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/**********************************************************************************************
*
* raymath v1.5 - 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
* - 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.
*
*
* LICENSE: zlib/libpng
*
* Copyright (c) 2015-2023 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 RL_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 RL_RMAPI __declspec( dllexport ) extern inline // We are building raylib as a Win32 shared library (.dll).
#elif defined( _WIN32 ) && defined( USE_LIBTYPE_SHARED )
#define RL_RMAPI __declspec( dllimport ) // We are using raylib as a Win32 shared library (.dll)
#else
#define RL_RMAPI extern inline // Provide external definition
#endif
#elif defined( RAYMATH_STATIC_INLINE )
#define RL_RMAPI static inline // Functions may be inlined, no external out-of-line definition
#else
#if defined( __TINYC__ )
#define RL_RMAPI static inline // plain inline not supported by tinycc (See issue #435)
#else
#define RL_RMAPI inline // Functions may be inlined or external definition used
#endif
#endif
//----------------------------------------------------------------------------------
// Defines and Macros
//----------------------------------------------------------------------------------
#ifndef PI
#define RL_PI 3.14159265358979323846f
#endif
#ifndef EPSILON
#define RL_EPSILON 0.000001f
#endif
#ifndef DEG2RAD
#define RL_DEG2RAD ( PI / 180.0f )
#endif
#ifndef RAD2DEG
#define RL_RAD2DEG ( 180.0f / PI )
#endif
// Get float vector for Matrix
#ifndef MatrixToFloat
#define RL_MatrixToFloat( mat ) ( MatrixToFloatV( mat ).v )
#endif
// Get float vector for Vector3
#ifndef Vector3ToFloat
#define RL_Vector3ToFloat( vec ) ( Vector3ToFloatV( vec ).v )
#endif
//----------------------------------------------------------------------------------
// Types and Structures Definition
//----------------------------------------------------------------------------------
#if ! defined( RL_VECTOR2_TYPE )
// Vector2 type
typedef struct Vector2
{
f32 x;
f32 y;
} Vector2;
#endif
#if ! defined( RL_VECTOR3_TYPE )
// Vector3 type
typedef struct Vector3
{
f32 x;
f32 y;
f32 z;
} Vector3;
#endif
#if ! defined( RL_VECTOR4_TYPE )
// Vector4 type
typedef struct Vector4
{
f32 x;
f32 y;
f32 z;
f32 w;
} Vector4;
#endif
#if ! defined( RL_QUATERNION_TYPE )
// Quaternion type
typedef Vector4 Quaternion;
#endif
#if ! defined( RL_MATRIX_TYPE )
// Matrix type (OpenGL style 4x4 - right handed, column major)
typedef struct Matrix
{
f32 m0, m4, m8, m12; // Matrix first row (4 components)
f32 m1, m5, m9, m13; // Matrix second row (4 components)
f32 m2, m6, m10, m14; // Matrix third row (4 components)
f32 m3, m7, m11, m15; // Matrix fourth row (4 components)
} Matrix;
#endif
// NOTE: Helper types to be used instead of array return types for *ToFloat functions
typedef struct float3
{
f32 v;
} float3;
typedef struct float16
{
f32 v;
} float16;
#include <math.h>
// Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), floor(), fminf(), fmaxf(), fabs()
//----------------------------------------------------------------------------------
// Module Functions Definition - Utils math
//----------------------------------------------------------------------------------
// Clamp float value
RMAPI float clamp( f32 value, f32 min, f32 max )
{
float result = ( value < min ) ? min : value;
if ( result > max )
result = max;
return result;
}
// Calculate linear interpolation between two floats
RMAPI float lerp( f32 start, f32 end, f32 amount )
{
float result = start + amount * ( end - start );
return result;
}
// Normalize input value within input range
RMAPI float normalize( f32 value, f32 start, f32 end )
{
float result = ( value - start ) / ( end - start );
return result;
}
// Remap input value within input range to output range
RMAPI float remap( f32 value, f32 inputStart, f32 inputEnd, f32 outputStart, f32 outputEnd )
{
float result = ( value - inputStart ) / ( inputEnd - inputStart ) * ( outputEnd - outputStart ) + outputStart;
return result;
}
// Wrap input value from min to max
RMAPI float wrap( f32 value, f32 min, f32 max )
{
float result = value - ( max - min ) * floorf( ( value - min ) / ( max - min ) );
return result;
}
// Check whether two given floats are almost equal
RMAPI int float_equals( f32 x, f32 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 vector2_zero( void )
{
Vector2 result = { 0.0f, 0.0f };
return result;
}
// Vector with components value 1.0f
RMAPI Vector2 vector2_one( void )
{
Vector2 result = { 1.0f, 1.0f };
return result;
}
// Add two vectors (v1 + v2)
RMAPI Vector2 vector2_add( Vector2 v1, Vector2 v2 )
{
Vector2 result = { v1.x + v2.x, v1.y + v2.y };
return result;
}
// Add vector and float value
RMAPI Vector2 vector2_add_value( Vector2 v, f32 add )
{
Vector2 result = { v.x + add, v.y + add };
return result;
}
// Subtract two vectors (v1 - v2)
RMAPI Vector2 vector2_subtract( Vector2 v1, Vector2 v2 )
{
Vector2 result = { v1.x - v2.x, v1.y - v2.y };
return result;
}
// Subtract vector by float value
RMAPI Vector2 vector2_subtract_value( Vector2 v, f32 sub )
{
Vector2 result = { v.x - sub, v.y - sub };
return result;
}
// Calculate vector length
RMAPI float vector2_length( Vector2 v )
{
float result = sqrtf( ( v.x * v.x ) + ( v.y * v.y ) );
return result;
}
// Calculate vector square length
RMAPI float vector2_length_sqr( Vector2 v )
{
float result = ( v.x * v.x ) + ( v.y * v.y );
return result;
}
// Calculate two vectors dot product
RMAPI float vector_2dot_product( Vector2 v1, Vector2 v2 )
{
float result = ( v1.x * v2.x + v1.y * v2.y );
return result;
}
// Calculate distance between two vectors
