src/gpacmp4/math.c

/*
*			GPAC - Multimedia Framework C SDK
*
*			Authors: Jean Le Feuvre
*			Copyright (c) Telecom ParisTech 2000-2012
*					All rights reserved
*
*  This file is part of GPAC / common tools sub-project
*
*  GPAC is free software; you can redistribute it and/or modify
*  it under the terms of the GNU Lesser General Public License as published by
*  the Free Software Foundation; either version 2, or (at your option)
*  any later version.
*
*  GPAC 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 Lesser General Public License for more details.
*
*  You should have received a copy of the GNU Lesser General Public
*  License along with this library; see the file COPYING.  If not, write to
*  the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
*
*
*	fixed-point trigo routines taken from freetype
*		Copyright 1996-2001, 2002, 2004 by
*		David Turner, Robert Wilhelm, and Werner Lemberg.
*	License: FTL or GPL
*
*/

#include <gpac/math.h>

u32 gf_get_bit_size(u32 MaxVal)
{
	u32 k = 0;
	while ((s32)MaxVal > ((1 << k) - 1)) k += 1;
	return k;
}

#ifdef GPAC_FIXED_POINT

#ifndef __GNUC__
#pragma message("Compiling with fixed-point arithmetic")
#endif

#if defined(__SYMBIAN32__) && !defined(__SERIES60_3X__)
typedef long long fix_s64;
#else
typedef s64 fix_s64;
#endif


/* the following is 0.2715717684432231 * 2^30 */
#define GF_TRIG_COSCALE  0x11616E8EUL

/* this table was generated for degrees */
#define GF_TRIG_MAX_ITERS  23

static const Fixed gf_trig_arctan_table[24] =
{
	4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L,
	58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
	57L, 29L, 14L, 7L, 4L, 2L, 1L
};

/* the Cordic shrink factor, multiplied by 2^32 */
#define GF_TRIG_SCALE    1166391785  /* 0x4585BA38UL */

#define GF_ANGLE_PI		(180<<16)
#define GF_ANGLE_PI2	(90<<16)
#define GF_ANGLE_2PI	(360<<16)

#define GF_PAD_FLOOR( x, n )  ( (x) & ~((n)-1) )
#define GF_PAD_ROUND( x, n )  GF_PAD_FLOOR( (x) + ((n)/2), n )
#define GF_PAD_CEIL( x, n )   GF_PAD_FLOOR( (x) + ((n)-1), n )

static GFINLINE s32 gf_trig_prenorm(GF_Point2D *vec)
{
	Fixed  x, y, z;
	s32 shift;
	x = vec->x;
	y = vec->y;
	z = ((x >= 0) ? x : -x) | ((y >= 0) ? y : -y);
	shift = 0;
	if (z < (1L << 27)) {
		do {
			shift++;
			z <<= 1;
		} while (z < (1L << 27));

		vec->x = x << shift;
		vec->y = y << shift;
	}
	else if (z >(1L << 28)) {
		do {
			shift++;
			z >>= 1;
		} while (z > (1L << 28));

		vec->x = x >> shift;
		vec->y = y >> shift;
		shift = -shift;
	}
	return shift;
}

#define ANGLE_RAD_TO_DEG(_th) ((s32) ( (((fix_s64)_th)*5729582)/100000))
#define ANGLE_DEG_TO_RAD(_th) ((s32) ( (((fix_s64)_th)*100000)/5729582))

static GFINLINE void gf_trig_pseudo_polarize(GF_Point2D *vec)
{
	Fixed         theta;
	Fixed         yi, i;
	Fixed         x, y;
	const Fixed  *arctanptr;

	x = vec->x;
	y = vec->y;

	/* Get the vector into the right half plane */
	theta = 0;
	if (x < 0) {
		x = -x;
		y = -y;
		theta = 2 * GF_ANGLE_PI2;
	}

	if (y > 0)
		theta = -theta;

	arctanptr = gf_trig_arctan_table;

	if (y < 0) {
		/* Rotate positive */
		yi = y + (x << 1);
		x = x - (y << 1);
		y = yi;
		theta -= *arctanptr++;  /* Subtract angle */
	}
	else {
		/* Rotate negative */
		yi = y - (x << 1);
		x = x + (y << 1);
		y = yi;
		theta += *arctanptr++;  /* Add angle */
	}

	i = 0;
	do {
		if (y < 0) {
			/* Rotate positive */
			yi = y + (x >> i);
			x = x - (y >> i);
			y = yi;
			theta -= *arctanptr++;
		}
		else {
			/* Rotate negative */
			yi = y - (x >> i);
			x = x + (y >> i);
			y = yi;
			theta += *arctanptr++;
		}
	} while (++i < GF_TRIG_MAX_ITERS);

	/* round theta */
	if (theta >= 0)
		theta = GF_PAD_ROUND(theta, 32);
	else
		theta = -GF_PAD_ROUND(-theta, 32);

	vec->x = x;
	vec->y = ANGLE_DEG_TO_RAD(theta);
}

GF_EXPORT
Fixed gf_atan2(Fixed dy, Fixed dx)
{
	GF_Point2D v;
	if (dx == 0 && dy == 0) return 0;
	v.x = dx;
	v.y = dy;
	gf_trig_prenorm(&v);
	gf_trig_pseudo_polarize(&v);
	return v.y;
}

/*define one of these to enable IntelGPP support and link to gpp_WMMX40_d.lib (debug) or gpp_WMMX40_r.lib (release)
this is not configured by default for lack of real perf increase.*/
#if defined(GPAC_USE_IGPP_HP) || defined(GPAC_USE_IGPP)
#   pragma message("Using IntelGPP math library")
#ifdef _DEBUG
#   pragma comment(lib, "gpp_WMMX40_d")
#else
#   pragma comment(lib, "gpp_WMMX40_r")
#endif

#include <gpp.h>

GF_EXPORT
Fixed gf_invfix(Fixed a)
{
	Fixed res;
	if (!a) return (s32)0x7FFFFFFFL;
	gppInv_16_32s(a, &res);
	return res;
}
GF_EXPORT
Fixed gf_divfix(Fixed a, Fixed b)
{
	Fixed res;
	if (!a) return 0;
	else if (!b) return (a<0) ? -(s32)0x7FFFFFFFL : (s32)0x7FFFFFFFL;
	else if (a == FIX_ONE) gppInv_16_32s(b, &res);
	else gppDiv_16_32s(a, b, &res);
	return res;
}

GF_EXPORT
Fixed gf_mulfix(Fixed a, Fixed b)
{
	Fixed  res;
	if (!a || !b) return 0;
	else if (b == FIX_ONE) return a;
	else gppMul_16_32s(a, b, &res);
	return res;
}

GF_EXPORT
Fixed gf_sqrt(Fixed x)
{
	Fixed res;
#ifdef GPAC_USE_IGPP_HP
	gppSqrtHP_16_32s(x, &res);
#else
	gppSqrtLP_16_32s(x, &res);
#endif
	return res;
}

GF_EXPORT
Fixed gf_cos(Fixed angle)
{
	Fixed res;
#ifdef GPAC_USE_IGPP_HP
	gppCosHP_16_32s(angle, &res);
#else
	gppCosLP_16_32s(angle, &res);
#endif
	return res;
}

GF_EXPORT
Fixed gf_sin(Fixed angle)
{
	Fixed res;
#ifdef GPAC_USE_IGPP_HP
	gppSinHP_16_32s(angle, &res);
#else
	gppSinLP_16_32s(angle, &res);
#endif
	return res;
}


GF_EXPORT
Fixed gf_tan(Fixed angle)
{
	Fixed cosa, sina;
#ifdef GPAC_USE_IGPP_HP
	gppSinCosHP_16_32s(angle, &sina, &cosa);
#else
	gppSinCosLP_16_32s(angle, &sina, &cosa);
#endif
	if (!cosa) return (sina<0) ? -GF_PI2 : GF_PI2;
	return gf_divfix(sina, cosa);
}

GF_EXPORT
GF_Point2D gf_v2d_from_polar(Fixed length, Fixed angle)
{
	GF_Point2D vec;
	Fixed cosa, sina;
#ifdef GPAC_USE_IGPP_HP
	gppSinCosHP_16_32s(angle, &sina, &cosa);
#else
	gppSinCosLP_16_32s(angle, &sina, &cosa);
#endif
	vec.x = gf_mulfix(length, cosa);
	vec.y = gf_mulfix(length, sina);
	return vec;
}

GF_EXPORT
Fixed gf_v2d_len(GF_Point2D *vec)
{
	Fixed a, b, res;
	if (!vec->x) return ABS(vec->y);
	if (!vec->y) return ABS(vec->x);
	gppSquare_16_32s(vec->x, &a);
	gppSquare_16_32s(vec->y, &b);
#ifdef GPAC_USE_IGPP_HP
	gppSqrtHP_16_32s(a + b, &res);
#else
	gppSqrtLP_16_32s(a + b, &res);
#endif
	return res;
}

#else

GF_EXPORT
Fixed gf_invfix(Fixed a)
{
	if (!a) return (s32)0x7FFFFFFFL;
	return gf_divfix(FIX_ONE, a);
}

GF_EXPORT
Fixed gf_divfix(Fixed a, Fixed b)
{
	s32 s;
	u32 q;
	if (!a) return 0;
	s = 1;
	if (a < 0) {
		a = -a;
		s = -1;
	}
	if (b < 0) {
		b = -b;
		s = -s;
	}

	if (b == 0)
		/* check for division by 0 */
		q = 0x7FFFFFFFL;
	else {
		/* compute result directly */
		q = (u32)((((fix_s64)a << 16) + (b >> 1)) / b);
	}
	return (s < 0 ? -(s32)q : (s32)q);
}

GF_EXPORT
Fixed gf_mulfix(Fixed a, Fixed b)
{
	Fixed  s;
	u32 ua, ub;
	if (!a || (b == 0x10000L)) return a;
	if (!b) return 0;

	s = a;
	a = ABS(a);
	s ^= b;
	b = ABS(b);

	ua = (u32)a;
	ub = (u32)b;

	if ((ua <= 2048) && (ub <= 1048576L)) {
		ua = (ua * ub + 0x8000L) >> 16;
	}
	else {
		u32 al = ua & 0xFFFFL;
		ua = (ua >> 16) * ub + al * (ub >> 16) + ((al * (ub & 0xFFFFL) + 0x8000L) >> 16);
	}
	if (ua & 0x80000000) s = -s;
	return (s < 0 ? -(Fixed)(s32)ua : (Fixed)ua);
}


