quakeforge/include/QF/mathlib.h

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/*
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
$Id$
*/
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#ifndef __mathlib_h
#define __mathlib_h
/** \defgroup mathlib Vector and matrix functions
\ingroup utils
*/
//@{
#include <math.h>
#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
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extern int nanmask;
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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)
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#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]; \
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} while (0)
#define VectorCopy(a,b) \
do { \
(b)[0] = (a)[0]; \
(b)[1] = (a)[1]; \
(b)[2] = (a)[2]; \
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} 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]; \
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} 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]; \
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} while (0)
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#define VectorLength(a) sqrt(DotProduct(a, a))
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#define VectorScale(a,b,c) \
do { \
(c)[0] = (a)[0] * (b); \
(c)[1] = (a)[1] * (b); \
(c)[2] = (a)[2] * (b); \
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} 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 VectorCompMin(a, b, c) \
do { \
(c)[0] = min ((a)[0], (b)[0]); \
(c)[1] = min ((a)[1], (b)[1]); \
(c)[2] = min ((a)[2], (b)[2]); \
} while (0)
#define VectorCompMax(a, b, c) \
do { \
(c)[0] = max ((a)[0], (b)[0]); \
(c)[1] = max ((a)[1], (b)[1]); \
(c)[2] = max ((a)[2], (b)[2]); \
} while (0)
#define VectorCompBound(a, b, c, d) \
do { \
(d)[0] = bound ((a)[0], (b)[0], (c)[0]); \
(d)[1] = bound ((a)[1], (b)[1], (c)[1]); \
(d)[2] = bound ((a)[2], (b)[2], (c)[2]); \
} while (0)
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#define VectorIsZero(a) (!(a)[0] && !(a)[1] && !(a)[2])
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#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)
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#define VectorBlend(v1,v2,b,v) \
do { \
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(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)
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//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 QuatCompMin(a, b, c) \
do { \
(c)[0] = min ((a)[0], (b)[0]); \
(c)[1] = min ((a)[1], (b)[1]); \
(c)[2] = min ((a)[2], (b)[2]); \
(c)[3] = min ((a)[3], (b)[3]); \
} while (0)
#define QuatCompMax(a, b, c) \
do { \
(c)[0] = max ((a)[0], (b)[0]); \
(c)[1] = max ((a)[1], (b)[1]); \
(c)[2] = max ((a)[2], (b)[2]); \
(c)[3] = max ((a)[3], (b)[3]); \
} while (0)
#define QuatCompBound(a, b, c, d) \
do { \
(d)[0] = bound ((a)[0], (b)[0], (c)[0]); \
(d)[1] = bound ((a)[1], (b)[1], (c)[1]); \
(d)[2] = bound ((a)[2], (b)[2], (c)[2]); \
(d)[3] = bound ((a)[3], (b)[3], (c)[3]); \
} while (0)
#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.
*/
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#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);
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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]);
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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 <em>negative</em> 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);
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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)
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#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
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#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;
}
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#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;
}
//@}
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#endif // __mathlib_h