0f;
result.m5 = ((float)nearPlane*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)farPlane + (float)nearPlane)/fn;
result.m11 = -1.0f;
result.m12 = 0.0f;
result.m13 = 0.0f;
result.m14 = -((float)farPlane*(float)nearPlane*2.0f)/fn;
result.m15 = 0.0f;
return result;
}
// Get perspective projection matrix
// NOTE: Fovy angle must be provided in radians
RMAPI Matrix MatrixPerspective(double fovY, double aspect, double nearPlane, double farPlane)
{
Matrix result = { 0 };
double top = nearPlane*tan(fovY*0.5);
double bottom = -top;
double right = top*aspect;
double left = -right;
// MatrixFrustum(-right, right, -top, top, near, far);
float rl = (float)(right - left);
float tb = (float)(top - bottom);
float fn = (float)(farPlane - nearPlane);
result.m0 = ((float)nearPlane*2.0f)/rl;
result.m5 = ((float)nearPlane*2.0f)/tb;
result.m8 = ((float)right + (float)left)/rl;
result.m9 = ((float)top + (float)bottom)/tb;
result.m10 = -((float)farPlane + (float)nearPlane)/fn;
result.m11 = -1.0f;
result.m14 = -((float)farPlane*(float)nearPlane*2.0f)/fn;
return result;
}
// Get orthographic projection matrix
RMAPI Matrix MatrixOrtho(double left, double right, double bottom, double top, double nearPlane, double farPlane)
{
Matrix result = { 0 };
float rl = (float)(right - left);
float tb = (float)(top - bottom);
float fn = (float)(farPlane - nearPlane);
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)farPlane + (float)nearPlane)/fn;
result.m15 = 1.0f;
return result;
}
// Get camera look-at matrix (view matrix)
RMAPI Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up)
{
Matrix result = { 0 };
float length = 0.0f;
float ilength = 0.0f;
// Vector3Subtract(eye, target)
Vector3 vz = { eye.x - target.x, eye.y - target.y, eye.z - target.z };
// Vector3Normalize(vz)
Vector3 v = vz;
length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
if (length == 0.0f) length = 1.0f;
ilength = 1.0f/length;
vz.x *= ilength;
vz.y *= ilength;
vz.z *= ilength;
// Vector3CrossProduct(up, vz)
Vector3 vx = { up.y*vz.z - up.z*vz.y, up.z*vz.x - up.x*vz.z, up.x*vz.y - up.y*vz.x };
// Vector3Normalize(x)
v = vx;
length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
if (length == 0.0f) length = 1.0f;
ilength = 1.0f/length;
vx.x *= ilength;
vx.y *= ilength;
vx.z *= ilength;
// Vector3CrossProduct(vz, vx)
Vector3 vy = { vz.y*vx.z - vz.z*vx.y, vz.z*vx.x - vz.x*vx.z, vz.x*vx.y - vz.y*vx.x };
result.m0 = vx.x;
result.m1 = vy.x;
result.m2 = vz.x;
result.m3 = 0.0f;
result.m4 = vx.y;
result.m5 = vy.y;
result.m6 = vz.y;
result.m7 = 0.0f;
result.m8 = vx.z;
result.m9 = vy.z;
result.m10 = vz.z;
result.m11 = 0.0f;
result.m12 = -(vx.x*eye.x + vx.y*eye.y + vx.z*eye.z); // Vector3DotProduct(vx, eye)
result.m13 = -(vy.x*eye.x + vy.y*eye.y + vy.z*eye.z); // Vector3DotProduct(vy, eye)
result.m14 = -(vz.x*eye.x + vz.y*eye.y + vz.z*eye.z); // Vector3DotProduct(vz, eye)
result.m15 = 1.0f;
return result;
}
// Get float array of matrix data
RMAPI float16 MatrixToFloatV(Matrix mat)
{
float16 result = { 0 };
result.v[0] = mat.m0;
result.v[1] = mat.m1;
result.v[2] = mat.m2;
result.v[3] = mat.m3;
result.v[4] = mat.m4;
result.v[5] = mat.m5;
result.v[6] = mat.m6;
result.v[7] = mat.m7;
result.v[8] = mat.m8;
result.v[9] = mat.m9;
result.v[10] = mat.m10;
result.v[11] = mat.m11;
result.v[12] = mat.m12;
result.v[13] = mat.m13;
result.v[14] = mat.m14;
result.v[15] = mat.m15;
return result;
}
//----------------------------------------------------------------------------------
// Module Functions Definition - Quaternion math
//----------------------------------------------------------------------------------
// Add two quaternions
RMAPI 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
RMAPI 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
RMAPI 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
RMAPI Quaternion QuaternionSubtractValue(Quaternion q, float sub)
{
Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub};
return result;
}
// Get identity quaternion
RMAPI Quaternion QuaternionIdentity(void)
{
Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
return result;
}
// Computes the length of a quaternion
RMAPI float QuaternionLength(Quaternion q)
{
float result = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
return result;
}