GF_EXPORT
Fixed gf_sqrt(Fixed x)
{
	u32 root, rem_hi, rem_lo, test_div;
	s32 count;
	root = 0;
	if (x > 0) {
		rem_hi = 0;
		rem_lo = x;
		count = 24;
		do {
			rem_hi = (rem_hi << 2) | (rem_lo >> 30);
			rem_lo <<= 2;
			root <<= 1;
			test_div = (root << 1) + 1;

			if (rem_hi >= test_div) {
				rem_hi -= test_div;
				root += 1;
			}
		} while (--count);
	}

	return (Fixed)root;
}


/* multiply a given value by the CORDIC shrink factor */
static Fixed gf_trig_downscale(Fixed  val)
{
	Fixed  s;
	fix_s64 v;
	s = val;
	val = (val >= 0) ? val : -val;
#ifdef _MSC_VER
	v = (val * (fix_s64)GF_TRIG_SCALE) + 0x100000000;
#else
	v = (val * (fix_s64)GF_TRIG_SCALE) + 0x100000000ULL;
#endif
	val = (Fixed)(v >> 32);
	return (s >= 0) ? val : -val;
}

static void gf_trig_pseudo_rotate(GF_Point2D*  vec, Fixed theta)
{
	s32 i;
	Fixed x, y, xtemp;
	const Fixed  *arctanptr;

	/*trig funcs are in degrees*/
	theta = ANGLE_RAD_TO_DEG(theta);

	x = vec->x;
	y = vec->y;

	/* Get angle between -90 and 90 degrees */
	while (theta <= -GF_ANGLE_PI2) {
		x = -x;
		y = -y;
		theta += GF_ANGLE_PI;
	}

	while (theta > GF_ANGLE_PI2) {
		x = -x;
		y = -y;
		theta -= GF_ANGLE_PI;
	}

	/* Initial pseudorotation, with left shift */
	arctanptr = gf_trig_arctan_table;
	if (theta < 0) {
		xtemp = x + (y << 1);
		y = y - (x << 1);
		x = xtemp;
		theta += *arctanptr++;
	}
	else {
		xtemp = x - (y << 1);
		y = y + (x << 1);
		x = xtemp;
		theta -= *arctanptr++;
	}
	/* Subsequent pseudorotations, with right shifts */
	i = 0;
	do {
		if (theta < 0) {
			xtemp = x + (y >> i);
			y = y - (x >> i);
			x = xtemp;
			theta += *arctanptr++;
		}
		else {
			xtemp = x - (y >> i);
			y = y + (x >> i);
			x = xtemp;
			theta -= *arctanptr++;
		}
	} while (++i < GF_TRIG_MAX_ITERS);

	vec->x = x;
	vec->y = y;
}

/* these macros return 0 for positive numbers, and -1 for negative ones */
#define GF_SIGN_LONG( x )   ( (x) >> ( 32 - 1 ) )
#define GF_SIGN_INT( x )    ( (x) >> ( 32 - 1 ) )
#define GF_SIGN_INT32( x )  ( (x) >> 31 )
#define GF_SIGN_INT16( x )  ( (x) >> 15 )

static void gf_v2d_rotate(GF_Point2D *vec, Fixed angle)
{
	s32 shift;
	GF_Point2D v;

	v.x = vec->x;
	v.y = vec->y;

	if (angle && (v.x != 0 || v.y != 0)) {
		shift = gf_trig_prenorm(&v);
		gf_trig_pseudo_rotate(&v, angle);
		v.x = gf_trig_downscale(v.x);
		v.y = gf_trig_downscale(v.y);

		if (shift > 0) {
			s32 half = 1L << (shift - 1);

			vec->x = (v.x + half + GF_SIGN_LONG(v.x)) >> shift;
			vec->y = (v.y + half + GF_SIGN_LONG(v.y)) >> shift;
		}
		else {
			shift = -shift;
			vec->x = v.x << shift;
			vec->y = v.y << shift;
		}
	}
}

GF_EXPORT
Fixed gf_v2d_len(GF_Point2D *vec)
{
	s32 shift;
	GF_Point2D v;
	v = *vec;

	/* handle trivial cases */
	if (v.x == 0) {
		return (v.y >= 0) ? v.y : -v.y;
	}
	else if (v.y == 0) {
		return (v.x >= 0) ? v.x : -v.x;
	}

	/* general case */
	shift = gf_trig_prenorm(&v);
	gf_trig_pseudo_polarize(&v);
	v.x = gf_trig_downscale(v.x);
	if (shift > 0)
		return (v.x + (1 << (shift - 1))) >> shift;

	return v.x << -shift;
}


GF_EXPORT
void gf_v2d_polarize(GF_Point2D *vec, Fixed *length, Fixed *angle)
{
	s32 shift;
	GF_Point2D v;
	v = *vec;
	if (v.x == 0 && v.y == 0)
		return;

	shift = gf_trig_prenorm(&v);
	gf_trig_pseudo_polarize(&v);
	v.x = gf_trig_downscale(v.x);
	*length = (shift >= 0) ? (v.x >> shift) : (v.x << -shift);
	*angle = v.y;
}

GF_EXPORT
GF_Point2D gf_v2d_from_polar(Fixed length, Fixed angle)
{
	GF_Point2D vec;
	vec.x = length;
	vec.y = 0;
	gf_v2d_rotate(&vec, angle);
	return vec;
}

GF_EXPORT
Fixed gf_cos(Fixed angle)
{
	GF_Point2D v;
	v.x = GF_TRIG_COSCALE >> 2;
	v.y = 0;
	gf_trig_pseudo_rotate(&v, angle);
	return v.x / (1 << 12);
}
GF_EXPORT
Fixed gf_sin(Fixed angle)
{
	return gf_cos(GF_PI2 - angle);
}
GF_EXPORT
Fixed gf_tan(Fixed angle)
{
	GF_Point2D v;
	v.x = GF_TRIG_COSCALE >> 2;
	v.y = 0;
	gf_trig_pseudo_rotate(&v, angle);
	return gf_divfix(v.y, v.x);
}

#endif

/*common parts*/
GF_EXPORT
Fixed gf_muldiv(Fixed a, Fixed b, Fixed c)
{
	s32 s, d;
	if (!b || !a) return 0;
	s = 1;
	if (a < 0) {
		a = -a;
		s = -1;
	}
	if (b < 0) {
		b = -b;
		s = -s;
	}
	if (c < 0) {
		c = -c;
		s = -s;
	}

	d = (s32)(c > 0 ? ((fix_s64)a * b + (c >> 1)) / c : 0x7FFFFFFFL);
	return (Fixed)((s > 0) ? d : -d);
}


GF_EXPORT
Fixed gf_ceil(Fixed a)
{
	return (a >= 0) ? (a + 0xFFFFL) & ~0xFFFFL : -((-a + 0xFFFFL) & ~0xFFFFL);
}

GF_EXPORT
Fixed gf_floor(Fixed a)
{
	return (a >= 0) ? (a & ~0xFFFFL) : -((-a) & ~0xFFFFL);
}


/*FIXME*/
GF_EXPORT
Fixed gf_acos(Fixed angle)
{
	return FLT2FIX((Float)acos(FIX2FLT(angle)));
}

/*FIXME*/
GF_EXPORT
Fixed gf_asin(Fixed angle)
{
	return FLT2FIX((Float)asin(FIX2FLT(angle)));
}


#else


GF_EXPORT
GF_Point2D gf_v2d_from_polar(Fixed length, Fixed angle)
{
	GF_Point2D vec;
	vec.x = length*(Float)cos(angle);
	vec.y = length*(Float)sin(angle);
	return vec;
}

GF_EXPORT
Fixed gf_v2d_len(GF_Point2D *vec)
{
	if (!vec->x) return ABS(vec->y);
	if (!vec->y) return ABS(vec->x);
	return (Fixed)sqrt(vec->x*vec->x + vec->y*vec->y);
}

/*

Fixed gf_cos(_a) { return (Float) cos(_a); }
Fixed gf_sin(_a) { return (Float) sin(_a); }
Fixed gf_tan(_a) { return (Float) tan(_a); }
Fixed gf_atan2(_y, _x) { return (Float) atan2(_y, _x); }
Fixed gf_sqrt(_x) { return (Float) sqrt(_x); }
Fixed gf_ceil(_a) { return (Float) ceil(_a); }
Fixed gf_floor(_a) { return (Float) floor(_a); }
Fixed gf_acos(_a) { return (Float) acos(_a); }
Fixed gf_asin(_a) { return (Float) asin(_a); }

*/

#endif

GF_EXPORT
Fixed gf_v2d_distance(GF_Point2D *a, GF_Point2D *b)
{
	GF_Point2D d;
	d.x = a->x - b->x;
	d.y = a->y - b->y;
	return gf_v2d_len(&d);
}

GF_EXPORT
Fixed gf_angle_diff(Fixed angle1, Fixed angle2)
{
	Fixed delta = angle2 - angle1;
#ifdef GPAC_FIXED_POINT
	delta %= GF_2PI;
	if (delta < 0) delta += GF_2PI;
	if (delta > GF_PI) delta -= GF_2PI;
#else
	while (delta < 0) delta += GF_2PI;
	while (delta > GF_PI) delta -= GF_2PI;
#endif
	return delta;
}


/*
2D MATRIX TOOLS
*/

GF_EXPORT
void gf_mx2d_add_matrix(GF_Matrix2D *_this, GF_Matrix2D *from)
{
	GF_Matrix2D bck;
	if (!_this || !from) return;

	if (gf_mx2d_is_identity(*from)) return;
	else if (gf_mx2d_is_identity(*_this)) {
		gf_mx2d_copy(*_this, *from);
		return;
	}
	gf_mx2d_copy(bck, *_this);
	_this->m[0] = gf_mulfix(from->m[0], bck.m[0]) + gf_mulfix(from->m[1], bck.m[3]);
	_this->m[1] = gf_mulfix(from->m[0], bck.m[1]) + gf_mulfix(from->m[1], bck.m[4]);
	_this->m[2] = gf_mulfix(from->m[0], bck.m[2]) + gf_mulfix(from->m[1], bck.m[5]) + from->m[2];
	_this->m[3] = gf_mulfix(from->m[3], bck.m[0]) + gf_mulfix(from->m[4], bck.m[3]);
	_this->m[4] = gf_mulfix(from->m[3], bck.m[1]) + gf_mulfix(from->m[4], bck.m[4]);
	_this->m[5] = gf_mulfix(from->m[3], bck.m[2]) + gf_mulfix(from->m[4], bck.m[5]) + from->m[5];
}