RMAPI float vector_2distance( 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 vector_2distance_sqr( 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 angle between two vectors
// NOTE: Angle is calculated from origin point (0, 0)
RMAPI float vector2_angle( 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 vector2_line_angle( 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 vector2_scale( Vector2 v, f32 scale )
{
Vector2 result = { v.x * scale, v.y * scale };
return result;
}
// Multiply vector by vector
RMAPI Vector2 vector2_multiply( Vector2 v1, Vector2 v2 )
{
Vector2 result = { v1.x * v2.x, v1.y * v2.y };
return result;
}
// Negate vector
RMAPI Vector2 vector2_negate( Vector2 v )
{
Vector2 result = { -v.x, -v.y };
return result;
}
// Divide vector by vector
RMAPI Vector2 vector_2divide( Vector2 v1, Vector2 v2 )
{
Vector2 result = { v1.x / v2.x, v1.y / v2.y };
return result;
}
// Normalize provided vector
RMAPI Vector2 vector2_normalize( 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 vector2_transform( 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 vector2_lerp( Vector2 v1, Vector2 v2, f32 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 vector2_reflect( 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;
}
// Rotate vector by angle
RMAPI Vector2 vector2_rotate( Vector2 v, f32 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 vector2_move_towards( Vector2 v, Vector2 target, f32 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 vector2_invert( 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 vector2_clamp( 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 vector2_clamp_value( Vector2 v, f32 min, f32 max )
{
Vector2 result = v;
float length = ( v.x * v.x ) + ( v.y * v.y );
if ( length > 0.0f )
{
length = sqrtf( length );
if ( length < min )
{
float scale = min / length;
result.x = v.x * scale;
result.y = v.y * scale;
}
else if ( length > max )
{
float 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 vector2_equals( 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;
}
//----------------------------------------------------------------------------------
// Module Functions Definition - Vector3 math
//----------------------------------------------------------------------------------
// Vector with components value 0.0f
RMAPI Vector3 vector3_zero( void )
{
Vector3 result = { 0.0f, 0.0f, 0.0f };
return result;
}
// Vector with components value 1.0f
RMAPI Vector3 vector3_one( void )
{
Vector3 result = { 1.0f, 1.0f, 1.0f };
return result;
}
// Add two vectors
RMAPI Vector3 vector3_add( 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 vector3_add_value( Vector3 v, f32 add )
{
Vector3 result = { v.x + add, v.y + add, v.z + add };
return result;
}
// Subtract two vectors
RMAPI Vector3 vector3_subtract( 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 vector3_subtract_value( Vector3 v, f32 sub )
{
Vector3 result = { v.x - sub, v.y - sub, v.z - sub };
return result;
}
// Multiply vector by scalar
RMAPI Vector3 vector3_scale( Vector3 v, f32 scalar )
{
Vector3 result = { v.x * scalar, v.y * scalar, v.z * scalar };
return result;
}
// Multiply vector by vector
RMAPI Vector3 vector3_multiply( 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 vector3_cross_product( 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 vector3_perpendicular( Vector3 v )
{
Vector3 result = { 0 };
float min = ( float )fabs( v.x );
Vector3 cardinalAxis = { 1.0f, 0.0f, 0.0f };
if ( fabsf( v.y ) < min )
{
min = ( float )fabs( 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 vector3_length( Vector3 const v )
{
float result = sqrtf( v.x * v.x + v.y * v.y + v.z * v.z );
return result;
}
// Calculate vector square length
RMAPI float vector3_length_sqr( Vector3 const v )
{
float result = v.x * v.x + v.y * v.y + v.z * v.z;
return result;
}
// Calculate two vectors dot product
RMAPI float vector_3dot_product( 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 vector_3distance( 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 vector_3distance_sqr( 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 vector3_angle( 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 vector3_negate( Vector3 v )
{
Vector3 result = { -v.x, -v.y, -v.z };
return result;
}
// Divide vector by vector
RMAPI Vector3 vector_3divide( 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 vector3_normalize( 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 vector3_project( 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 vector3_reject( 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 vector3_ortho_normalize( 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 vector3_transform( 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 vector3_rotate_by_quaternion( 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 vector3_rotate_by_axis_angle( Vector3 v, Vector3 axis, f32 angle )
{
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;
}
// Calculate linear interpolation between two vectors
RMAPI Vector3 vector3_lerp( Vector3 v1, Vector3 v2, f32 amount )
{
Vector3 result = { 0 };
result.x = v1.x + amount * ( v2.x - v1.x );
result.y = v1.y + amount * ( v2.y - v1.y );
result.z = v1.z + amount * ( v2.z - v1.z );
return result;
}
// Calculate reflected vector to normal
RMAPI Vector3 vector3_reflect( 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 vector3_min( 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 vector3_max( 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 vector3_barycenter( 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 vector3_unproject( 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 vector3_to_float_v( 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 vector3_invert( 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 vector3_clamp( 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 vector3_clamp_value( Vector3 v, f32 min, f32 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 );