// Normalize provided quaternion
RMAPI Quaternion QuaternionNormalize(Quaternion q)
{
Quaternion result = { 0 };
float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
if (length == 0.0f) length = 1.0f;
float 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
RMAPI Quaternion QuaternionInvert(Quaternion q)
{
Quaternion result = q;
float lengthSq = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
if (lengthSq != 0.0f)
{
float invLength = 1.0f/lengthSq;
result.x *= -invLength;
result.y *= -invLength;
result.z *= -invLength;
result.w *= invLength;
}
return result;
}
// Calculate two quaternion multiplication
RMAPI 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
RMAPI Quaternion QuaternionScale(Quaternion q, float mul)
{
Quaternion result = { 0 };
result.x = q.x*mul;
result.y = q.y*mul;
result.z = q.z*mul;
result.w = q.w*mul;
return result;
}
// Divide two quaternions
RMAPI 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
RMAPI 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
RMAPI Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount)
{
Quaternion result = { 0 };
// QuaternionLerp(q1, q2, amount)
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);
// QuaternionNormalize(q);
Quaternion q = result;
float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
if (length == 0.0f) length = 1.0f;
float 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;
}
// Calculates spherical linear interpolation between two quaternions
RMAPI Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
{
Quaternion result = { 0 };
#if !defined(EPSILON)
#define EPSILON 0.000001f
#endif
float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w;
if (cosHalfTheta < 0)
{
q2.x = -q2.x; q2.y = -q2.y; q2.z = -q2.z; q2.w = -q2.w;
cosHalfTheta = -cosHalfTheta;
}
if (fabsf(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 (fabsf(sinHalfTheta) < EPSILON)
{
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 cubic spline interpolation using Cubic Hermite Spline algorithm
// as described in the GLTF 2.0 specification: https://registry.khronos.org/glTF/specs/2.0/glTF-2.0.html#interpolation-cubic
RMAPI Quaternion QuaternionCubicHermiteSpline(Quaternion q1, Quaternion outTangent1, Quaternion q2, Quaternion inTangent2, float t)
{
float t2 = t*t;
float t3 = t2*t;
float h00 = 2*t3 - 3*t2 + 1;
float h10 = t3 - 2*t2 + t;
float h01 = -2*t3 + 3*t2;
float h11 = t3 - t2;
Quaternion p0 = QuaternionScale(q1, h00);
Quaternion m0 = QuaternionScale(outTangent1, h10);
Quaternion p1 = QuaternionScale(q2, h01);
Quaternion m1 = QuaternionScale(inTangent2, h11);
Quaternion result = { 0 };
result = QuaternionAdd(p0, m0);
result = QuaternionAdd(result, p1);
result = QuaternionAdd(result, m1);
result = QuaternionNormalize(result);
return result;
}
// Calculate quaternion based on the rotation from one vector to another
RMAPI Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to)
{
Quaternion result = { 0 };
float cos2Theta = (from.x*to.x + from.y*to.y + from.z*to.z); // Vector3DotProduct(from, to)
Vector3 cross = { from.y*to.z - from.z*to.y, from.z*to.x - from.x*to.z, from.x*to.y - from.y*to.x }; // Vector3CrossProduct(from, to)
result.x = cross.x;
result.y = cross.y;
result.z = cross.z;
result.w = 1.0f + cos2Theta;
// QuaternionNormalize(q);
// NOTE: Normalize to essentially nlerp the original and identity to 0.5
Quaternion q = result;
float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
if (length == 0.0f) length = 1.0f;
float 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;
}
// Get a quaternion for a given rotation matrix
RMAPI Quaternion QuaternionFromMatrix(Matrix mat)
{
Quaternion result = { 0 };
float fourWSquaredMinus1 = mat.m0 + mat.m5 + mat.m10;
float fourXSquaredMinus1 = mat.m0 - mat.m5 - mat.m10;
float fourYSquaredMinus1 = mat.m5 - mat.m0 - mat.m10;
float fourZSquaredMinus1 = mat.m10 - mat.m0 - mat.m5;
int biggestIndex = 0;
float fourBiggestSquaredMinus1 = fourWSquaredMinus1;
if (fourXSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourXSquaredMinus1;
biggestIndex = 1;
}
if (fourYSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourYSquaredMinus1;
biggestIndex = 2;
}
if (fourZSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourZSquaredMinus1;
biggestIndex = 3;
}
float biggestVal = sqrtf(fourBiggestSquaredMinus1 + 1.0f)*0.5f;