GF_EXPORT
void gf_mx2d_pre_multiply(GF_Matrix2D *_this, GF_Matrix2D *with)
{
	GF_Matrix2D bck;
	if (!_this || !with) return;

	if (gf_mx2d_is_identity(*with)) return;
	else if (gf_mx2d_is_identity(*_this)) {
		gf_mx2d_copy(*_this, *with);
		return;
	}
	gf_mx2d_copy(bck, *_this);
	_this->m[0] = gf_mulfix(bck.m[0], with->m[0]) + gf_mulfix(bck.m[1], with->m[3]);
	_this->m[1] = gf_mulfix(bck.m[0], with->m[1]) + gf_mulfix(bck.m[1], with->m[4]);
	_this->m[2] = gf_mulfix(bck.m[0], with->m[2]) + gf_mulfix(bck.m[1], with->m[5]) + bck.m[2];
	_this->m[3] = gf_mulfix(bck.m[3], with->m[0]) + gf_mulfix(bck.m[4], with->m[3]);
	_this->m[4] = gf_mulfix(bck.m[3], with->m[1]) + gf_mulfix(bck.m[4], with->m[4]);
	_this->m[5] = gf_mulfix(bck.m[3], with->m[2]) + gf_mulfix(bck.m[4], with->m[5]) + bck.m[5];
}


GF_EXPORT
void gf_mx2d_add_translation(GF_Matrix2D *_this, Fixed cx, Fixed cy)
{
	GF_Matrix2D tmp;
	if (!_this || (!cx && !cy)) return;
	gf_mx2d_init(tmp);
	tmp.m[2] = cx;
	tmp.m[5] = cy;
	gf_mx2d_add_matrix(_this, &tmp);
}


GF_EXPORT
void gf_mx2d_add_rotation(GF_Matrix2D *_this, Fixed cx, Fixed cy, Fixed angle)
{
	GF_Matrix2D tmp;
	if (!_this) return;
	gf_mx2d_init(tmp);

	gf_mx2d_add_translation(_this, -cx, -cy);

	tmp.m[0] = gf_cos(angle);
	tmp.m[4] = tmp.m[0];
	tmp.m[3] = gf_sin(angle);
	tmp.m[1] = -1 * tmp.m[3];
	gf_mx2d_add_matrix(_this, &tmp);
	gf_mx2d_add_translation(_this, cx, cy);
}

GF_EXPORT
void gf_mx2d_add_scale(GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y)
{
	GF_Matrix2D tmp;
	if (!_this || ((scale_x == FIX_ONE) && (scale_y == FIX_ONE))) return;
	gf_mx2d_init(tmp);
	tmp.m[0] = scale_x;
	tmp.m[4] = scale_y;
	gf_mx2d_add_matrix(_this, &tmp);
}

GF_EXPORT
void gf_mx2d_add_scale_at(GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y, Fixed cx, Fixed cy, Fixed angle)
{
	GF_Matrix2D tmp;
	if (!_this) return;
	gf_mx2d_init(tmp);
	if (angle) {
		gf_mx2d_add_rotation(_this, cx, cy, -angle);
	}
	tmp.m[0] = scale_x;
	tmp.m[4] = scale_y;
	gf_mx2d_add_matrix(_this, &tmp);
	if (angle) gf_mx2d_add_rotation(_this, cx, cy, angle);
}

GF_EXPORT
void gf_mx2d_add_skew(GF_Matrix2D *_this, Fixed skew_x, Fixed skew_y)
{
	GF_Matrix2D tmp;
	if (!_this || (!skew_x && !skew_y)) return;
	gf_mx2d_init(tmp);
	tmp.m[1] = skew_x;
	tmp.m[3] = skew_y;
	gf_mx2d_add_matrix(_this, &tmp);
}

GF_EXPORT
void gf_mx2d_add_skew_x(GF_Matrix2D *_this, Fixed angle)
{
	GF_Matrix2D tmp;
	if (!_this) return;
	gf_mx2d_init(tmp);
	tmp.m[1] = gf_tan(angle);
	tmp.m[3] = 0;
	gf_mx2d_add_matrix(_this, &tmp);
}

GF_EXPORT
void gf_mx2d_add_skew_y(GF_Matrix2D *_this, Fixed angle)
{
	GF_Matrix2D tmp;
	if (!_this) return;
	gf_mx2d_init(tmp);
	tmp.m[1] = 0;
	tmp.m[3] = gf_tan(angle);
	gf_mx2d_add_matrix(_this, &tmp);
}


GF_EXPORT
void gf_mx2d_inverse(GF_Matrix2D *_this)
{
#ifdef GPAC_FIXED_POINT
	Float _det, _max;
	s32 sign, scale;
#endif
	Fixed det;
	GF_Matrix2D tmp;
	if (!_this) return;
	if (gf_mx2d_is_identity(*_this)) return;

#ifdef GPAC_FIXED_POINT
	/*we must compute the determinent as a float to avoid fixed-point overflow*/
	_det = FIX2FLT(_this->m[0])*FIX2FLT(_this->m[4]) - FIX2FLT(_this->m[1])*FIX2FLT(_this->m[3]);
	if (!_det) {
		gf_mx2d_init(*_this);
		return;
	}
	sign = _det<0 ? -1 : 1;
	_det *= sign;
	scale = 1;
	_max = FIX2FLT(FIX_MAX);
	while (_det / scale > _max) {
		scale *= 10;
	}
	det = sign * FLT2FIX(_det / scale);
#else
	det = gf_mulfix(_this->m[0], _this->m[4]) - gf_mulfix(_this->m[1], _this->m[3]);
	if (!det) {
		gf_mx2d_init(*_this);
		return;
	}
#endif

	tmp.m[0] = gf_divfix(_this->m[4], det);
	tmp.m[1] = -1 * gf_divfix(_this->m[1], det);
	tmp.m[2] = gf_mulfix(gf_divfix(_this->m[1], det), _this->m[5]) - gf_mulfix(gf_divfix(_this->m[4], det), _this->m[2]);

	tmp.m[3] = -1 * gf_divfix(_this->m[3], det);
	tmp.m[4] = gf_divfix(_this->m[0], det);
	tmp.m[5] = gf_mulfix(gf_divfix(_this->m[3], det), _this->m[2]) - gf_mulfix(gf_divfix(_this->m[5], det), _this->m[0]);

#ifdef GPAC_FIXED_POINT
	if (scale>1) {
		tmp.m[0] /= scale;
		tmp.m[1] /= scale;
		tmp.m[2] /= scale;
		tmp.m[3] /= scale;
		tmp.m[4] /= scale;
		tmp.m[5] /= scale;
	}
#endif

	gf_mx2d_copy(*_this, tmp);
}

Bool gf_mx2d_decompose(GF_Matrix2D *mx, GF_Point2D *scale, Fixed *rotate, GF_Point2D *translate)
{
	Fixed det, angle;
	Fixed tmp[6];
	if (!mx) return GF_FALSE;

	memcpy(tmp, mx->m, sizeof(Fixed) * 6);
	translate->x = tmp[2];
	translate->y = tmp[5];

	/*check ac+bd=0*/
	det = gf_mulfix(tmp[0], tmp[3]) + gf_mulfix(tmp[1], tmp[4]);
	if (ABS(det) > FIX_EPSILON) {
		scale->x = scale->y = 0;
		*rotate = 0;
		return GF_FALSE;
	}
	angle = gf_atan2(tmp[3], tmp[4]);
	if (angle < FIX_EPSILON) {
		scale->x = tmp[0];
		scale->y = tmp[4];
	}
	else {
		det = gf_cos(angle);
		scale->x = gf_divfix(tmp[0], det);
		scale->y = gf_divfix(tmp[4], det);
	}
	*rotate = angle;
	return GF_TRUE;
}

GF_EXPORT
void gf_mx2d_apply_coords(GF_Matrix2D *_this, Fixed *x, Fixed *y)
{
	Fixed _x, _y;
	if (!_this || !x || !y) return;
	_x = gf_mulfix(*x, _this->m[0]) + gf_mulfix(*y, _this->m[1]) + _this->m[2];
	_y = gf_mulfix(*x, _this->m[3]) + gf_mulfix(*y, _this->m[4]) + _this->m[5];
	*x = _x;
	*y = _y;
}

GF_EXPORT
void gf_mx2d_apply_point(GF_Matrix2D *_this, GF_Point2D *pt)
{
	gf_mx2d_apply_coords(_this, &pt->x, &pt->y);
}

GF_EXPORT
void gf_mx2d_apply_rect(GF_Matrix2D *_this, GF_Rect *rc)
{

	GF_Point2D c1, c2, c3, c4;
	c1.x = c2.x = rc->x;
	c3.x = c4.x = rc->x + rc->width;
	c1.y = c3.y = rc->y;
	c2.y = c4.y = rc->y - rc->height;
	gf_mx2d_apply_point(_this, &c1);
	gf_mx2d_apply_point(_this, &c2);
	gf_mx2d_apply_point(_this, &c3);
	gf_mx2d_apply_point(_this, &c4);
	rc->x = MIN(c1.x, MIN(c2.x, MIN(c3.x, c4.x)));
	rc->width = MAX(c1.x, MAX(c2.x, MAX(c3.x, c4.x))) - rc->x;
	rc->height = MIN(c1.y, MIN(c2.y, MIN(c3.y, c4.y)));
	rc->y = MAX(c1.y, MAX(c2.y, MAX(c3.y, c4.y)));
	rc->height = rc->y - rc->height;
	assert(rc->height >= 0);
	assert(rc->width >= 0);
}

/*
RECTANGLE TOOLS
*/

/*transform rect to smallest covering integer pixels rect - this is needed to make sure clearing
of screen is correctly handled, otherwise we have troubles with bitmap hardware blitting (always integer)*/
GF_EXPORT
GF_IRect gf_rect_pixelize(GF_Rect *r)
{
	GF_IRect rc;
	rc.x = FIX2INT(gf_floor(r->x));
	rc.y = FIX2INT(gf_ceil(r->y));
	rc.width = FIX2INT(gf_ceil(r->x + r->width)) - rc.x;
	rc.height = rc.y - FIX2INT(gf_floor(r->y - r->height));
	return rc;
}


