mathlib.h

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/*
Copyright (C) 1996-1997 Id Software, Inc.
 
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
 
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  
 
See the GNU General Public License for more details.
 
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 
*/
// mathlib.h
 
typedef float vec_t;
typedef vec_t vec2_t[2];
typedef vec_t vec3_t[3];
typedef vec_t vec4_t[4];
typedef vec_t vec5_t[5];
 
typedef int ivec_t;
typedef ivec_t ivec2_t[2];
typedef ivec_t ivec3_t[3];
typedef ivec_t ivec4_t[4];
typedef ivec_t ivec5_t[5];
 
/*16-byte aligned vectors, for auto-vectorising, should propogate to structs
sse and altivec can unroll loops using aligned reads, which should be faster... 4 at once.
*/
typedef FTE_ALIGN(16) vec3_t avec3_t;
typedef FTE_ALIGN(16) vec4_t avec4_t;
typedef FTE_ALIGN(4) qbyte byte_vec4_t[4];
 
//VECV_STRIDE is used only as an argument for opengl.
#ifdef FTE_TARGET_WEB
        //emscripten is alergic to explicit strides without packed attributes, at least in emulated code.
        //so we need to keep everything packed. screw sse-friendly packing.
        #define vecV_t vec3_t
        #define VECV_STRIDE 0
#else
        #define vecV_t avec4_t
        #define VECV_STRIDE sizeof(vecV_t)
#endif
 
typedef int     fixed4_t;
typedef int     fixed8_t;
typedef int     fixed16_t;
 
#ifndef M_PI
#define M_PI            3.14159265358979323846  // matches value in gcc v2 math.h
#endif
 
struct mplane_s;
 
extern vec3_t vec3_origin;
 
#define bound(min,num,max) ((num) >= (min) ? ((num) < (max) ? (num) : (max)) : (min))
 
#define nanmask (255<<23)
#define IS_NAN(x) (((*(int *)&x)&nanmask)==nanmask)
 
#define FloatInterpolate(a, bness, b, c) ((c) = (a) + (b - a)*bness)
 
#define DotProduct_Double(x,y) ((double)(x)[0]*(double)(y)[0]+(double)(x)[1]*(double)(y)[1]+(double)(x)[2]*(double)(y)[2])      //cast to doubles, to try to replicate x87 precision in 64bit sse builds etc. there'll still be a precision difference though.
#define DotProduct(x,y) ((x)[0]*(y)[0]+(x)[1]*(y)[1]+(x)[2]*(y)[2])
#define DotProduct2(x,y) ((x)[0]*(y)[0]+(x)[1]*(y)[1])
#define DotProduct4(x,y) ((x)[0]*(y)[0]+(x)[1]*(y)[1]+(x)[2]*(y)[2]+(x)[3]*(y)[3])
#define VectorSubtract(a,b,c) do{(c)[0]=(a)[0]-(b)[0];(c)[1]=(a)[1]-(b)[1];(c)[2]=(a)[2]-(b)[2];}while(0)
#define VectorAdd(a,b,c) do{(c)[0]=(a)[0]+(b)[0];(c)[1]=(a)[1]+(b)[1];(c)[2]=(a)[2]+(b)[2];}while(0)
#define VectorCopy(a,b) do{(b)[0]=(a)[0];(b)[1]=(a)[1];(b)[2]=(a)[2];}while(0)
#define VectorScale(a,s,b) do{(b)[0]=(s)*(a)[0];(b)[1]=(s)*(a)[1];(b)[2]=(s)*(a)[2];}while(0)
#define VectorMul(a,s,b) do{(b)[0]=(s)[0]*(a)[0];(b)[1]=(s)[1]*(a)[1];(b)[2]=(s)[2]*(a)[2];}while(0)
#define VectorClear(a)                  ((a)[0]=(a)[1]=(a)[2]=0)
#define VectorSet(r,x,y,z) do{(r)[0] = x; (r)[1] = y;(r)[2] = z;}while(0)
#define VectorNegate(a,b)               ((b)[0]=-(a)[0],(b)[1]=-(a)[1],(b)[2]=-(a)[2])
#define VectorLength(a)         Length(a)
#define VectorMA(a,s,b,c) do{(c)[0] = (a)[0] + (s)*(b)[0];(c)[1] = (a)[1] + (s)*(b)[1];(c)[2] = (a)[2] + (s)*(b)[2];}while(0)
#define VectorEquals(a,b) ((a)[0] == (b)[0] && (a)[1] == (b)[1] && (a)[2] == (b)[2])
#define VectorAvg(a,b,c)                ((c)[0]=((a)[0]+(b)[0])*0.5f,(c)[1]=((a)[1]+(b)[1])*0.5f, (c)[2]=((a)[2]+(b)[2])*0.5f)
#define VectorInterpolate(a, bness, b, c) FloatInterpolate((a)[0], bness, (b)[0], (c)[0]),FloatInterpolate((a)[1], bness, (b)[1], (c)[1]),FloatInterpolate((a)[2], bness, (b)[2], (c)[2])
#define Vector2Clear(a)                 ((a)[0]=(a)[1]=0)
#define Vector2Copy(a,b) do{(b)[0]=(a)[0];(b)[1]=(a)[1];}while(0)
#define Vector2Set(r,x,y) do{(r)[0] = x; (r)[1] = y;}while(0)
#define Vector2MA(a,s,b,c) do{(c)[0] = (a)[0] + (s)*(b)[0];(c)[1] = (a)[1] + (s)*(b)[1];}while(0)
#define Vector2Interpolate(a, bness, b, c) FloatInterpolate((a)[0], bness, (b)[0], (c)[0]),FloatInterpolate((a)[1], bness, (b)[1], (c)[1])
 
