/********************************************************************************************** * * 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) 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; #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 // 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, float 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, float amount ) { float result = start + amount * ( end - start ); return result; } // Normalize input value within input range RMAPI float normalize( f32 value, f32 start, float 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, float 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, float 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, 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 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, float 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, float 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, float 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, 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 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, 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 vector2_move_towards( 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 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, float 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, float 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, float sub ) { Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; return result; } // Multiply vector by scalar RMAPI Vector3 vector3_scale( Vector3 v, float 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, float 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, float amount ) { Vector3 result = { 0 }; result.x = v1.x + amount * ( v2.x - v1.x ); result.y = v1.y + amount * ( v2.y - v1.y ); result.z = v1.z + amount * ( v2.z - v1.z ); return result; } // Calculate reflected vector to normal 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, 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 ); 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, 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 - 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, 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 matrix_rotate( 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 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, 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 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, float 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, float 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, 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 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, 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 quaternion_nlerp( 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 quaternion_slerp( 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 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, 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) 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, 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 quaternion_from_euler( f32 pitch, f32 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 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