/*adds @rc2 to @rc1 - the new @rc1 contains the old @rc1 and @rc2*/
GF_EXPORT
void gf_rect_union(GF_Rect *rc1, GF_Rect *rc2)
{
	if (!rc1->width || !rc1->height) {
		*rc1 = *rc2;
		return;
	}
	if (!rc2->width || !rc2->height) return;
	if (rc2->x < rc1->x) {
		rc1->width += rc1->x - rc2->x;
		rc1->x = rc2->x;
	}
	if (rc2->x + rc2->width > rc1->x + rc1->width) rc1->width = rc2->x + rc2->width - rc1->x;
	if (rc2->y > rc1->y) {
		rc1->height += rc2->y - rc1->y;
		rc1->y = rc2->y;
	}
	if (rc2->y - rc2->height < rc1->y - rc1->height) rc1->height = rc1->y - rc2->y + rc2->height;
}

GF_EXPORT
GF_Rect gf_rect_center(Fixed w, Fixed h)
{
	GF_Rect rc;
	rc.x = -w / 2;
	rc.y = h / 2;
	rc.width = w;
	rc.height = h;
	return rc;
}

GF_EXPORT
Bool gf_rect_overlaps(GF_Rect rc1, GF_Rect rc2)
{
	if (!rc2.height || !rc2.width || !rc1.height || !rc1.width) return GF_FALSE;
	if (rc2.x + rc2.width <= rc1.x) return GF_FALSE;
	if (rc2.x >= rc1.x + rc1.width) return GF_FALSE;
	if (rc2.y - rc2.height >= rc1.y) return GF_FALSE;
	if (rc2.y <= rc1.y - rc1.height) return GF_FALSE;
	return GF_TRUE;
}

GF_EXPORT
Bool gf_rect_equal(GF_Rect rc1, GF_Rect rc2)
{
	if ((rc1.x == rc2.x) && (rc1.y == rc2.y) && (rc1.width == rc2.width) && (rc1.height == rc2.height))
		return GF_TRUE;
	return GF_FALSE;
}

#ifdef GPAC_FIXED_POINT

/* check if dimension is larger than FIX_ONE*/
#define IS_HIGH_DIM(_v)	((_v > FIX_ONE) || (_v < (s32)0xFFFF0000))
/* check if any vector dimension is larger than FIX_ONE*/
#define VEC_HIGH_MAG(_v)	(IS_HIGH_DIM(_v.x) || IS_HIGH_DIM(_v.y) || IS_HIGH_DIM(_v.z) )

//#define FLOAT_COMPUTE

GF_EXPORT
Fixed gf_vec_len(GF_Vec v)
{
	/*commented out atm - weird results (not enough precision?)...*/
	//#if defined(GPAC_USE_IGPP_HP) || defined (GPAC_USE_IGPP)
#if 0
	Fixed res;
	gppVec3DLength_16_32s((GPP_VEC3D *)&v, &res);
	return res;
#elif defined(FLOAT_COMPUTE)
	return FLT2FIX(sqrt(FIX2FLT(v.x) * FIX2FLT(v.x) + FIX2FLT(v.y)*FIX2FLT(v.y) + FIX2FLT(v.z)*FIX2FLT(v.z)));
#else

	/*high-magnitude vector, use low precision on frac part to avoid overflow*/
	if (VEC_HIGH_MAG(v)) {
		v.x >>= 8;
		v.y >>= 8;
		v.z >>= 8;
		return gf_sqrt(gf_mulfix(v.x, v.x) + gf_mulfix(v.y, v.y) + gf_mulfix(v.z, v.z)) << 8;
	}
	/*low-res vector*/
	return gf_sqrt(gf_mulfix(v.x, v.x) + gf_mulfix(v.y, v.y) + gf_mulfix(v.z, v.z));
#endif
}

GF_EXPORT
Fixed gf_vec_lensq(GF_Vec v)
{
	/*commented out atm - weird results (not enough precision?)...*/
	//#if defined(GPAC_USE_IGPP_HP) || defined (GPAC_USE_IGPP)
#if 0
	Fixed res;
	gppVec3DLengthSq_16_32s((GPP_VEC3D *)&v, &res);
	return res;
#elif defined(FLOAT_COMPUTE)
	return FLT2FIX(FIX2FLT(v.x) * FIX2FLT(v.x) + FIX2FLT(v.y)*FIX2FLT(v.y) + FIX2FLT(v.z)*FIX2FLT(v.z));
#else

	/*high-magnitude vector, use low precision on frac part to avoid overflow*/
	if (VEC_HIGH_MAG(v)) {
		v.x >>= 8;
		v.y >>= 8;
		v.z >>= 8;
		return (gf_mulfix(v.x, v.x) + gf_mulfix(v.y, v.y) + gf_mulfix(v.z, v.z)) << 16;
	}
	return gf_mulfix(v.x, v.x) + gf_mulfix(v.y, v.y) + gf_mulfix(v.z, v.z);

#endif
}

GF_EXPORT
Fixed gf_vec_dot(GF_Vec v1, GF_Vec v2)
{
	/*commented out atm - weird results (not enough precision?)...*/
	//#if defined(GPAC_USE_IGPP_HP) || defined (GPAC_USE_IGPP)
#if 0
	Fixed res;
	gppVec3DDot_16_32s((GPP_VEC3D *)&v1, (GPP_VEC3D *)&v2, &res);
	return res;
#elif defined(FLOAT_COMPUTE)
	Float fr = FIX2FLT(v1.x)*FIX2FLT(v2.x) + FIX2FLT(v1.y)*FIX2FLT(v2.y) + FIX2FLT(v1.z)*FIX2FLT(v2.z);
	return FLT2FIX(fr);
#else
	/*both high-magnitude vectors, use low precision on frac part to avoid overflow
	if only one is, the dot product should still be in proper range*/
	if (0 && VEC_HIGH_MAG(v1) && VEC_HIGH_MAG(v2)) {
		v1.x >>= 4;
		v1.y >>= 4;
		v1.z >>= 4;
		v2.x >>= 4;
		v2.y >>= 4;
		v2.z >>= 4;
		return (gf_mulfix(v1.x, v2.x) + gf_mulfix(v1.y, v2.y) + gf_mulfix(v1.z, v2.z)) << 8;
	}
	return gf_mulfix(v1.x, v2.x) + gf_mulfix(v1.y, v2.y) + gf_mulfix(v1.z, v2.z);

#endif
}

GF_EXPORT
void gf_vec_norm(GF_Vec *v)
{
	/*commented out atm - weird results (not enough precision?)...*/
	//#if defined(GPAC_USE_IGPP_HP) || defined (GPAC_USE_IGPP)
#if 0
	gppVec3DNormalize_16_32s((GPP_VEC3D *)&v);
#else
	Fixed __res = gf_vec_len(*v);
	v->x = gf_divfix(v->x, __res);
	v->y = gf_divfix(v->y, __res);
	v->z = gf_divfix(v->z, __res);
#endif
}

GF_EXPORT
GF_Vec gf_vec_scale(GF_Vec v, Fixed f)
{
	GF_Vec res;
	res.x = gf_mulfix(v.x, f);
	res.y = gf_mulfix(v.y, f);
	res.z = gf_mulfix(v.z, f);
	return res;
}

GF_EXPORT
GF_Vec gf_vec_cross(GF_Vec v1, GF_Vec v2)
{
	GF_Vec res;
	/*commented out atm - weird results (not enough precision?)...*/
	//#if defined(GPAC_USE_IGPP_HP) || defined (GPAC_USE_IGPP)
#if 0
	gppVec3DCross_16_32s((GPP_VEC3D *)&v1, (GPP_VEC3D *)&v2, (GPP_VEC3D *)&res);
	return res;
#elif defined(FLOAT_COMPUTE)
	res.x = FLT2FIX(FIX2FLT(v1.y)*FIX2FLT(v2.z) - FIX2FLT(v2.y)*FIX2FLT(v1.z));
	res.y = FLT2FIX(FIX2FLT(v2.x)*FIX2FLT(v1.z) - FIX2FLT(v1.x)*FIX2FLT(v2.z));
	res.z = FLT2FIX(FIX2FLT(v1.x)*FIX2FLT(v2.y) - FIX2FLT(v2.x)*FIX2FLT(v1.y));
	return res;
#else

	/*both high-magnitude vectors, use low precision on frac part to avoid overflow
	if only one is, the cross product should still be in proper range*/
	if (VEC_HIGH_MAG(v1) && VEC_HIGH_MAG(v2)) {
		v1.x >>= 8;
		v1.y >>= 8;
		v1.z >>= 8;
		v2.x >>= 8;
		v2.y >>= 8;
		v2.z >>= 8;
		res.x = gf_mulfix(v1.y, v2.z) - gf_mulfix(v2.y, v1.z);
		res.y = gf_mulfix(v2.x, v1.z) - gf_mulfix(v1.x, v2.z);
		res.z = gf_mulfix(v1.x, v2.y) - gf_mulfix(v2.x, v1.y);
		res.x <<= 16;
		res.y <<= 16;
		res.z <<= 16;
		return res;
	}
	res.x = gf_mulfix(v1.y, v2.z) - gf_mulfix(v2.y, v1.z);
	res.y = gf_mulfix(v2.x, v1.z) - gf_mulfix(v1.x, v2.z);
	res.z = gf_mulfix(v1.x, v2.y) - gf_mulfix(v2.x, v1.y);

#endif
	return res;
}

#else

GF_EXPORT
Fixed gf_vec_len(GF_Vec v) {
	return gf_sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
}
GF_EXPORT
Fixed gf_vec_lensq(GF_Vec v) {
	return v.x*v.x + v.y*v.y + v.z*v.z;
}
GF_EXPORT
Fixed gf_vec_dot(GF_Vec v1, GF_Vec v2) {
	return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
}
GF_EXPORT
void gf_vec_norm(GF_Vec *v)
{
	Fixed __res = gf_vec_len(*v);
	if (!__res) return;
	if (__res == FIX_ONE) return;
	__res = 1.0f / __res;
	v->x *= __res;
	v->y *= __res;
	v->z *= __res;
}

GF_EXPORT
GF_Vec gf_vec_scale(GF_Vec v, Fixed f)
{
	GF_Vec res = v;
	res.x *= f;
	res.y *= f;
	res.z *= f;
	return res;
}

