quakeforge/libs/util/mathlib.c

/*
	mathlib.c

	math primitives

	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

*/
static const char rcsid[] = 
	"$Id$";

#ifdef HAVE_CONFIG_H
# include "config.h"
#endif
#ifdef HAVE_STRING_H
# include <string.h>
#endif
#ifdef HAVE_STRINGS_H
# include <strings.h>
#endif

#include <math.h>

#define IMPLEMENT_R_CullBox

#include "QF/mathlib.h"
#include "QF/qtypes.h"
#include "QF/sys.h"

int			nanmask = 255 << 23;
mplane_t	frustum[4];
vec3_t		vec3_origin = { 0, 0, 0 };

#define DEG2RAD(a) (a * (M_PI / 180.0))


void
ProjectPointOnPlane (vec3_t dst, const vec3_t p, const vec3_t normal)
{
	float		inv_denom, d;
	vec3_t		n;

	inv_denom = 1.0F / DotProduct (normal, normal);

	d = DotProduct (normal, p) * inv_denom;

	n[0] = normal[0] * inv_denom;
	n[1] = normal[1] * inv_denom;
	n[2] = normal[2] * inv_denom;

	dst[0] = p[0] - d * n[0];
	dst[1] = p[1] - d * n[1];
	dst[2] = p[2] - d * n[2];
}

//  assumes "src" is normalized
void
PerpendicularVector (vec3_t dst, const vec3_t src)
{
	int			pos, i;
	float		minelem = 1.0F;
	vec3_t		tempvec;

	/* find the smallest magnitude axially aligned vector */
	for (pos = 0, i = 0; i < 3; i++) {
		if (fabs (src[i]) < minelem) {
			pos = i;
			minelem = fabs (src[i]);
		}
	}
	tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
	tempvec[pos] = 1.0F;

	/* project the point onto the plane defined by src */
	ProjectPointOnPlane (dst, tempvec, src);

	/* normalize the result */
	VectorNormalize (dst);
}

#if defined(_WIN32) && !defined(__GNUC__)
# pragma optimize( "", off )
#endif

void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
{
	float d;

	right[0] = forward[2];
	right[1] = -forward[0];
	right[2] = forward[1];

	d = DotProduct(forward, right);
	right[0] -= d * forward[0];
	right[1] -= d * forward[1];
	right[2] -= d * forward[2];
	VectorNormalize(right);
	CrossProduct(right, forward, up);
}

void
RotatePointAroundVector (vec3_t dst, const vec3_t dir, const vec3_t point,
						 float degrees)
{
	float       m[3][3];
	float       im[3][3];
	float       zrot[3][3];
	float       tmpmat[3][3];
	float       rot[3][3];
	int         i;
	vec3_t      vr, vup, vf;

	vf[0] = dir[0];
	vf[1] = dir[1];
	vf[2] = dir[2];

	PerpendicularVector (vr, dir);
	CrossProduct (vr, vf, vup);

	m[0][0] = vr[0];
	m[1][0] = vr[1];
	m[2][0] = vr[2];

	m[0][1] = vup[0];
	m[1][1] = vup[1];
	m[2][1] = vup[2];

	m[0][2] = vf[0];
	m[1][2] = vf[1];
	m[2][2] = vf[2];

	memcpy (im, m, sizeof (im));

	im[0][1] = m[1][0];
	im[0][2] = m[2][0];
	im[1][0] = m[0][1];
	im[1][2] = m[2][1];
	im[2][0] = m[0][2];
	im[2][1] = m[1][2];

	memset (zrot, 0, sizeof (zrot));
	zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;

	zrot[0][0] = cos (DEG2RAD (degrees));
	zrot[0][1] = sin (DEG2RAD (degrees));
	zrot[1][0] = -sin (DEG2RAD (degrees));
	zrot[1][1] = cos (DEG2RAD (degrees));

	R_ConcatRotations (m, zrot, tmpmat);
	R_ConcatRotations (tmpmat, im, rot);

	for (i = 0; i < 3; i++) {
		dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] *
			point[2];
	}
}

#if defined(_WIN32) && !defined(__GNUC__)
# pragma optimize( "", on )
#endif

float
anglemod (float a)
{
#if 0
	if (a >= 0)
		a -= 360 * (int) (a / 360);
	else
		a += 360 * (1 + (int) (-a / 360));
#endif
	a = (360.0 / 65536) * ((int) (a * (65536 / 360.0)) & 65535);
	return a;
}

/*
	BOPS_Error

	Split out like this for ASM to call.
*/
void
BOPS_Error (void)
{
	Sys_Error ("BoxOnPlaneSide:  Bad signbits");
}