float mult = 0.25f/biggestVal;
switch (biggestIndex)
{
case 0:
result.w = biggestVal;
result.x = (mat.m6 - mat.m9)*mult;
result.y = (mat.m8 - mat.m2)*mult;
result.z = (mat.m1 - mat.m4)*mult;
break;
case 1:
result.x = biggestVal;
result.w = (mat.m6 - mat.m9)*mult;
result.y = (mat.m1 + mat.m4)*mult;
result.z = (mat.m8 + mat.m2)*mult;
break;
case 2:
result.y = biggestVal;
result.w = (mat.m8 - mat.m2)*mult;
result.x = (mat.m1 + mat.m4)*mult;
result.z = (mat.m6 + mat.m9)*mult;
break;
case 3:
result.z = biggestVal;
result.w = (mat.m1 - mat.m4)*mult;
result.x = (mat.m8 + mat.m2)*mult;
result.y = (mat.m6 + mat.m9)*mult;
break;
}
return result;
}
// Get a matrix for a given quaternion
RMAPI Matrix QuaternionToMatrix(Quaternion q)
{
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 }; // MatrixIdentity()
float a2 = q.x*q.x;
float b2 = q.y*q.y;
float c2 = q.z*q.z;
float ac = q.x*q.z;
float ab = q.x*q.y;
float bc = q.y*q.z;
float ad = q.w*q.x;
float bd = q.w*q.y;
float cd = q.w*q.z;
result.m0 = 1 - 2*(b2 + c2);
result.m1 = 2*(ab + cd);
result.m2 = 2*(ac - bd);
result.m4 = 2*(ab - cd);
result.m5 = 1 - 2*(a2 + c2);
result.m6 = 2*(bc + ad);
result.m8 = 2*(ac + bd);
result.m9 = 2*(bc - ad);
result.m10 = 1 - 2*(a2 + b2);
return result;
}
// Get rotation quaternion for an angle and axis
// NOTE: Angle must be provided in radians
RMAPI Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle)
{
Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
float axisLength = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
if (axisLength != 0.0f)
{
angle *= 0.5f;
float length = 0.0f;
float ilength = 0.0f;
// Vector3Normalize(axis)
length = axisLength;
if (length == 0.0f) length = 1.0f;
ilength = 1.0f/length;
axis.x *= ilength;
axis.y *= ilength;
axis.z *= ilength;
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(q);
Quaternion q = result;
length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
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;
}
// Get the rotation angle and axis for a given quaternion
RMAPI void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
{
if (fabsf(q.w) > 1.0f)
{
// QuaternionNormalize(q);
float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
if (length == 0.0f) length = 1.0f;
float ilength = 1.0f/length;
q.x = q.x*ilength;
q.y = q.y*ilength;
q.z = q.z*ilength;
q.w = q.w*ilength;
}
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 > EPSILON)
{
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;
}
// Get the quaternion equivalent to Euler angles
// NOTE: Rotation order is ZYX
RMAPI Quaternion QuaternionFromEuler(float pitch, float yaw, float roll)
{
Quaternion result = { 0 };
float x0 = cosf(pitch*0.5f);
float x1 = sinf(pitch*0.5f);
float y0 = cosf(yaw*0.5f);
float y1 = sinf(yaw*0.5f);
float z0 = cosf(roll*0.5f);
float z1 = sinf(roll*0.5f);
result.x = x1*y0*z0 - x0*y1*z1;
result.y = x0*y1*z0 + x1*y0*z1;
result.z = x0*y0*z1 - x1*y1*z0;
result.w = x0*y0*z0 + x1*y1*z1;
return result;
}
// Get the Euler angles equivalent to quaternion (roll, pitch, yaw)
// NOTE: Angles are returned in a Vector3 struct in radians
RMAPI 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);
// 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);
// 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);
return result;
}
// Transform a quaternion given a transformation matrix
RMAPI 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;
}
// Check whether two given quaternions are almost equal
RMAPI int QuaternionEquals(Quaternion p, Quaternion q)
{
#if !defined(EPSILON)
#define EPSILON 0.000001f
#endif
int result = (((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) &&
((fabsf(p.w - q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))))) ||
(((fabsf(p.x + q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
((fabsf(p.y + q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
((fabsf(p.z + q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) &&
((fabsf(p.w + q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w))))));
return result;
}
// Decompose a transformation matrix into its rotational, translational and scaling components
RMAPI void MatrixDecompose(Matrix mat, Vector3 *translation, Quaternion *rotation, Vector3 *scale)
{
// Extract translation.
