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fwk_math.h
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fwk_math.h
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// -----------------------------------------------------------------------------
// math framework: rand, ease, vec2, vec3, vec4, quat, mat2, mat33, mat34, mat4
// - rlyeh, public domain
//
// Credits: @ands+@krig+@vurtun (PD), @datenwolf (WTFPL2), @evanw+@barerose (CC0), @sgorsten (Unlicense).
#define C_EPSILON (1e-6)
#define C_PI (3.14159265358979323846f) // (3.141592654f)
#define TO_RAD (C_PI/180)
#define TO_DEG (180/C_PI)
// ----------------------------------------------------------------------------
//#define ptr(type) 0[&(type).x]
#define vec2i(x, y ) C_CAST(vec2i,(int)(x), (int)(y) )
#define vec3i(x, y, z ) C_CAST(vec3i,(int)(x), (int)(y), (int)(z) )
#define vec2(x, y ) C_CAST(vec2, (float)(x), (float)(y) )
#define vec3(x, y, z ) C_CAST(vec3, (float)(x), (float)(y), (float)(z), )
#define vec4(x, y, z, w) C_CAST(vec4, (float)(x), (float)(y), (float)(z), (float)(w))
#define quat(x, y, z, w) C_CAST(quat, (float)(x), (float)(y), (float)(z), (float)(w))
#define axis(x, y, z) C_CAST(axis, (float)(x), (float)(y), (float)(z))
#define mat33(...) C_CAST(mat33, __VA_ARGS__ )
#define mat34(...) C_CAST(mat34, __VA_ARGS__ )
#define mat44(...) C_CAST(mat44, __VA_ARGS__ )
typedef union vec2i{ struct { int X,Y; }; struct { int x,y; }; struct { int r,g; }; struct { int w,h; }; struct { int min,max; }; struct { int from,to; }; struct { int src,dst; }; int v2[2]; int array[1]; } vec2i;
typedef union vec3i{ struct { int X,Y,Z; }; struct { int x,y,z; }; struct { int r,g,b; }; struct { int w,h,d; }; struct { int min,max; }; struct { int from,to,step; }; struct { int src,dst; }; int v3[3]; int array[1]; } vec3i;
typedef union vec2 { struct { float X,Y; }; struct { float x,y; }; struct { float r,g; }; struct { float w,h; }; struct { float min,max; }; struct { float from,to; }; struct { float src,dst; }; float v2[2]; float array[1]; } vec2;
typedef union vec3 { struct { float X,Y,Z; }; struct { float x,y,z; }; struct { float r,g,b; }; struct { float min,max; }; struct { float from,to; }; vec2 xy; vec2 rg; vec2 wh; float v3[3]; float array[1]; } vec3;
typedef union vec4 { struct { float X,Y,Z,W; }; struct { float x,y,z,w; }; struct { float r,g,b,a; }; struct { float min,max; }; struct { float from,to; }; vec2 xy; vec3 xyz; vec2 rg; vec3 rgb; vec2 wh; vec3 whd; float v4[4]; float array[1]; } vec4;
typedef union quat { struct { float X,Y,Z,W; }; struct { float x,y,z,w; }; vec3 xyz; vec4 xyzw; float v4[4]; float array[1]; } quat;
typedef float mat33[9];
typedef float mat34[12];
typedef float mat44[16];
// ----------------------------------------------------------------------------
API void randset(uint64_t state);
API uint64_t rand64(void);
API double randf(void); // [0, 1) interval
API int randi(int mini, int maxi); // [mini, maxi) interval
// ----------------------------------------------------------------------------
API float simplex1( float x );
API float simplex2( vec2 xy );
API float simplex3( vec3 xyz );
API float simplex4( vec4 xyzw );
// ----------------------------------------------------------------------------
API float deg (float radians);
API float rad (float degrees);
API int mini (int a, int b);
API int maxi (int a, int b);
API int absi (int a );
API int clampi (int v,int a,int b);
API float minf (float a, float b);
API float maxf (float a, float b);
API float absf (float a );
API float pmodf (float a, float b);
API float signf (float a) ;
API float clampf (float v,float a,float b);
API float mixf (float a,float b,float t);