GF_EXPORT
GF_Vec gf_vec_cross(GF_Vec v1, GF_Vec v2)
{
	GF_Vec res;
	res.x = v1.y*v2.z - v2.y*v1.z;
	res.y = v2.x*v1.z - v1.x*v2.z;
	res.z = v1.x*v2.y - v2.x*v1.y;
	return res;
}

#endif


GF_EXPORT
void gf_mx2d_from_mx(GF_Matrix2D *mat2D, GF_Matrix *mat)
{
	gf_mx2d_init(*mat2D);
	mat2D->m[0] = mat->m[0];
	mat2D->m[1] = mat->m[4];
	mat2D->m[2] = mat->m[12];
	mat2D->m[3] = mat->m[1];
	mat2D->m[4] = mat->m[5];
	mat2D->m[5] = mat->m[13];
}

GF_EXPORT
void gf_mx_apply_rect(GF_Matrix *mat, GF_Rect *rc)
{
	GF_Matrix2D mat2D;
	gf_mx2d_from_mx(&mat2D, mat);
	gf_mx2d_apply_rect(&mat2D, rc);
}

GF_EXPORT
void gf_mx_add_matrix(GF_Matrix *mat, GF_Matrix *mul)
{
	GF_Matrix tmp;
	gf_mx_init(tmp);

	tmp.m[0] = gf_mulfix(mat->m[0], mul->m[0]) + gf_mulfix(mat->m[4], mul->m[1]) + gf_mulfix(mat->m[8], mul->m[2]);
	tmp.m[4] = gf_mulfix(mat->m[0], mul->m[4]) + gf_mulfix(mat->m[4], mul->m[5]) + gf_mulfix(mat->m[8], mul->m[6]);
	tmp.m[8] = gf_mulfix(mat->m[0], mul->m[8]) + gf_mulfix(mat->m[4], mul->m[9]) + gf_mulfix(mat->m[8], mul->m[10]);
	tmp.m[12] = gf_mulfix(mat->m[0], mul->m[12]) + gf_mulfix(mat->m[4], mul->m[13]) + gf_mulfix(mat->m[8], mul->m[14]) + mat->m[12];
	tmp.m[1] = gf_mulfix(mat->m[1], mul->m[0]) + gf_mulfix(mat->m[5], mul->m[1]) + gf_mulfix(mat->m[9], mul->m[2]);
	tmp.m[5] = gf_mulfix(mat->m[1], mul->m[4]) + gf_mulfix(mat->m[5], mul->m[5]) + gf_mulfix(mat->m[9], mul->m[6]);
	tmp.m[9] = gf_mulfix(mat->m[1], mul->m[8]) + gf_mulfix(mat->m[5], mul->m[9]) + gf_mulfix(mat->m[9], mul->m[10]);
	tmp.m[13] = gf_mulfix(mat->m[1], mul->m[12]) + gf_mulfix(mat->m[5], mul->m[13]) + gf_mulfix(mat->m[9], mul->m[14]) + mat->m[13];
	tmp.m[2] = gf_mulfix(mat->m[2], mul->m[0]) + gf_mulfix(mat->m[6], mul->m[1]) + gf_mulfix(mat->m[10], mul->m[2]);
	tmp.m[6] = gf_mulfix(mat->m[2], mul->m[4]) + gf_mulfix(mat->m[6], mul->m[5]) + gf_mulfix(mat->m[10], mul->m[6]);
	tmp.m[10] = gf_mulfix(mat->m[2], mul->m[8]) + gf_mulfix(mat->m[6], mul->m[9]) + gf_mulfix(mat->m[10], mul->m[10]);
	tmp.m[14] = gf_mulfix(mat->m[2], mul->m[12]) + gf_mulfix(mat->m[6], mul->m[13]) + gf_mulfix(mat->m[10], mul->m[14]) + mat->m[14];
	memcpy(mat->m, tmp.m, sizeof(Fixed) * 16);
}

GF_EXPORT
void gf_mx_add_matrix_2d(GF_Matrix *mat, GF_Matrix2D *mat2D)
{
	GF_Matrix tmp;
	gf_mx_init(tmp);

	tmp.m[0] = gf_mulfix(mat->m[0], mat2D->m[0]) + gf_mulfix(mat->m[4], mat2D->m[3]);
	tmp.m[4] = gf_mulfix(mat->m[0], mat2D->m[1]) + gf_mulfix(mat->m[4], mat2D->m[4]);
	tmp.m[8] = mat->m[8];
	tmp.m[12] = gf_mulfix(mat->m[0], mat2D->m[2]) + gf_mulfix(mat->m[4], mat2D->m[5]) + mat->m[12];
	tmp.m[1] = gf_mulfix(mat->m[1], mat2D->m[0]) + gf_mulfix(mat->m[5], mat2D->m[3]);
	tmp.m[5] = gf_mulfix(mat->m[1], mat2D->m[1]) + gf_mulfix(mat->m[5], mat2D->m[4]);
	tmp.m[9] = mat->m[9];
	tmp.m[13] = gf_mulfix(mat->m[1], mat2D->m[2]) + gf_mulfix(mat->m[5], mat2D->m[5]) + mat->m[13];
	tmp.m[2] = gf_mulfix(mat->m[2], mat2D->m[0]) + gf_mulfix(mat->m[6], mat2D->m[3]);
	tmp.m[6] = gf_mulfix(mat->m[2], mat2D->m[1]) + gf_mulfix(mat->m[6], mat2D->m[4]);
	tmp.m[10] = mat->m[10];
	tmp.m[14] = gf_mulfix(mat->m[2], mat2D->m[2]) + gf_mulfix(mat->m[6], mat2D->m[5]) + mat->m[14];
	memcpy(mat->m, tmp.m, sizeof(Fixed) * 16);
}


GF_EXPORT
void gf_mx_add_translation(GF_Matrix *mat, Fixed tx, Fixed ty, Fixed tz)
{
	Fixed tmp[3];
	u32 i;
	tmp[0] = mat->m[12];
	tmp[1] = mat->m[13];
	tmp[2] = mat->m[14];
	for (i = 0; i<3; i++)
		tmp[i] += (gf_mulfix(tx, mat->m[i]) + gf_mulfix(ty, mat->m[i + 4]) + gf_mulfix(tz, mat->m[i + 8]));
	mat->m[12] = tmp[0];
	mat->m[13] = tmp[1];
	mat->m[14] = tmp[2];
}

GF_EXPORT
void gf_mx_add_scale(GF_Matrix *mat, Fixed sx, Fixed sy, Fixed sz)
{
	Fixed tmp[3];
	u32 i, j;

	tmp[0] = sx;
	tmp[1] = sy;
	tmp[2] = sz;

	for (i = 0; i<3; i++) {
		for (j = 0; j<3; j++) {
			mat->m[i * 4 + j] = gf_mulfix(mat->m[j + 4 * i], tmp[i]);
		}
	}
}

GF_EXPORT
void gf_mx_add_rotation(GF_Matrix *mat, Fixed angle, Fixed x, Fixed y, Fixed z)
{
	GF_Matrix tmp;
	Fixed xx, yy, zz, xy, xz, yz;
	Fixed nor = gf_sqrt(gf_mulfix(x, x) + gf_mulfix(y, y) + gf_mulfix(z, z));
	Fixed cos_a = gf_cos(angle);
	Fixed sin_a = gf_sin(angle);
	Fixed icos_a = FIX_ONE - cos_a;

	if (nor && (nor != FIX_ONE)) {
		x = gf_divfix(x, nor);
		y = gf_divfix(y, nor);
		z = gf_divfix(z, nor);
	}
	xx = gf_mulfix(x, x);
	yy = gf_mulfix(y, y);
	zz = gf_mulfix(z, z);
	xy = gf_mulfix(x, y);
	xz = gf_mulfix(x, z);
	yz = gf_mulfix(y, z);
	gf_mx_init(tmp);
	tmp.m[0] = gf_mulfix(icos_a, xx) + cos_a;
	tmp.m[1] = gf_mulfix(xy, icos_a) + gf_mulfix(z, sin_a);
	tmp.m[2] = gf_mulfix(xz, icos_a) - gf_mulfix(y, sin_a);

	tmp.m[4] = gf_mulfix(xy, icos_a) - gf_mulfix(z, sin_a);
	tmp.m[5] = gf_mulfix(icos_a, yy) + cos_a;
	tmp.m[6] = gf_mulfix(yz, icos_a) + gf_mulfix(x, sin_a);

	tmp.m[8] = gf_mulfix(xz, icos_a) + gf_mulfix(y, sin_a);
	tmp.m[9] = gf_mulfix(yz, icos_a) - gf_mulfix(x, sin_a);
	tmp.m[10] = gf_mulfix(icos_a, zz) + cos_a;

	gf_mx_add_matrix(mat, &tmp);
}

GF_EXPORT
void gf_mx_from_mx2d(GF_Matrix *mat, GF_Matrix2D *mat2D)
{
	gf_mx_init(*mat);
	mat->m[0] = mat2D->m[0];
	mat->m[4] = mat2D->m[1];
	mat->m[12] = mat2D->m[2];
	mat->m[1] = mat2D->m[3];
	mat->m[5] = mat2D->m[4];
	mat->m[13] = mat2D->m[5];
}

GF_EXPORT
Bool gf_mx_equal(GF_Matrix *mx1, GF_Matrix *mx2)
{
	if (mx1->m[0] != mx2->m[0]) return GF_FALSE;
	if (mx1->m[1] != mx2->m[1]) return GF_FALSE;
	if (mx1->m[2] != mx2->m[2]) return GF_FALSE;
	if (mx1->m[4] != mx2->m[4]) return GF_FALSE;
	if (mx1->m[5] != mx2->m[5]) return GF_FALSE;
	if (mx1->m[6] != mx2->m[6]) return GF_FALSE;
	if (mx1->m[8] != mx2->m[8]) return GF_FALSE;
	if (mx1->m[9] != mx2->m[9]) return GF_FALSE;
	if (mx1->m[10] != mx2->m[10]) return GF_FALSE;
	if (mx1->m[12] != mx2->m[12]) return GF_FALSE;
	if (mx1->m[13] != mx2->m[13]) return GF_FALSE;
	if (mx1->m[14] != mx2->m[14]) return GF_FALSE;
	return GF_TRUE;
}