#define Vector4Copy(a,b) do{(b)[0]=(a)[0];(b)[1]=(a)[1];(b)[2]=(a)[2];(b)[3]=(a)[3];}while(0)
#define Vector4Scale(in,scale,out)              ((out)[0]=(in)[0]*scale,(out)[1]=(in)[1]*scale,(out)[2]=(in)[2]*scale,(out)[3]=(in)[3]*scale)
#define Vector4Add(a,b,c)               ((c)[0]=(((a[0])+(b[0]))),(c)[1]=(((a[1])+(b[1]))),(c)[2]=(((a[2])+(b[2]))),(c)[3]=(((a[3])+(b[3]))))
#define Vector4Set(r,x,y,z,w) (r)[0] = x, (r)[1] = y, (r)[2] = z, (r)[3]=w
#define Vector4Interpolate(a, bness, b, c) FloatInterpolate((a)[0], bness, (b)[0], (c)[0]),FloatInterpolate((a)[1], bness, (b)[1], (c)[1]),FloatInterpolate((a)[2], bness, (b)[2], (c)[2]),FloatInterpolate((a)[3], bness, (b)[3], (c)[3])
#define Vector4MA(a,s,b,c) do{(c)[0] = (a)[0] + (s)*(b)[0];(c)[1] = (a)[1] + (s)*(b)[1];(c)[2] = (a)[2] + (s)*(b)[2];(c)[3] = (a)[3] + (s)*(b)[3];}while(0)
 
typedef float matrix3x4[3][4];
typedef float matrix3x3[3][3];
 
 
#define BOX_ON_PLANE_SIDE(emins, emaxs, p)      \
        (((p)->type < 3)?                                               \
        (                                                                               \
                ((p)->dist <= (emins)[(p)->type])?      \
                        1                                                               \
                :                                                                       \
                (                                                                       \
                        ((p)->dist >= (emaxs)[(p)->type])?\
                                2                                                       \
                        :                                                               \
                                3                                                       \
                )                                                                       \
        )                                                                               \
        :                                                                               \
                BoxOnPlaneSide( (emins), (emaxs), (p)))
 
typedef struct {
        float m[4][4];
} matrix4x4_t;
 