API float slerpf (float a,float b,float t);
API float fractf (float a);
// ----------------------------------------------------------------------------
API vec2 ptr2 (const float *a );
//
API vec2 neg2 (vec2 a );
API vec2 add2 (vec2 a, vec2 b);
API vec2 sub2 (vec2 a, vec2 b);
API vec2 mul2 (vec2 a, vec2 b);
API vec2 div2 (vec2 a, vec2 b);
API vec2 inc2 (vec2 a, float b);
API vec2 dec2 (vec2 a, float b);
API vec2 scale2 (vec2 a, float b);
API vec2 pmod2 (vec2 a, float b);
API vec2 min2 (vec2 a, vec2 b);
API vec2 max2 (vec2 a, vec2 b);
API vec2 abs2 (vec2 a );
API vec2 floor2 (vec2 a );
API vec2 fract2 (vec2 a );
API vec2 ceil2 (vec2 a );
API float dot2 (vec2 a, vec2 b);
API vec2 refl2 (vec2 a, vec2 b);
API float cross2 (vec2 a, vec2 b);
API float len2sq (vec2 a );
API float len2 (vec2 a );
API vec2 norm2 (vec2 a );
API int finite2 (vec2 a );
API vec2 mix2 (vec2 a,vec2 b,float t);
API vec2 clamp2(vec2 v,vec2 a,vec2 b);
API vec2 clamp2f(vec2 v,float a,float b);
// ----------------------------------------------------------------------------
API vec3 rnd3 (void); // @todo: rnd2,rnd4,rndq
API vec3 ptr3 (const float *a );
API vec3 vec23 (vec2 a, float z );
//
API vec3 neg3 (vec3 a );
API vec3 add3 (vec3 a, vec3 b);
API vec3 sub3 (vec3 a, vec3 b);
API vec3 mul3 (vec3 a, vec3 b);
API vec3 div3 (vec3 a, vec3 b);
API vec3 inc3 (vec3 a, float b);
API vec3 dec3 (vec3 a, float b);
API vec3 scale3 (vec3 a, float b);
API vec3 pmod3 (vec3 a, float b);
API vec3 min3 (vec3 a, vec3 b);
API vec3 max3 (vec3 a, vec3 b);
API vec3 abs3 (vec3 a );
API vec3 floor3 (vec3 a );
API vec3 fract3 (vec3 a );
API vec3 ceil3 (vec3 a );
API vec3 cross3 (vec3 a, vec3 b);
API float dot3 (vec3 a, vec3 b);
API vec3 refl3 (vec3 a, vec3 b);
API float len3sq (vec3 a );
API float len3 (vec3 a );
API vec3 norm3 (vec3 a );
API vec3 norm3sq (vec3 a );
API int finite3 (vec3 a );
API vec3 mix3 (vec3 a,vec3 b,float t);
API vec3 clamp3(vec3 v,vec3 a,vec3 b);
API vec3 clamp3f(vec3 v,float a,float b);
//vec3 tricross3 (vec3 a, vec3 b, vec3 c);
API void ortho3 (vec3 *left, vec3 *up, vec3 v);
API vec3 rotatex3 (vec3 dir, float degrees);
API vec3 rotatey3 (vec3 dir, float degrees);
API vec3 rotatez3 (vec3 dir, float degrees);
// ----------------------------------------------------------------------------
API vec4 ptr4 (const float *a );
API vec4 vec34 (vec3 a, float w );
//
API vec4 neg4 (vec4 a );
API vec4 add4 (vec4 a, vec4 b);
API vec4 sub4 (vec4 a, vec4 b);
API vec4 mul4 (vec4 a, vec4 b);
API vec4 div4 (vec4 a, vec4 b);
API vec4 inc4 (vec4 a, float b);
API vec4 dec4 (vec4 a, float b);
API vec4 scale4 (vec4 a, float b);
API vec4 pmod4 (vec4 a, float b);
API vec4 min4 (vec4 a, vec4 b);
API vec4 max4 (vec4 a, vec4 b);
API vec4 abs4 (vec4 a );
API vec4 floor4 (vec4 a );
API vec4 fract4 (vec4 a );
API vec4 ceil4 (vec4 a );
API float dot4 (vec4 a, vec4 b);
API vec4 refl4 (vec4 a, vec4 b);
API float len4sq (vec4 a );
API float len4 (vec4 a );
API vec4 norm4 (vec4 a );
API vec4 norm4sq (vec4 a );
API int finite4 (vec4 a );
API vec4 mix4 (vec4 a,vec4 b,float t);
API vec4 clamp4(vec4 v,vec4 a,vec4 b);
API vec4 clamp4f(vec4 v,float a,float b);
// vec4 cross4(vec4 v0, vec4 v1);
// ----------------------------------------------------------------------------
API quat idq ( );
API quat ptrq (const float *a );
API quat vec3q (vec3 a, float w );
API quat vec4q (vec4 a );
//
API quat negq (quat a );
API quat conjq (quat a );
API quat addq (quat a, quat b);
API quat subq (quat a, quat b);
API quat mulq (quat p, quat q);
API quat scaleq (quat a, float s);
API quat normq (quat a );
API float dotq (quat a, quat b);
API quat mixq(quat a, quat b, float t);
/* quat lerpq(quat a, quat b, float s);
