/* mathlib.h Vector math library 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: Free Software Foundation, Inc. 59 Temple Place - Suite 330 Boston, MA 02111-1307, USA $Id$ */ #ifndef __mathlib_h #define __mathlib_h /** \defgroup mathlib Vector and matrix functions \ingroup utils */ //@{ #include #include "QF/qtypes.h" #ifndef max # define max(a,b) ((a) > (b) ? (a) : (b)) #endif #ifndef min # define min(a,b) ((a) < (b) ? (a) : (b)) #endif #ifndef bound # define bound(a,b,c) (max(a, min(b, c))) #endif #ifndef M_PI # define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h #endif extern int nanmask; extern const vec_t * const vec3_origin; extern const vec_t * const quat_origin; #define EQUAL_EPSILON 0.001 #define RINT(x) (floor ((x) + 0.5)) #define IS_NAN(x) (((*(int *) (char *) &x) & nanmask) == nanmask) #define DotProduct(a,b) ((a)[0] * (b)[0] + (a)[1] * (b)[1] + (a)[2] * (b)[2]) #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 VectorNegate(a,b) \ do { \ (b)[0] = -(a)[0]; \ (b)[1] = -(a)[1]; \ (b)[2] = -(a)[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 VectorMultAdd(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 VectorMultSub(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 VectorLength(a) sqrt(DotProduct(a, a)) #define VectorScale(a,b,c) \ do { \ (c)[0] = (a)[0] * (b); \ (c)[1] = (a)[1] * (b); \ (c)[2] = (a)[2] * (b); \ } while (0) #define Vector3Scale(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 VectorCompCompare(x, op, y) \ (((x)[0] op (y)[0]) && ((x)[1] op (y)[1]) && ((x)[2] op (y)[2])) #define VectorCompare(x, y) VectorCompCompare (x, ==, y) #define VectorIsZero(a) (!(a)[0] && !(a)[1] && !(a)[2]) #define VectorZero(a) ((a)[2] = (a)[1] = (a)[0] = 0); #define VectorSet(a,b,c,d) \ do { \ (d)[0] = a; \ (d)[1] = b; \ (d)[2] = c; \ } while (0) #define VectorBlend(v1,v2,b,v) \ do { \ (v)[0] = (v1)[0] * (1 - (b)) + (v2)[0] * (b); \ (v)[1] = (v1)[1] * (1 - (b)) + (v2)[1] * (b); \ (v)[2] = (v1)[2] * (1 - (b)) + (v2)[2] * (b); \ } while (0) //For printf etc #define VectorExpand(v) (v)[0], (v)[1], (v)[2] #define QDotProduct(a,b) ((a)[0] * (b)[0] + (a)[1] * (b)[1] \ + (a)[2] * (b)[2] + (a)[3] * (b)[3]) #define QuatSubtract(a,b,c) \ do { \ (c)[0] = (a)[0] - (b)[0]; \ (c)[1] = (a)[1] - (b)[1]; \ (c)[2] = (a)[2] - (b)[2]; \ (c)[3] = (a)[3] - (b)[3]; \ } while (0) #define QuatNegate(a,b) \ do { \ (b)[0] = -(a)[0]; \ (b)[1] = -(a)[1]; \ (b)[2] = -(a)[2]; \ (b)[3] = -(a)[3]; \ } while (0) #define QuatConj(a,b) \ do { \ (b)[0] = (a)[0]; \ (b)[1] = -(a)[1]; \ (b)[2] = -(a)[2]; \ (b)[3] = -(a)[3]; \ } while (0) #define QuatAdd(a,b,c) \ do { \ (c)[0] = (a)[0] + (b)[0]; \ (c)[1] = (a)[1] + (b)[1]; \ (c)[2] = (a)[2] + (b)[2]; \ (c)[3] = (a)[3] + (b)[3]; \ } while (0) #define QuatCopy(a,b) \ do { \ (b)[0] = (a)[0]; \ (b)[1] = (a)[1]; \ (b)[2] = (a)[2]; \ (b)[3] = (a)[3]; \ } while (0) #define QuatMultAdd(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) #define QuatMultSub(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) #define QuatLength(a) sqrt(QDotProduct(a, a)) #define QuatScale(a,b,c) \ do { \ (c)[0] = (a)[0] * (b); \ (c)[1] = (a)[1] * (b); \ (c)[2] = (a)[2] * (b); \ (c)[3] = (a)[3] * (3); \ } while (0) #define QuatCompCompare(x, op, y) \ (((x)[0] op (y)[0]) && ((x)[1] op (y)[1]) \ && ((x)[2] op (y)[2]) && ((x)[3] op (y)[3])) #define QuatCompare(x, y) QuatCompCompare (x, ==, y) #define QuatIsZero(a) (!(a)[0] && !(a)[1] && !(a)[2] && !(a)[3]) #define QuatZero(a) ((a)[3] = (a)[2] = (a)[1] = (a)[0] = 0); #define QuatSet(a,b,c,d,e) \ do { \ (e)[0] = a; \ (e)[1] = b; \ (e)[2] = c; \ (e)[3] = d; \ } while (0) #define QuatBlend(v1,v2,b,v) \ do { \ (v)[0] = (v1)[0] * (1 - (b)) + (v2)[0] * (b); \ (v)[1] = (v1)[1] * (1 - (b)) + (v2)[1] * (b); \ (v)[2] = (v1)[2] * (1 - (b)) + (v2)[2] * (b); \ (v)[3] = (v1)[3] * (1 - (b)) + (v2)[3] * (b); \ } while (0) //For printf etc #define QuatExpand(q) (q)[0], (q)[1], (q)[2], (q)[3] /* * VectorDistance, the distance between two points. * Yes, this is the same as sqrt(VectorSubtract then DotProduct), * however that way would involve more vars, this is cheaper. */ #define VectorDistance_fast(a, b) \ ((((a)[0] - (b)[0]) * ((a)[0] - (b)[0])) + \ (((a)[1] - (b)[1]) * ((a)[1] - (b)[1])) + \ (((a)[2] - (b)[2]) * ((a)[2] - (b)[2]))) #define VectorDistance(a, b) sqrt(VectorDistance_fast(a, b)) #define qfrandom(MAX) ((float) MAX * (rand() * (1.0 / (RAND_MAX + 1.0)))) // up / down #define PITCH 0 // left / right #define YAW 1 // fall over #define ROLL 2 vec_t _DotProduct (const vec3_t v1, const vec3_t v2); void _VectorAdd (const vec3_t veca, const vec3_t vecb, vec3_t out); void _VectorCopy (const vec3_t in, vec3_t out); int _VectorCompare (const vec3_t v1, const vec3_t v2); // uses EQUAL_EPSILON vec_t _VectorLength (const vec3_t v); void _VectorMA (const vec3_t veca, float scale, const vec3_t vecb, vec3_t vecc); void _VectorScale (const vec3_t in, vec_t scale, vec3_t out); void _VectorSubtract (const vec3_t veca, const vec3_t vecb, vec3_t out); void CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross); vec_t _VectorNormalize (vec3_t v); // returns vector length int Q_log2(int val); void R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3]); void R_ConcatTransforms (float in1[3][4], float in2[3][4], float out[3][4]); void FloorDivMod (double numer, double denom, int *quotient, int *rem); fixed16_t Invert24To16(fixed16_t val); fixed16_t Mul16_30(fixed16_t multiplier, fixed16_t multiplicand); int GreatestCommonDivisor (int i1, int i2); /** Convert quake angles to basis vectors. The basis vectors form a left handed system (although the world is right handed). When all angles are 0, \a forward points along the world X axis, \a right along the negative Y axis, and \a up along the Z axis. Rotation is done by: -# Rotating YAW degrees counterclockwise around the local Z axis -# Rotating PITCH degrees clockwise around the new local negative Y axis (or counterclockwise around the new local Y axis). -# Rotating ROLL degrees counterclockwise around the local X axis Thus when used for the player from the first person perspective, positive YAW turns to the left, positive PITCH looks down, and positive ROLL leans to the right. \f[ YAW=\begin{array}{ccc} c_{y} & s_{y} & 0\\ -s_{y} & c_{y} & 0\\ 0 & 0 & 1 \end{array} \f] \f[ PITCH=\begin{array}{ccc} c_{p} & 0 & -s_{p}\\ 0 & 1 & 0\\ s_{p} & 0 & c_{p} \end{array} \f] \f[ ROLL=\begin{array}{ccc} 1 & 0 & 0\\ 0 & c_{r} & -s_{r}\\ 0 & s_{r} & c_{r} \end{array} \f] \f[ ROLL\,(PITCH\,YAW)=\begin{array}{c} forward\\ -right\\ up \end{array} \f] \param angles The rotation angles. \param forward The vector pointing forward. \param right The vector pointing to the right. \param up The vector pointing up. */ void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up); void AngleQuat (const vec3_t angles, quat_t q); void VectorVectors (const vec3_t forward, vec3_t right, vec3_t up); int BoxOnPlaneSide (const vec3_t emins, const vec3_t emaxs, struct plane_s *plane); float anglemod (float a); void RotatePointAroundVector (vec3_t dst, const vec3_t axis, const vec3_t point, float degrees); void QuatMult (const quat_t q1, const quat_t q2, quat_t out); void QuatInverse (const quat_t in, quat_t out); void QuatToMatrix (const quat_t q, vec_t *m, int homogenous, int vertical); #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))) #define PlaneDist(point,plane) \ ((plane)->type < 3 ? (point)[(plane)->type] \ : DotProduct((point), (plane)->normal)) #define PlaneDiff(point,plane) \ (PlaneDist (point, plane) - (plane)->dist) #define PlaneFlip(sp, dp) \ do { \ (dp)->dist = -(sp)->dist; \ VectorNegate ((sp)->normal, (dp)->normal); \ } while (0) extern plane_t * const frustum; extern inline qboolean R_CullBox (const vec3_t mins, const vec3_t maxs); extern inline qboolean R_CullSphere (const vec3_t origin, const float radius); extern inline float VectorNormalize (vec3_t v); // returns vector length #ifndef IMPLEMENT_R_Cull extern inline #else VISIBLE #endif qboolean R_CullBox (const vec3_t mins, const vec3_t maxs) { int i; for (i=0 ; i < 4 ; i++) if (BoxOnPlaneSide (mins, maxs, &frustum[i]) == 2) return true; return false; } #ifndef IMPLEMENT_R_Cull extern inline #else VISIBLE #endif qboolean R_CullSphere (const vec3_t origin, const float radius) { int i; float r; for (i = 0; i < 4; i++) { r = DotProduct (origin, frustum[i].normal) - frustum[i].dist; if (r <= -radius) return true; } return false; } #ifndef IMPLEMENT_VectorNormalize extern inline #else VISIBLE #endif float VectorNormalize (vec3_t v) { float length; length = DotProduct (v, v); if (length) { float ilength; length = sqrt (length); ilength = 1.0 / length; v[0] *= ilength; v[1] *= ilength; v[2] *= ilength; } return length; } //@} #endif // __mathlib_h