#ifndef USE_INTEL_ASM

/*
	BoxOnPlaneSide

	Returns 1, 2, or 1 + 2
*/
int
BoxOnPlaneSide (vec3_t emins, vec3_t emaxs, mplane_t *p)
{
	float       dist1, dist2;
	int         sides;

#if 0
	// this is done by the BOX_ON_PLANE_SIDE macro before
	// calling this function

	// fast axial cases
	if (p->type < 3) {
		if (p->dist <= emins[p->type])
			return 1;
		if (p->dist >= emaxs[p->type])
			return 2;
		return 3;
	}
#endif

	// general case
	switch (p->signbits) {
		case 0:
			dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emaxs[2];
			dist2 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
				p->normal[2] * emins[2];
			break;
		case 1:
			dist1 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emaxs[2];
			dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
				p->normal[2] * emins[2];
			break;
		case 2:
			dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
				p->normal[2] * emaxs[2];
			dist2 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emins[2];
			break;
		case 3:
			dist1 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
				p->normal[2] * emaxs[2];
			dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emins[2];
			break;
		case 4:
			dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emins[2];
			dist2 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
				p->normal[2] * emaxs[2];
			break;
		case 5:
			dist1 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emins[2];
			dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
				p->normal[2] * emaxs[2];
			break;
		case 6:
			dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
				p->normal[2] * emins[2];
			dist2 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emaxs[2];
			break;
		case 7:
			dist1 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
				p->normal[2] * emins[2];
			dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
				p->normal[2] * emaxs[2];
			break;
		default:
			dist1 = dist2 = 0;			// shut up compiler
			BOPS_Error ();
			break;
	}

#if 0
	int         i;
	vec3_t      corners[2];

	for (i = 0; i < 3; i++) {
		if (plane->normal[i] < 0) {
			corners[0][i] = emins[i];
			corners[1][i] = emaxs[i];
		} else {
			corners[1][i] = emins[i];
			corners[0][i] = emaxs[i];
		}
	}
	dist = DotProduct (plane->normal, corners[0]) - plane->dist;
	dist2 = DotProduct (plane->normal, corners[1]) - plane->dist;
	sides = 0;
	if (dist1 >= 0)
		sides = 1;
	if (dist2 < 0)
		sides |= 2;
#endif

	sides = 0;
	if (dist1 >= p->dist)
		sides = 1;
	if (dist2 < p->dist)
		sides |= 2;

#ifdef PARANOID
	if (sides == 0)
		Sys_Error ("BoxOnPlaneSide: sides==0");
#endif

	return sides;
}
#endif

void
AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
{
	float       angle, sr, sp, sy, cr, cp, cy;

	angle = angles[YAW] * (M_PI * 2 / 360);
	sy = sin (angle);
	cy = cos (angle);
	angle = angles[PITCH] * (M_PI * 2 / 360);
	sp = sin (angle);
	cp = cos (angle);
	angle = angles[ROLL] * (M_PI * 2 / 360);
	sr = sin (angle);
	cr = cos (angle);

	forward[0] = cp * cy;
	forward[1] = cp * sy;
	forward[2] = -sp;
	right[0] = (-1 * sr * sp * cy + -1 * cr * -sy);
	right[1] = (-1 * sr * sp * sy + -1 * cr * cy);
	right[2] = -1 * sr * cp;
	up[0] = (cr * sp * cy + -sr * -sy);
	up[1] = (cr * sp * sy + -sr * cy);
	up[2] = cr * cp;
}

int
_VectorCompare (vec3_t v1, vec3_t v2)
{
	int         i;

	for (i = 0; i < 3; i++)
		if (v1[i] != v2[i])
			return 0;

	return 1;
}

void
_VectorMA (vec3_t veca, float scale, vec3_t vecb, vec3_t vecc)
{
	vecc[0] = veca[0] + scale * vecb[0];
	vecc[1] = veca[1] + scale * vecb[1];
	vecc[2] = veca[2] + scale * vecb[2];
}

vec_t
_DotProduct (vec3_t v1, vec3_t v2)
{
	return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}

void
_VectorSubtract (vec3_t veca, vec3_t vecb, vec3_t out)
{
	out[0] = veca[0] - vecb[0];
	out[1] = veca[1] - vecb[1];
	out[2] = veca[2] - vecb[2];
}

void
_VectorAdd (vec3_t veca, vec3_t vecb, vec3_t out)
{
	out[0] = veca[0] + vecb[0];
	out[1] = veca[1] + vecb[1];
	out[2] = veca[2] + vecb[2];
}