translation->x = mat.m12;
translation->y = mat.m13;
translation->z = mat.m14;
// Extract upper-left for determinant computation
const float a = mat.m0;
const float b = mat.m4;
const float c = mat.m8;
const float d = mat.m1;
const float e = mat.m5;
const float f = mat.m9;
const float g = mat.m2;
const float h = mat.m6;
const float i = mat.m10;
const float A = e*i - f*h;
const float B = f*g - d*i;
const float C = d*h - e*g;
// Extract scale
const float det = a*A + b*B + c*C;
Vector3 abc = { a, b, c };
Vector3 def = { d, e, f };
Vector3 ghi = { g, h, i };
float scalex = Vector3Length(abc);
float scaley = Vector3Length(def);
float scalez = Vector3Length(ghi);
Vector3 s = { scalex, scaley, scalez };
if (det < 0) s = Vector3Negate(s);
*scale = s;
// Remove scale from the matrix if it is not close to zero
Matrix clone = mat;
if (!FloatEquals(det, 0))
{
clone.m0 /= s.x;
clone.m4 /= s.x;
clone.m8 /= s.x;
clone.m1 /= s.y;
clone.m5 /= s.y;
clone.m9 /= s.y;
clone.m2 /= s.z;
clone.m6 /= s.z;
clone.m10 /= s.z;
// Extract rotation
*rotation = QuaternionFromMatrix(clone);
}
else
{
// Set to identity if close to zero
*rotation = QuaternionIdentity();
}
}
#if defined(__cplusplus) && !defined(RAYMATH_DISABLE_CPP_OPERATORS)
// Optional C++ math operators
//-------------------------------------------------------------------------------
// Vector2 operators
static constexpr Vector2 Vector2Zeros = { 0, 0 };
static constexpr Vector2 Vector2Ones = { 1, 1 };
static constexpr Vector2 Vector2UnitX = { 1, 0 };
static constexpr Vector2 Vector2UnitY = { 0, 1 };
inline Vector2 operator + (const Vector2& lhs, const Vector2& rhs)
{
return Vector2Add(lhs, rhs);
}
inline const Vector2& operator += (Vector2& lhs, const Vector2& rhs)
{
lhs = Vector2Add(lhs, rhs);
return lhs;
}
inline Vector2 operator - (const Vector2& lhs, const Vector2& rhs)
{
return Vector2Subtract(lhs, rhs);
}
inline const Vector2& operator -= (Vector2& lhs, const Vector2& rhs)
{
lhs = Vector2Subtract(lhs, rhs);
return lhs;
}
inline Vector2 operator * (const Vector2& lhs, const float& rhs)
{
return Vector2Scale(lhs, rhs);
}
inline const Vector2& operator *= (Vector2& lhs, const float& rhs)
{
lhs = Vector2Scale(lhs, rhs);
return lhs;
}
inline Vector2 operator * (const Vector2& lhs, const Vector2& rhs)
{
return Vector2Multiply(lhs, rhs);
}
inline const Vector2& operator *= (Vector2& lhs, const Vector2& rhs)
{
lhs = Vector2Multiply(lhs, rhs);
return lhs;
}
inline Vector2 operator * (const Vector2& lhs, const Matrix& rhs)
{
return Vector2Transform(lhs, rhs);
}
inline const Vector2& operator *= (Vector2& lhs, const Matrix& rhs)
{
lhs = Vector2Transform(lhs, rhs);
return lhs;
}
inline Vector2 operator / (const Vector2& lhs, const float& rhs)
{
return Vector2Scale(lhs, 1.0f/rhs);
}
inline const Vector2& operator /= (Vector2& lhs, const float& rhs)
{
lhs = Vector2Scale(lhs, 1.0f/rhs);
return lhs;
}
inline Vector2 operator / (const Vector2& lhs, const Vector2& rhs)
{
return Vector2Divide(lhs, rhs);
}
inline const Vector2& operator /= (Vector2& lhs, const Vector2& rhs)
{
lhs = Vector2Divide(lhs, rhs);
return lhs;