GF_EXPORT
void gf_mx_inverse(GF_Matrix *mx)
{
#ifdef GPAC_FIXED_POINT
	Float _det, _max;
	s32 sign, scale;
#endif
	Fixed det;
	GF_Matrix rev;
	gf_mx_init(rev);

	assert(!((mx->m[3] != 0) || (mx->m[7] != 0) || (mx->m[11] != 0) || (mx->m[15] != FIX_ONE)));


#ifdef GPAC_FIXED_POINT
	/*we must compute the determinent as a float to avoid fixed-point overflow*/
	_det = FIX2FLT(mx->m[0])*FIX2FLT(mx->m[5])*FIX2FLT(mx->m[10]);
	_det += FIX2FLT(mx->m[1])*FIX2FLT(mx->m[6])*FIX2FLT(mx->m[8]);
	_det += FIX2FLT(mx->m[2])*FIX2FLT(mx->m[4])*FIX2FLT(mx->m[9]);
	_det -= FIX2FLT(mx->m[2])*FIX2FLT(mx->m[5])*FIX2FLT(mx->m[8]);
	_det -= FIX2FLT(mx->m[1])*FIX2FLT(mx->m[4])*FIX2FLT(mx->m[10]);
	_det -= FIX2FLT(mx->m[0])*FIX2FLT(mx->m[6])*FIX2FLT(mx->m[9]);

	if (!_det) {
		gf_mx2d_init(*mx);
		return;
	}
	sign = _det<0 ? -1 : 1;
	_det *= sign;
	scale = 1;
	_max = FIX2FLT(FIX_MAX);
	while (_det / scale > _max) {
		scale *= 10;
	}
	det = sign * FLT2FIX(_det / scale);
#else
	det = gf_mulfix(gf_mulfix(mx->m[0], mx->m[5]), mx->m[10]);
	det += gf_mulfix(gf_mulfix(mx->m[1], mx->m[6]), mx->m[8]);
	det += gf_mulfix(gf_mulfix(mx->m[2], mx->m[4]), mx->m[9]);
	det -= gf_mulfix(gf_mulfix(mx->m[2], mx->m[5]), mx->m[8]);
	det -= gf_mulfix(gf_mulfix(mx->m[1], mx->m[4]), mx->m[10]);
	det -= gf_mulfix(gf_mulfix(mx->m[0], mx->m[6]), mx->m[9]);
	if (!det) {
		gf_mx2d_init(*mx);
		return;
	}
#endif


	/* Calculate inverse(A) = adj(A) / det(A) */
	rev.m[0] = gf_muldiv(mx->m[5], mx->m[10], det) - gf_muldiv(mx->m[6], mx->m[9], det);
	rev.m[4] = -gf_muldiv(mx->m[4], mx->m[10], det) + gf_muldiv(mx->m[6], mx->m[8], det);
	rev.m[8] = gf_muldiv(mx->m[4], mx->m[9], det) - gf_muldiv(mx->m[5], mx->m[8], det);
	rev.m[1] = -gf_muldiv(mx->m[1], mx->m[10], det) + gf_muldiv(mx->m[2], mx->m[9], det);
	rev.m[5] = gf_muldiv(mx->m[0], mx->m[10], det) - gf_muldiv(mx->m[2], mx->m[8], det);
	rev.m[9] = -gf_muldiv(mx->m[0], mx->m[9], det) + gf_muldiv(mx->m[1], mx->m[8], det);
	rev.m[2] = gf_muldiv(mx->m[1], mx->m[6], det) - gf_muldiv(mx->m[2], mx->m[5], det);
	rev.m[6] = -gf_muldiv(mx->m[0], mx->m[6], det) + gf_muldiv(mx->m[2], mx->m[4], det);
	rev.m[10] = gf_muldiv(mx->m[0], mx->m[5], det) - gf_muldiv(mx->m[1], mx->m[4], det);

#ifdef GPAC_FIXED_POINT
	if (scale>1) {
		rev.m[0] /= scale;
		rev.m[4] /= scale;
		rev.m[8] /= scale;
		rev.m[1] /= scale;
		rev.m[5] /= scale;
		rev.m[9] /= scale;
		rev.m[2] /= scale;
		rev.m[6] /= scale;
		rev.m[10] /= scale;
	}
#endif

	/* do translation part*/
	rev.m[12] = -(gf_mulfix(mx->m[12], rev.m[0]) + gf_mulfix(mx->m[13], rev.m[4]) + gf_mulfix(mx->m[14], rev.m[8]));
	rev.m[13] = -(gf_mulfix(mx->m[12], rev.m[1]) + gf_mulfix(mx->m[13], rev.m[5]) + gf_mulfix(mx->m[14], rev.m[9]));
	rev.m[14] = -(gf_mulfix(mx->m[12], rev.m[2]) + gf_mulfix(mx->m[13], rev.m[6]) + gf_mulfix(mx->m[14], rev.m[10]));
	gf_mx_copy(*mx, rev);
}

GF_EXPORT
void gf_mx_transpose(GF_Matrix *mx)
{
	GF_Matrix rev;
	int i, j;

	gf_mx_init(rev);
	for (i = 0; i<4; i++) {
		for (j = 0; j<4; j++) {
			rev.m[i * 4 + j] = mx->m[j * 4 + i];
		}
	}


	gf_mx_copy(*mx, rev);
}


GF_EXPORT
void gf_mx_apply_vec(GF_Matrix *mx, GF_Vec *pt)
{
	GF_Vec res;
	res.x = gf_mulfix(pt->x, mx->m[0]) + gf_mulfix(pt->y, mx->m[4]) + gf_mulfix(pt->z, mx->m[8]) + mx->m[12];
	res.y = gf_mulfix(pt->x, mx->m[1]) + gf_mulfix(pt->y, mx->m[5]) + gf_mulfix(pt->z, mx->m[9]) + mx->m[13];
	res.z = gf_mulfix(pt->x, mx->m[2]) + gf_mulfix(pt->y, mx->m[6]) + gf_mulfix(pt->z, mx->m[10]) + mx->m[14];
	*pt = res;
}

GF_EXPORT
void gf_mx_ortho(GF_Matrix *mx, Fixed left, Fixed right, Fixed bottom, Fixed top, Fixed z_near, Fixed z_far)
{
	gf_mx_init(*mx);
	mx->m[0] = gf_divfix(2 * FIX_ONE, right - left);
	mx->m[5] = gf_divfix(2 * FIX_ONE, top - bottom);
	mx->m[10] = gf_divfix(-2 * FIX_ONE, z_far - z_near);
	mx->m[12] = gf_divfix(right + left, right - left);
	mx->m[13] = gf_divfix(top + bottom, top - bottom);
	mx->m[14] = gf_divfix(z_far + z_near, z_far - z_near);
	mx->m[15] = FIX_ONE;
}

GF_EXPORT
void gf_mx_perspective(GF_Matrix *mx, Fixed fieldOfView, Fixed aspectRatio, Fixed z_near, Fixed z_far)
{
	Fixed f = gf_divfix(gf_cos(fieldOfView / 2), gf_sin(fieldOfView / 2));
	gf_mx_init(*mx);
	mx->m[0] = gf_divfix(f, aspectRatio);
	mx->m[5] = f;
	mx->m[10] = gf_divfix(z_far + z_near, z_near - z_far);

	mx->m[11] = -FIX_ONE;
	mx->m[14] = 2 * gf_muldiv(z_near, z_far, z_near - z_far);

	mx->m[15] = 0;
}

GF_EXPORT
void gf_mx_lookat(GF_Matrix *mx, GF_Vec eye, GF_Vec center, GF_Vec upVector)
{
	GF_Vec f, s, u;

	gf_vec_diff(f, center, eye);
	gf_vec_norm(&f);
	gf_vec_norm(&upVector);

	s = gf_vec_cross(f, upVector);
	u = gf_vec_cross(s, f);
	gf_mx_init(*mx);

	mx->m[0] = s.x;
	mx->m[1] = u.x;
	mx->m[2] = -f.x;
	mx->m[4] = s.y;
	mx->m[5] = u.y;
	mx->m[6] = -f.y;
	mx->m[8] = s.z;
	mx->m[9] = u.z;
	mx->m[10] = -f.z;

	gf_mx_add_translation(mx, -eye.x, -eye.y, -eye.z);
}

GF_Vec4 gf_quat_from_matrix(GF_Matrix *mx);

GF_EXPORT
void gf_mx_decompose(GF_Matrix *mx, GF_Vec *translate, GF_Vec *scale, GF_Vec4 *rotate, GF_Vec *shear)
{
	u32 i, j;
	GF_Vec4 quat;
	Fixed locmat[16];
	GF_Matrix tmp;
	GF_Vec row0, row1, row2;
	Fixed shear_xy, shear_xz, shear_yz;
	assert(mx->m[15]);

	memcpy(locmat, mx->m, sizeof(Fixed) * 16);
	/*no perspective*/
	locmat[3] = locmat[7] = locmat[11] = 0;
	/*normalize*/
	for (i = 0; i<4; i++) {
		for (j = 0; j<4; j++) {
			locmat[4 * i + j] = gf_divfix(locmat[4 * i + j], locmat[15]);
		}
	}
	translate->x = locmat[12];
	translate->y = locmat[13];
	translate->z = locmat[14];
	locmat[12] = locmat[13] = locmat[14] = 0;
	row0.x = locmat[0];
	row0.y = locmat[1];
	row0.z = locmat[2];
	row1.x = locmat[4];
	row1.y = locmat[5];
	row1.z = locmat[6];
	row2.x = locmat[8];
	row2.y = locmat[9];
	row2.z = locmat[10];

	scale->x = gf_vec_len(row0);
	gf_vec_norm(&row0);
	shear_xy = gf_vec_dot(row0, row1);
	row1.x -= gf_mulfix(row0.x, shear_xy);
	row1.y -= gf_mulfix(row0.y, shear_xy);
	row1.z -= gf_mulfix(row0.z, shear_xy);

	scale->y = gf_vec_len(row1);
	gf_vec_norm(&row1);
	shear->x = gf_divfix(shear_xy, scale->y);

	shear_xz = gf_vec_dot(row0, row2);
	row2.x -= gf_mulfix(row0.x, shear_xz);
	row2.y -= gf_mulfix(row0.y, shear_xz);
	row2.z -= gf_mulfix(row0.z, shear_xz);
	shear_yz = gf_vec_dot(row1, row2);
	row2.x -= gf_mulfix(row1.x, shear_yz);
	row2.y -= gf_mulfix(row1.y, shear_yz);
	row2.z -= gf_mulfix(row1.z, shear_yz);

	scale->z = gf_vec_len(row2);
	gf_vec_norm(&row2);
	shear->y = gf_divfix(shear_xz, scale->z);
	shear->z = gf_divfix(shear_yz, scale->z);

	locmat[0] = row0.x;
	locmat[4] = row1.x;
	locmat[8] = row2.x;
	locmat[1] = row0.y;
	locmat[5] = row1.y;
	locmat[9] = row2.y;
	locmat[2] = row0.z;
	locmat[6] = row1.z;
	locmat[10] = row2.z;

	memcpy(tmp.m, locmat, sizeof(Fixed) * 16);
	quat = gf_quat_from_matrix(&tmp);
	*rotate = gf_quat_to_rotation(&quat);
}