void
_VectorCopy (vec3_t in, vec3_t out)
{
	out[0] = in[0];
	out[1] = in[1];
	out[2] = in[2];
}

void
CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross)
{
	cross[0] = v1[1] * v2[2] - v1[2] * v2[1];
	cross[1] = v1[2] * v2[0] - v1[0] * v2[2];
	cross[2] = v1[0] * v2[1] - v1[1] * v2[0];
}

double      sqrt (double x);

vec_t
_Length (vec3_t v)
{
	float		length;
	int			i;

	length = 0;
	for (i = 0; i < 3; i++)
		length += v[i] * v[i];
	length = sqrt (length);				// FIXME

	return length;
}

float
VectorNormalize (vec3_t v)
{
	float		length, ilength;

	length = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
	length = sqrt (length);				// FIXME

	if (length) {
		ilength = 1 / length;
		v[0] *= ilength;
		v[1] *= ilength;
		v[2] *= ilength;
	}

	return length;

}

void
VectorInverse (vec3_t v)
{
	v[0] = -v[0];
	v[1] = -v[1];
	v[2] = -v[2];
}

void
_VectorScale (vec3_t in, vec_t scale, vec3_t out)
{
	out[0] = in[0] * scale;
	out[1] = in[1] * scale;
	out[2] = in[2] * scale;
}

int
Q_log2 (int val)
{
	int         answer = 0;

	while ((val >>= 1) != 0)
		answer++;
	return answer;
}

void
R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3])
{
	out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
		in1[0][2] * in2[2][0];
	out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
		in1[0][2] * in2[2][1];
	out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
		in1[0][2] * in2[2][2];
	out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
		in1[1][2] * in2[2][0];
	out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
		in1[1][2] * in2[2][1];
	out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
		in1[1][2] * in2[2][2];
	out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
		in1[2][2] * in2[2][0];
	out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
		in1[2][2] * in2[2][1];
	out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
		in1[2][2] * in2[2][2];
}

void
R_ConcatTransforms (float in1[3][4], float in2[3][4], float out[3][4])
{
	out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
		in1[0][2] * in2[2][0];
	out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
		in1[0][2] * in2[2][1];
	out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
		in1[0][2] * in2[2][2];
	out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] +
		in1[0][2] * in2[2][3] + in1[0][3];
	out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
		in1[1][2] * in2[2][0];
	out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
		in1[1][2] * in2[2][1];
	out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
		in1[1][2] * in2[2][2];
	out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] +
		in1[1][2] * in2[2][3] + in1[1][3];
	out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
		in1[2][2] * in2[2][0];
	out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
		in1[2][2] * in2[2][1];
	out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
		in1[2][2] * in2[2][2];
	out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] +
		in1[2][2] * in2[2][3] + in1[2][3];
}

/*
	FloorDivMod

	Returns mathematically correct (floor-based) quotient and remainder for
	numer and denom, both of which should contain no fractional part. The
	quotient must fit in 32 bits.
*/
void
FloorDivMod (double numer, double denom, int *quotient, int *rem)
{
	double		x;
	int			q, r;

#ifndef PARANOID
	if (denom <= 0.0)
		Sys_Error ("FloorDivMod: bad denominator %f\n", denom);

//	if ((floor(numer) != numer) || (floor(denom) != denom))
//		Sys_Error ("FloorDivMod: non-integer numer or denom %f %f\n",
//				   numer, denom);
#endif

	if (numer >= 0.0) {

		x = floor (numer / denom);
		q = (int) x;
		r = (int) floor (numer - (x * denom));
	} else {
		// perform operations with positive values, and fix mod to make
		// floor-based
		x = floor (-numer / denom);
		q = -(int) x;
		r = (int) floor (-numer - (x * denom));
		if (r != 0) {
			q--;
			r = (int) denom - r;
		}
	}

	*quotient = q;
	*rem = r;
}

int
GreatestCommonDivisor (int i1, int i2)
{
	if (i1 > i2) {
		if (i2 == 0)
			return (i1);
		return GreatestCommonDivisor (i2, i1 % i2);
	} else {
		if (i1 == 0)
			return (i2);
		return GreatestCommonDivisor (i1, i2 % i1);
	}
}

#ifndef USE_INTEL_ASM
/*
  Invert24To16

  Inverts an 8.24 value to a 16.16 value
  TODO: move to nonintel.c
*/
fixed16_t
Invert24To16 (fixed16_t val)
{
	if (val < 256)
		return (0xFFFFFFFF);

	return (fixed16_t)
		(((double) 0x10000 * (double) 0x1000000 / (double) val) + 0.5);
}
#endif