if ( length < min )
{
float scale = min / length;
result.x = v.x * scale;
result.y = v.y * scale;
result.z = v.z * scale;
}
else if ( length > max )
{
float 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 vector3_equals( 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 vector3_refract( Vector3 v, Vector3 n, f32 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 - Matrix math
//----------------------------------------------------------------------------------
// Compute matrix determinant
RMAPI float matrix_determinant( 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 matrix_trace( Matrix mat )
{
float result = ( mat.m0 + mat.m5 + mat.m10 + mat.m15 );
return result;
}
// Transposes provided matrix
RMAPI Matrix matrix_transpose( 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 matrix_invert( 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 matrix_identity( 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 matrix_add( 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 matrix_subtract( 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 matrix_multiply( 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 matrix_translate( f32 x, f32 y, f32 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 matrix_rotate( Vector3 axis, f32 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 matrix_rotate_x( f32 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 matrix_rotate_y( f32 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 matrix_rotate_z( f32 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 matrix_rotate_xyz( 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 matrix_rotate_zyx( 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 matrix_scale( f32 x, f32 y, f32 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 matrix_frustum( double left, double right, double bottom, double top, double near, double far )
{
Matrix result = { 0 };
float rl = ( float )( right - left );
float tb = ( float )( top - bottom );
float fn = ( float )( far - near );
result.m0 = ( ( float )near * 2.0f ) / rl;
result.m1 = 0.0f;
result.m2 = 0.0f;
result.m3 = 0.0f;
result.m4 = 0.0f;
result.m5 = ( ( float )near * 2.0f ) / tb;
result.m6 = 0.0f;
result.m7 = 0.0f;
result.m8 = ( ( float )right + ( float )left ) / rl;
result.m9 = ( ( float )top + ( float )bottom ) / tb;
result.m10 = -( ( float )far + ( float )near ) / fn;
result.m11 = -1.0f;
result.m12 = 0.0f;
result.m13 = 0.0f;
result.m14 = -( ( float )far * ( float )near * 2.0f ) / fn;
result.m15 = 0.0f;
return result;
}
// Get perspective projection matrix
// NOTE: Fovy angle must be provided in radians
RMAPI Matrix matrix_perspective( 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 matrix_ortho( 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 matrix_look_at( 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 matrix_to_float_v( 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 quaternion_add( 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 quaternion_add_value( Quaternion q, f32 add )
{
Quaternion result = { q.x + add, q.y + add, q.z + add, q.w + add };
return result;
}
// Subtract two quaternions
RMAPI Quaternion quaternion_subtract( 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 quaternion_subtract_value( Quaternion q, f32 sub )
{
Quaternion result = { q.x - sub, q.y - sub, q.z - sub, q.w - sub };
return result;
}
// Get identity quaternion
RMAPI Quaternion quaternion_identity( void )
{
Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
return result;
}
// Computes the length of a quaternion
RMAPI float quaternion_length( 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 quaternion_normalize( 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 quaternion_invert( 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 quaternion_multiply( 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 quaternion_scale( Quaternion q, f32 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 quaternion_divide( 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 quaternion_lerp( Quaternion q1, Quaternion q2, f32 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 quaternion_nlerp( Quaternion q1, Quaternion q2, f32 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 quaternion_slerp( Quaternion q1, Quaternion q2, f32 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 based on the rotation from one vector to another
RMAPI Quaternion quaternion_from_vector3_to_vector3( 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 quaternion_from_matrix( 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 quaternion_to_matrix( 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 quaternion_from_axis_angle( Vector3 axis, f32 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)
Vector3 v = axis;
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;
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 quaternion_to_axis_angle( Quaternion q, Vector3* outAxis, f32* 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 quaternion_from_euler( f32 pitch, f32 yaw, f32 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 quaternion_to_euler( 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 quaternion_transform( 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 quaternion_equals( 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;
}
#endif
// RAYMATH_H
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