GF_EXPORT
void gf_mx_apply_bbox_sphere(GF_Matrix *mx, GF_BBox *box)
{
	Fixed var;
	gf_mx_apply_vec(mx, &box->min_edge);
	gf_mx_apply_vec(mx, &box->max_edge);

	if (box->min_edge.x > box->max_edge.x)
	{
		var = box->min_edge.x;
		box->min_edge.x = box->max_edge.x;
		box->max_edge.x = var;
	}
	if (box->min_edge.y > box->max_edge.y)
	{
		var = box->min_edge.y;
		box->min_edge.y = box->max_edge.y;
		box->max_edge.y = var;
	}
	if (box->min_edge.z > box->max_edge.z)
	{
		var = box->min_edge.z;
		box->min_edge.z = box->max_edge.z;
		box->max_edge.z = var;
	}
	gf_bbox_refresh(box);
}

GF_EXPORT
void gf_mx_apply_bbox(GF_Matrix *mx, GF_BBox *box)
{
	u32 i;
	GF_Vec v[4];
	v[0] = box->min_edge;
	v[1] = box->min_edge;
	v[1].x = box->max_edge.x;
	v[2] = box->min_edge;
	v[2].y = box->max_edge.y;
	v[3] = box->min_edge;
	v[3].z = box->max_edge.z;
	box->max_edge.x = box->max_edge.y = box->max_edge.z = -FIX_MAX;
	box->min_edge.x = box->min_edge.y = box->min_edge.z = FIX_MAX;
	for (i = 0; i<4; i++) {
		gf_mx_apply_vec(mx, &v[i]);
		if (box->min_edge.x > v[i].x) box->min_edge.x = v[i].x;
		if (box->min_edge.y > v[i].y) box->min_edge.y = v[i].y;
		if (box->min_edge.z > v[i].z) box->min_edge.z = v[i].z;
		if (box->max_edge.x < v[i].x) box->max_edge.x = v[i].x;
		if (box->max_edge.y < v[i].y) box->max_edge.y = v[i].y;
		if (box->max_edge.z < v[i].z) box->max_edge.z = v[i].z;
	}
	gf_bbox_refresh(box);
}

// Apply the rotation portion of a matrix to a vector.
GF_EXPORT
void gf_mx_rotate_vector(GF_Matrix *mx, GF_Vec *pt)
{
	GF_Vec res;
	Fixed den;
	res.x = gf_mulfix(pt->x, mx->m[0]) + gf_mulfix(pt->y, mx->m[4]) + gf_mulfix(pt->z, mx->m[8]);
	res.y = gf_mulfix(pt->x, mx->m[1]) + gf_mulfix(pt->y, mx->m[5]) + gf_mulfix(pt->z, mx->m[9]);
	res.z = gf_mulfix(pt->x, mx->m[2]) + gf_mulfix(pt->y, mx->m[6]) + gf_mulfix(pt->z, mx->m[10]);
	den = gf_mulfix(pt->x, mx->m[3]) + gf_mulfix(pt->y, mx->m[7]) + gf_mulfix(pt->z, mx->m[11]) + mx->m[15];
	if (den == 0) return;
	res.x = gf_divfix(res.x, den);
	res.y = gf_divfix(res.y, den);
	res.z = gf_divfix(res.z, den);
	*pt = res;
}

GF_EXPORT
void gf_mx_rotation_matrix_from_vectors(GF_Matrix *mx, GF_Vec x, GF_Vec y, GF_Vec z)
{
	mx->m[0] = x.x;
	mx->m[1] = y.x;
	mx->m[2] = z.x;
	mx->m[3] = 0;
	mx->m[4] = x.y;
	mx->m[5] = y.y;
	mx->m[6] = z.y;
	mx->m[7] = 0;
	mx->m[8] = x.z;
	mx->m[9] = y.z;
	mx->m[10] = z.z;
	mx->m[11] = 0;
	mx->m[12] = 0;
	mx->m[13] = 0;
	mx->m[14] = 0;
	mx->m[15] = FIX_ONE;
}


/*we should only need a full matrix product for frustrum setup*/
GF_EXPORT
void gf_mx_add_matrix_4x4(GF_Matrix *mat, GF_Matrix *mul)
{
	GF_Matrix tmp;
	gf_mx_init(tmp);
	tmp.m[0] = gf_mulfix(mat->m[0], mul->m[0]) + gf_mulfix(mat->m[4], mul->m[1]) + gf_mulfix(mat->m[8], mul->m[2]) + gf_mulfix(mat->m[12], mul->m[3]);
	tmp.m[1] = gf_mulfix(mat->m[1], mul->m[0]) + gf_mulfix(mat->m[5], mul->m[1]) + gf_mulfix(mat->m[9], mul->m[2]) + gf_mulfix(mat->m[13], mul->m[3]);
	tmp.m[2] = gf_mulfix(mat->m[2], mul->m[0]) + gf_mulfix(mat->m[6], mul->m[1]) + gf_mulfix(mat->m[10], mul->m[2]) + gf_mulfix(mat->m[14], mul->m[3]);
	tmp.m[3] = gf_mulfix(mat->m[3], mul->m[0]) + gf_mulfix(mat->m[7], mul->m[1]) + gf_mulfix(mat->m[11], mul->m[2]) + gf_mulfix(mat->m[15], mul->m[3]);
	tmp.m[4] = gf_mulfix(mat->m[0], mul->m[4]) + gf_mulfix(mat->m[4], mul->m[5]) + gf_mulfix(mat->m[8], mul->m[6]) + gf_mulfix(mat->m[12], mul->m[7]);
	tmp.m[5] = gf_mulfix(mat->m[1], mul->m[4]) + gf_mulfix(mat->m[5], mul->m[5]) + gf_mulfix(mat->m[9], mul->m[6]) + gf_mulfix(mat->m[13], mul->m[7]);
	tmp.m[6] = gf_mulfix(mat->m[2], mul->m[4]) + gf_mulfix(mat->m[6], mul->m[5]) + gf_mulfix(mat->m[10], mul->m[6]) + gf_mulfix(mat->m[14], mul->m[7]);
	tmp.m[7] = gf_mulfix(mat->m[3], mul->m[4]) + gf_mulfix(mat->m[7], mul->m[5]) + gf_mulfix(mat->m[11], mul->m[6]) + gf_mulfix(mat->m[15], mul->m[7]);
	tmp.m[8] = gf_mulfix(mat->m[0], mul->m[8]) + gf_mulfix(mat->m[4], mul->m[9]) + gf_mulfix(mat->m[8], mul->m[10]) + gf_mulfix(mat->m[12], mul->m[11]);
	tmp.m[9] = gf_mulfix(mat->m[1], mul->m[8]) + gf_mulfix(mat->m[5], mul->m[9]) + gf_mulfix(mat->m[9], mul->m[10]) + gf_mulfix(mat->m[13], mul->m[11]);
	tmp.m[10] = gf_mulfix(mat->m[2], mul->m[8]) + gf_mulfix(mat->m[6], mul->m[9]) + gf_mulfix(mat->m[10], mul->m[10]) + gf_mulfix(mat->m[14], mul->m[11]);
	tmp.m[11] = gf_mulfix(mat->m[3], mul->m[8]) + gf_mulfix(mat->m[7], mul->m[9]) + gf_mulfix(mat->m[11], mul->m[10]) + gf_mulfix(mat->m[15], mul->m[11]);
	tmp.m[12] = gf_mulfix(mat->m[0], mul->m[12]) + gf_mulfix(mat->m[4], mul->m[13]) + gf_mulfix(mat->m[8], mul->m[14]) + gf_mulfix(mat->m[12], mul->m[15]);
	tmp.m[13] = gf_mulfix(mat->m[1], mul->m[12]) + gf_mulfix(mat->m[5], mul->m[13]) + gf_mulfix(mat->m[9], mul->m[14]) + gf_mulfix(mat->m[13], mul->m[15]);
	tmp.m[14] = gf_mulfix(mat->m[2], mul->m[12]) + gf_mulfix(mat->m[6], mul->m[13]) + gf_mulfix(mat->m[10], mul->m[14]) + gf_mulfix(mat->m[14], mul->m[15]);
	tmp.m[15] = gf_mulfix(mat->m[3], mul->m[12]) + gf_mulfix(mat->m[7], mul->m[13]) + gf_mulfix(mat->m[11], mul->m[14]) + gf_mulfix(mat->m[15], mul->m[15]);
	memcpy(mat->m, tmp.m, sizeof(Fixed) * 16);
}


GF_EXPORT
void gf_mx_apply_vec_4x4(GF_Matrix *mx, GF_Vec4 *vec)
{
	GF_Vec4 res;
	res.x = gf_mulfix(mx->m[0], vec->x) + gf_mulfix(mx->m[4], vec->y) + gf_mulfix(mx->m[8], vec->z) + gf_mulfix(mx->m[12], vec->q);
	res.y = gf_mulfix(mx->m[1], vec->x) + gf_mulfix(mx->m[5], vec->y) + gf_mulfix(mx->m[9], vec->z) + gf_mulfix(mx->m[13], vec->q);
	res.z = gf_mulfix(mx->m[2], vec->x) + gf_mulfix(mx->m[6], vec->y) + gf_mulfix(mx->m[10], vec->z) + gf_mulfix(mx->m[14], vec->q);
	res.q = gf_mulfix(mx->m[3], vec->x) + gf_mulfix(mx->m[7], vec->y) + gf_mulfix(mx->m[11], vec->z) + gf_mulfix(mx->m[15], vec->q);
	*vec = res;
}