return norm(quat((1-s)*a.x + s*b.x, (1-s)*a.y + s*b.y, (1-s)*a.z + s*b.z, (1-s)*a.w + s*b.w));
}*/
API quat slerpq(quat a, quat b, float s);
API quat rotationq(float deg,float x,float y,float z);
API quat mat44q (mat44 M);
API vec3 rotate3q_2(vec3 v, quat q);
API vec3 rotate3q(vec3 v, quat r);
// euler <-> quat
API vec3 euler (quat q);
API quat eulerq (vec3 pyr_degrees);
// ----------------------------------------------------------------------------
API void scaling33(mat33 m, float x, float y, float z);
API void scale33(mat33 m, float x, float y, float z);
API void id33(mat33 m);
API void extract33(mat33 m, const mat44 m4);
API void copy33(mat33 m, const mat33 a);//
API vec3 mulv33(mat33 m, vec3 v);
API void multiply33x2(mat33 m, const mat33 a, const mat33 b);
API void rotation33(mat33 m, float degrees, float x,float y,float z);
API void rotationq33(mat33 m, quat q);
API void rotate33(mat33 r, float degrees, float x,float y,float z);
API void compose33(mat33 m, quat r, vec3 s);
// ----------------------------------------------------------------------------
API void id34(mat34 m);
API void copy34(mat34 m, const mat34 a);
API void scale34(mat34 m, float s);
API void add34(mat34 m, mat34 n);
API void muladd34(mat34 m, mat34 n, float s);
API void add34x2(mat34 m, mat34 n, mat34 o);
API void lerp34(mat34 m, mat34 n, mat34 o, float alpha); // mix34?
API void multiply34x2(mat34 m, const mat34 m0, const mat34 m1);
API void multiply34(mat34 m, const mat34 a);
API void multiply34x3(mat34 m, const mat34 a, const mat34 b, const mat34 c);
API void compose34(mat34 m, vec3 t, quat q, vec3 s);
API void invert34(mat34 m, const mat34 o);
// ----------------------------------------------------------------------------
API void id44(mat44 m);
API void identity44(mat44 m);
API void copy44(mat44 m, const mat44 a);
API void multiply44x2(mat44 m, const mat44 a, const mat44 b);
API void multiply44x3(mat44 m, const mat44 a, const mat44 b, const mat44 c);
API void multiply44(mat44 m, const mat44 a);
// ---
API void ortho44(mat44 m, float l, float r, float b, float t, float n, float f);
API void frustum44(mat44 m, float l, float r, float b, float t, float n, float f);
API void perspective44(mat44 m, float fovy_degrees, float aspect, float nearp, float farp);
API void lookat44(mat44 m, vec3 eye, vec3 center, vec3 up);
// ---
API void translation44(mat44 m, float x, float y, float z);
API void translate44(mat44 m, float x, float y, float z);
API void relocate44(mat44 m, float x, float y, float z);
API void rotationq44(mat44 m, quat q);
API void rotation44(mat44 m, float degrees, float x, float y, float z);
API void rotate44(mat44 m, float degrees, float x, float y, float z);
API void scaling44(mat44 m, float x, float y, float z);
API void scale44(mat44 m, float x, float y, float z);
// ---
API void transpose44(mat44 m, const mat44 a);
API float det44(const mat44 M);
API bool invert44(mat44 T, const mat44 M);
API void compose44(mat44 m, vec3 t, quat q, vec3 s);
// ----------------------------------------------------------------------------
API vec3 transformq(const quat q, const vec3 v);
API vec3 transform33(const mat33 m, vec3 p);
API vec3 transform344(const mat44 m, const vec3 p);
API vec4 transform444(const mat44 m, const vec4 p);
API bool unproject44(vec3 *out, vec3 xyd, vec4 viewport, mat44 mvp);
// ----------------------------------------------------------------------------
// debugging and utils
API void print2i( vec2i v );
API void print3i( vec3i v );
API void print2( vec2 v );
API void print3( vec3 v );
API void print4( vec4 v );
API void printq( quat q );
API void print33( float *m );
API void print34( float *m );
API void print44( float *m );