//vec_t         _DotProduct (vec3_t v1, vec3_t v2);
//void          _VectorAdd (vec3_t veca, vec3_t vecb, vec3_t out);
//void          _VectorCopy (vec3_t in, vec3_t out);
//void          _VectorSubtract (vec3_t veca, vec3_t vecb, vec3_t out);
void            AddPointToBounds (const vec3_t v, vec3_t mins, vec3_t maxs);
float           anglemod (float a);
void            QDECL AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up);
void            QDECL AngleVectorsMesh (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up);
void            QDECL VectorAngles (const float *forward, const float *up, float *angles, qboolean meshpitch);  //up may be NULL
void VARGS      BOPS_Error (void);
int VARGS       BoxOnPlaneSide (const vec3_t emins, const vec3_t emaxs, const struct mplane_s *plane);
void            ClearBounds (vec3_t mins, vec3_t maxs);
float           ColorNormalize (const vec3_t in, vec3_t out);
void            CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross);
void            FloorDivMod (double numer, double denom, int *quotient, int *rem);
int                     GreatestCommonDivisor (int i1, int i2);
fixed16_t       Invert24To16 (fixed16_t val);
vec_t           Length (const vec3_t v);
void            MakeNormalVectors (const vec3_t forward, vec3_t right, vec3_t up);
float           Q_rsqrt(float number);
 
/*
_CM means column major.
_RM means row major
Note that openGL is column-major.
Logical C code uses row-major.
mat3x4 is always row-major (and functions can accept many RM mat4x4)
*/
 
void            Matrix3_Multiply (vec3_t *in1, vec3_t *in2, vec3_t *out);
void            Matrix4x4_Identity(float *outm);
qboolean        Matrix4_Invert(const float *m, float *out);
void            Matrix3x4_Invert (const float *in1, float *out);
void            QDECL Matrix3x4_Invert_Simple (const float *in1, float *out);
void            Matrix3x4_InvertTo4x4_Simple (const float *in1, float *out);
void            Matrix3x3_RM_Invert_Simple(const vec3_t in[3], vec3_t out[3]);
void            Matrix4x4_RM_CreateTranslate (float *out, float x, float y, float z);
void            Matrix4x4_CM_CreateTranslate (float *out, float x, float y, float z);
void            Matrix4x4_CM_ModelMatrixFromAxis (float *modelview, const vec3_t pn, const vec3_t right, const vec3_t up, const vec3_t vieworg);
void            Matrix4x4_CM_ModelMatrix(float *modelview, vec_t x, vec_t y, vec_t z, vec_t pitch, vec_t yaw, vec_t roll, vec_t scale);
void            Matrix4x4_CM_ModelViewMatrix (float *modelview, const vec3_t viewangles, const vec3_t vieworg);
void            Matrix4x4_CM_ModelViewMatrixFromAxis (float *modelview, const vec3_t pn, const vec3_t right, const vec3_t up, const vec3_t vieworg);
void            Matrix4x4_CM_LightMatrixFromAxis(float *modelview, const vec3_t px, const vec3_t py, const vec3_t pz, const vec3_t vieworg);    //
void            Matrix4_CreateFromQuakeEntity (float *matrix, float x, float y, float z, float pitch, float yaw, float roll, float scale);
void            Matrix4_Multiply (const float *a, const float *b, float *out);
void            Matrix3x4_Multiply(const float *a, const float *b, float *out);
qboolean        Matrix4x4_CM_Project (const vec3_t in, vec3_t out, const vec3_t viewangles, const vec3_t vieworg, float fovx, float fovy);
void            Matrix4x4_CM_Transform3x3(const float *matrix, const float *vector, float *product);
void            Matrix4x4_CM_Transform3 (const float *matrix, const float *vector, float *product);
void            Matrix4x4_CM_Transform4 (const float *matrix, const float *vector, float *product);
void            Matrix4x4_CM_Transform34(const float *matrix, const vec3_t vector, vec4_t product);
void            Matrix4x4_CM_UnProject (const vec3_t in, vec3_t out, const vec3_t viewangles, const vec3_t vieworg, float fovx, float fovy);
void            Matrix3x4_RM_FromAngles(const vec3_t angles, const vec3_t origin, float *out);
void            Matrix3x4_RM_FromVectors(float *out, const float vx[3], const float vy[3], const float vz[3], const float t[3]);
void            Matrix4x4_RM_FromVectors(float *out, const float vx[3], const float vy[3], const float vz[3], const float t[3]);
void            Matrix3x4_RM_ToVectors(const float *in, float vx[3], float vy[3], float vz[3], float t[3]);
void            Matrix3x4_RM_Transform3(const float *matrix, const float *vector, float *product);
void            Matrix3x4_RM_Transform3x3(const float *matrix, const float *vector, float *product);
 