}
inline bool operator == (const Vector2& lhs, const Vector2& rhs)
{
return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y);
}
inline bool operator != (const Vector2& lhs, const Vector2& rhs)
{
return !FloatEquals(lhs.x, rhs.x) || !FloatEquals(lhs.y, rhs.y);
}
// Vector3 operators
static constexpr Vector3 Vector3Zeros = { 0, 0, 0 };
static constexpr Vector3 Vector3Ones = { 1, 1, 1 };
static constexpr Vector3 Vector3UnitX = { 1, 0, 0 };
static constexpr Vector3 Vector3UnitY = { 0, 1, 0 };
static constexpr Vector3 Vector3UnitZ = { 0, 0, 1 };
inline Vector3 operator + (const Vector3& lhs, const Vector3& rhs)
{
return Vector3Add(lhs, rhs);
}
inline const Vector3& operator += (Vector3& lhs, const Vector3& rhs)
{
lhs = Vector3Add(lhs, rhs);
return lhs;
}
inline Vector3 operator - (const Vector3& lhs, const Vector3& rhs)
{
return Vector3Subtract(lhs, rhs);
}
inline const Vector3& operator -= (Vector3& lhs, const Vector3& rhs)
{
lhs = Vector3Subtract(lhs, rhs);
return lhs;
}
inline Vector3 operator * (const Vector3& lhs, const float& rhs)
{
return Vector3Scale(lhs, rhs);
}
inline const Vector3& operator *= (Vector3& lhs, const float& rhs)
{
lhs = Vector3Scale(lhs, rhs);
return lhs;
}
inline Vector3 operator * (const Vector3& lhs, const Vector3& rhs)
{
return Vector3Multiply(lhs, rhs);
}
inline const Vector3& operator *= (Vector3& lhs, const Vector3& rhs)
{
lhs = Vector3Multiply(lhs, rhs);
return lhs;
}
inline Vector3 operator * (const Vector3& lhs, const Matrix& rhs)
{
return Vector3Transform(lhs, rhs);
}
inline const Vector3& operator *= (Vector3& lhs, const Matrix& rhs)
{
lhs = Vector3Transform(lhs, rhs);
return lhs;
}
inline Vector3 operator / (const Vector3& lhs, const float& rhs)
{
return Vector3Scale(lhs, 1.0f/rhs);
}
inline const Vector3& operator /= (Vector3& lhs, const float& rhs)
{
lhs = Vector3Scale(lhs, 1.0f/rhs);
return lhs;
}
inline Vector3 operator / (const Vector3& lhs, const Vector3& rhs)
{
return Vector3Divide(lhs, rhs);
}
inline const Vector3& operator /= (Vector3& lhs, const Vector3& rhs)
{
lhs = Vector3Divide(lhs, rhs);
return lhs;
}
inline bool operator == (const Vector3& lhs, const Vector3& rhs)
{
return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y) && FloatEquals(lhs.z, rhs.z);
}
inline bool operator != (const Vector3& lhs, const Vector3& rhs)
{
return !FloatEquals(lhs.x, rhs.x) || !FloatEquals(lhs.y, rhs.y) || !FloatEquals(lhs.z, rhs.z);
}
// Vector4 operators
static constexpr Vector4 Vector4Zeros = { 0, 0, 0, 0 };
static constexpr Vector4 Vector4Ones = { 1, 1, 1, 1 };
static constexpr Vector4 Vector4UnitX = { 1, 0, 0, 0 };
static constexpr Vector4 Vector4UnitY = { 0, 1, 0, 0 };
static constexpr Vector4 Vector4UnitZ = { 0, 0, 1, 0 };
static constexpr Vector4 Vector4UnitW = { 0, 0, 0, 1 };
inline Vector4 operator + (const Vector4& lhs, const Vector4& rhs)
{
return Vector4Add(lhs, rhs);
}
inline const Vector4& operator += (Vector4& lhs, const Vector4& rhs)
{
lhs = Vector4Add(lhs, rhs);
return lhs;
}
inline Vector4 operator - (const Vector4& lhs, const Vector4& rhs)
{
return Vector4Subtract(lhs, rhs);
}