float           *Matrix4x4_CM_NewRotation(float a, float x, float y, float z);
float           *Matrix4x4_CM_NewTranslation(float x, float y, float z);
 
void Bones_To_PosQuat4(int numbones, const float *matrix, short *result);
void QDECL GenMatrixPosQuat4Scale(const vec3_t pos, const vec4_t quat, const vec3_t scale, float result[12]);
void QuaternionSlerp(const vec4_t p, vec4_t q, float t, vec4_t qt);
 
#define AngleVectorsFLU(a,f,l,u) do{AngleVectors(a,f,l,u);VectorNegate(l,l);}while(0)
 
//projection matricies of different types... gesh
void            Matrix4x4_CM_Orthographic (float *proj, float xmin, float xmax, float ymax, float ymin, float znear, float zfar);
void Matrix4x4_CM_OrthographicD3D(float *proj, float xmin, float xmax, float ymax, float ymin, float znear, float zfar);
void            Matrix4x4_CM_Projection_Offset(float *proj, float fovl, float fovr, float fovu, float fovd, float neard, float fard, qboolean d3d);
void            Matrix4x4_CM_Projection_Far(float *proj, float fovx, float fovy, float neard, float fard, qboolean d3d);
void            Matrix4x4_CM_Projection2 (float *proj, float fovx, float fovy, float neard);
void            Matrix4x4_CM_Projection_Inf(float *proj, float fovx, float fovy, float neard, qboolean d3d);
 
fixed16_t       Mul16_30 (fixed16_t multiplier, fixed16_t multiplicand);
int                     Q_log2 (int val);
 
void            Matrix3x4_InvertTo3x3(const float *in, float *result);
 
fixed16_t       Mul16_30 (fixed16_t multiplier, fixed16_t multiplicand);
int                     Q_log2 (int val);
void            R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3]);
void            R_ConcatRotationsPad (float in1[3][4], float in2[3][4], float out[3][4]);
void            QDECL R_ConcatTransforms (const matrix3x4 in1, const matrix3x4 in2, matrix3x4 out);
void            R_ConcatTransformsAxis (const float in1[3][3], const float in2[3][4], float out[3][4]);
void            PerpendicularVector(vec3_t dst, const vec3_t src);
void            RotatePointAroundVector (vec3_t dst, const vec3_t dir, const vec3_t point, float degrees);
void            RotateLightVector(const vec3_t *axis, const vec3_t origin, const vec3_t lightpoint, vec3_t result);
int                     VectorCompare (const vec3_t v1, const vec3_t v2);
int                     Vector4Compare (const vec4_t v1, const vec4_t v2);
void            VectorInverse (vec3_t v);
void            _VectorMA (const vec3_t veca, const float scale, const vec3_t vecb, vec3_t vecc);
float           QDECL VectorNormalize (vec3_t v);               // returns vector length
vec_t           QDECL VectorNormalize2 (const vec3_t v, vec3_t out);
void            VectorNormalizeFast(vec3_t v);
void            VectorTransform (const vec3_t in1, const matrix3x4 in2, vec3_t out);
void            VectorVectors (const vec3_t forward, vec3_t right, vec3_t up);