inline const Vector4& operator -= (Vector4& lhs, const Vector4& rhs)
{
lhs = Vector4Subtract(lhs, rhs);
return lhs;
}
inline Vector4 operator * (const Vector4& lhs, const float& rhs)
{
return Vector4Scale(lhs, rhs);
}
inline const Vector4& operator *= (Vector4& lhs, const float& rhs)
{
lhs = Vector4Scale(lhs, rhs);
return lhs;
}
inline Vector4 operator * (const Vector4& lhs, const Vector4& rhs)
{
return Vector4Multiply(lhs, rhs);
}
inline const Vector4& operator *= (Vector4& lhs, const Vector4& rhs)
{
lhs = Vector4Multiply(lhs, rhs);
return lhs;
}
inline Vector4 operator / (const Vector4& lhs, const float& rhs)
{
return Vector4Scale(lhs, 1.0f/rhs);
}
inline const Vector4& operator /= (Vector4& lhs, const float& rhs)
{
lhs = Vector4Scale(lhs, 1.0f/rhs);
return lhs;
}
inline Vector4 operator / (const Vector4& lhs, const Vector4& rhs)
{
return Vector4Divide(lhs, rhs);
}
inline const Vector4& operator /= (Vector4& lhs, const Vector4& rhs)
{
lhs = Vector4Divide(lhs, rhs);
return lhs;
}
inline bool operator == (const Vector4& lhs, const Vector4& rhs)
{
return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y) && FloatEquals(lhs.z, rhs.z) && FloatEquals(lhs.w, rhs.w);
}
inline bool operator != (const Vector4& lhs, const Vector4& rhs)
{
return !FloatEquals(lhs.x, rhs.x) || !FloatEquals(lhs.y, rhs.y) || !FloatEquals(lhs.z, rhs.z) || !FloatEquals(lhs.w, rhs.w);
}
// Quaternion operators
static constexpr Quaternion QuaternionZeros = { 0, 0, 0, 0 };
static constexpr Quaternion QuaternionOnes = { 1, 1, 1, 1 };
static constexpr Quaternion QuaternionUnitX = { 0, 0, 0, 1 };
inline Quaternion operator + (const Quaternion& lhs, const float& rhs)
{
return QuaternionAddValue(lhs, rhs);
}
inline const Quaternion& operator += (Quaternion& lhs, const float& rhs)
{
lhs = QuaternionAddValue(lhs, rhs);
return lhs;
}
inline Quaternion operator - (const Quaternion& lhs, const float& rhs)
{
return QuaternionSubtractValue(lhs, rhs);
}
inline const Quaternion& operator -= (Quaternion& lhs, const float& rhs)
{
lhs = QuaternionSubtractValue(lhs, rhs);
return lhs;
}
inline Quaternion operator * (const Quaternion& lhs, const Matrix& rhs)
{
return QuaternionTransform(lhs, rhs);
}
inline const Quaternion& operator *= (Quaternion& lhs, const Matrix& rhs)
{
lhs = QuaternionTransform(lhs, rhs);
return lhs;
}
// Matrix operators
inline Matrix operator + (const Matrix& lhs, const Matrix& rhs)
{
return MatrixAdd(lhs, rhs);
}
inline const Matrix& operator += (Matrix& lhs, const Matrix& rhs)
{
lhs = MatrixAdd(lhs, rhs);
return lhs;
}
inline Matrix operator - (const Matrix& lhs, const Matrix& rhs)
{
return MatrixSubtract(lhs, rhs);
}
inline const Matrix& operator -= (Matrix& lhs, const Matrix& rhs)
{
lhs = MatrixSubtract(lhs, rhs);
return lhs;
}
inline Matrix operator * (const Matrix& lhs, const Matrix& rhs)
{
return MatrixMultiply(lhs, rhs);
}
inline const Matrix& operator *= (Matrix& lhs, const Matrix& rhs)
{
lhs = MatrixMultiply(lhs, rhs);
return lhs;
}
//-------------------------------------------------------------------------------
#endif // C++ operators
#endif // RAYMATH_H