/*
*	Taken from MESA/GLU (LGPL)
*
* Compute inverse of 4x4 transformation matrix.
* Code contributed by Jacques Leroy jle@star.be
* Return 1 for success, 0 for failure (singular matrix)
*/

GF_EXPORT
Bool gf_mx_inverse_4x4(GF_Matrix *mx)
{

#define SWAP_ROWS(a, b) { Fixed *_tmp = a; (a)=(b); (b)=_tmp; }
	Fixed wtmp[4][8];
	Fixed m0, m1, m2, m3, s;
	Fixed *r0, *r1, *r2, *r3;
	GF_Matrix res;
	r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
	r0[0] = mx->m[0];
	r0[1] = mx->m[4];
	r0[2] = mx->m[8];
	r0[3] = mx->m[12];
	r0[4] = FIX_ONE;
	r0[5] = r0[6] = r0[7] = 0;
	r1[0] = mx->m[1];
	r1[1] = mx->m[5];
	r1[2] = mx->m[9];
	r1[3] = mx->m[13];
	r1[5] = FIX_ONE;
	r1[4] = r1[6] = r1[7] = 0;
	r2[0] = mx->m[2];
	r2[1] = mx->m[6];
	r2[2] = mx->m[10];
	r2[3] = mx->m[14];
	r2[6] = FIX_ONE;
	r2[4] = r2[5] = r2[7] = 0;
	r3[0] = mx->m[3];
	r3[1] = mx->m[7];
	r3[2] = mx->m[11];
	r3[3] = mx->m[15];
	r3[7] = FIX_ONE;
	r3[4] = r3[5] = r3[6] = 0;

	/* choose pivot - or die */
	if (ABS(r3[0]) > ABS(r2[0])) SWAP_ROWS(r3, r2);
	if (ABS(r2[0]) > ABS(r1[0])) SWAP_ROWS(r2, r1);
	if (ABS(r1[0]) > ABS(r0[0])) SWAP_ROWS(r1, r0);
	if (r0[0] == 0) return GF_FALSE;

	/*eliminate first variable*/
	m1 = gf_divfix(r1[0], r0[0]);
	m2 = gf_divfix(r2[0], r0[0]);
	m3 = gf_divfix(r3[0], r0[0]);
	s = r0[1];
	r1[1] -= gf_mulfix(m1, s);
	r2[1] -= gf_mulfix(m2, s);
	r3[1] -= gf_mulfix(m3, s);
	s = r0[2];
	r1[2] -= gf_mulfix(m1, s);
	r2[2] -= gf_mulfix(m2, s);
	r3[2] -= gf_mulfix(m3, s);
	s = r0[3];
	r1[3] -= gf_mulfix(m1, s);
	r2[3] -= gf_mulfix(m2, s);
	r3[3] -= gf_mulfix(m3, s);
	s = r0[4];
	if (s != 0) {
		r1[4] -= gf_mulfix(m1, s);
		r2[4] -= gf_mulfix(m2, s);
		r3[4] -= gf_mulfix(m3, s);
	}
	s = r0[5];
	if (s != 0) {
		r1[5] -= gf_mulfix(m1, s);
		r2[5] -= gf_mulfix(m2, s);
		r3[5] -= gf_mulfix(m3, s);
	}
	s = r0[6];
	if (s != 0) {
		r1[6] -= gf_mulfix(m1, s);
		r2[6] -= gf_mulfix(m2, s);
		r3[6] -= gf_mulfix(m3, s);
	}
	s = r0[7];
	if (s != 0) {
		r1[7] -= gf_mulfix(m1, s);
		r2[7] -= gf_mulfix(m2, s);
		r3[7] -= gf_mulfix(m3, s);
	}

	/* choose pivot - or die */
	if (fabs(r3[1]) > fabs(r2[1])) SWAP_ROWS(r3, r2);
	if (fabs(r2[1]) > fabs(r1[1])) SWAP_ROWS(r2, r1);
	if (r1[1] == 0) return GF_FALSE;

	/* eliminate second variable */
	m2 = gf_divfix(r2[1], r1[1]);
	m3 = gf_divfix(r3[1], r1[1]);
	r2[2] -= gf_mulfix(m2, r1[2]);
	r3[2] -= gf_mulfix(m3, r1[2]);
	r2[3] -= gf_mulfix(m2, r1[3]);
	r3[3] -= gf_mulfix(m3, r1[3]);
	s = r1[4];
	if (s != 0) {
		r2[4] -= gf_mulfix(m2, s);
		r3[4] -= gf_mulfix(m3, s);
	}
	s = r1[5];
	if (s != 0) {
		r2[5] -= gf_mulfix(m2, s);
		r3[5] -= gf_mulfix(m3, s);
	}
	s = r1[6];
	if (s != 0) {
		r2[6] -= gf_mulfix(m2, s);
		r3[6] -= gf_mulfix(m3, s);
	}
	s = r1[7];
	if (s != 0) {
		r2[7] -= gf_mulfix(m2, s);
		r3[7] -= gf_mulfix(m3, s);
	}

	/* choose pivot - or die */
	if (fabs(r3[2]) > fabs(r2[2])) SWAP_ROWS(r3, r2);
	if (r2[2] == 0) return GF_FALSE;

	/* eliminate third variable */
	m3 = gf_divfix(r3[2], r2[2]);
	r3[3] -= gf_mulfix(m3, r2[3]);
	r3[4] -= gf_mulfix(m3, r2[4]);
	r3[5] -= gf_mulfix(m3, r2[5]);
	r3[6] -= gf_mulfix(m3, r2[6]);
	r3[7] -= gf_mulfix(m3, r2[7]);
	/* last check */
	if (r3[3] == 0) return GF_FALSE;

	s = gf_invfix(r3[3]);		/* now back substitute row 3 */
	r3[4] = gf_mulfix(r3[4], s);
	r3[5] = gf_mulfix(r3[5], s);
	r3[6] = gf_mulfix(r3[6], s);
	r3[7] = gf_mulfix(r3[7], s);

	m2 = r2[3];			/* now back substitute row 2 */
	s = gf_invfix(r2[2]);
	r2[4] = gf_mulfix(s, r2[4] - gf_mulfix(r3[4], m2));
	r2[5] = gf_mulfix(s, r2[5] - gf_mulfix(r3[5], m2));
	r2[6] = gf_mulfix(s, r2[6] - gf_mulfix(r3[6], m2));
	r2[7] = gf_mulfix(s, r2[7] - gf_mulfix(r3[7], m2));
	m1 = r1[3];
	r1[4] -= gf_mulfix(r3[4], m1);
	r1[5] -= gf_mulfix(r3[5], m1);
	r1[6] -= gf_mulfix(r3[6], m1);
	r1[7] -= gf_mulfix(r3[7], m1);
	m0 = r0[3];
	r0[4] -= gf_mulfix(r3[4], m0);
	r0[5] -= gf_mulfix(r3[5], m0);
	r0[6] -= gf_mulfix(r3[6], m0);
	r0[7] -= gf_mulfix(r3[7], m0);

	m1 = r1[2];			/* now back substitute row 1 */
	s = gf_invfix(r1[1]);
	r1[4] = gf_mulfix(s, r1[4] - gf_mulfix(r2[4], m1));
	r1[5] = gf_mulfix(s, r1[5] - gf_mulfix(r2[5], m1));
	r1[6] = gf_mulfix(s, r1[6] - gf_mulfix(r2[6], m1));
	r1[7] = gf_mulfix(s, r1[7] - gf_mulfix(r2[7], m1));
	m0 = r0[2];
	r0[4] -= gf_mulfix(r2[4], m0);
	r0[5] -= gf_mulfix(r2[5], m0);
	r0[6] -= gf_mulfix(r2[6], m0);
	r0[7] -= gf_mulfix(r2[7], m0);

	m0 = r0[1];			/* now back substitute row 0 */
	s = gf_invfix(r0[0]);
	r0[4] = gf_mulfix(s, r0[4] - gf_mulfix(r1[4], m0));
	r0[5] = gf_mulfix(s, r0[5] - gf_mulfix(r1[5], m0));
	r0[6] = gf_mulfix(s, r0[6] - gf_mulfix(r1[6], m0));
	r0[7] = gf_mulfix(s, r0[7] - gf_mulfix(r1[7], m0));

	gf_mx_init(res)
		res.m[0] = r0[4];
	res.m[4] = r0[5];
	res.m[8] = r0[6];
	res.m[12] = r0[7];
	res.m[1] = r1[4];
	res.m[5] = r1[5], res.m[9] = r1[6];
	res.m[13] = r1[7];
	res.m[2] = r2[4];
	res.m[6] = r2[5];
	res.m[10] = r2[6];
	res.m[14] = r2[7];
	res.m[3] = r3[4];
	res.m[7] = r3[5];
	res.m[11] = r3[6];
	res.m[15] = r3[7];
	gf_mx_copy(*mx, res);
	return GF_TRUE;
#undef SWAP_ROWS

}


GF_EXPORT
Bool gf_plane_exists_intersection(GF_Plane *plane, GF_Plane *with)
{
	GF_Vec cross;
	cross = gf_vec_cross(with->normal, plane->normal);
	return gf_vec_lensq(cross) > FIX_EPSILON;
}

GF_EXPORT
Bool gf_plane_intersect_line(GF_Plane *plane, GF_Vec *linepoint, GF_Vec *linevec, GF_Vec *outPoint)
{
	Fixed t, t2;
	t2 = gf_vec_dot(plane->normal, *linevec);
	if (t2 == 0) return GF_FALSE;
	t = -gf_divfix((gf_vec_dot(plane->normal, *linepoint) + plane->d), t2);
	if (t<0) return GF_FALSE;
	*outPoint = gf_vec_scale(*linevec, t);
	gf_vec_add(*outPoint, *linepoint, *outPoint);
	return GF_TRUE;
}

GF_EXPORT
Bool gf_plane_intersect_plane(GF_Plane *plane, GF_Plane *with, GF_Vec *linepoint, GF_Vec *linevec)
{
	Fixed fn00 = gf_vec_len(plane->normal);
	Fixed fn01 = gf_vec_dot(plane->normal, with->normal);
	Fixed fn11 = gf_vec_len(with->normal);
	Fixed det = gf_mulfix(fn00, fn11) - gf_mulfix(fn01, fn01);
	if (fabs(det) > FIX_EPSILON) {
		Fixed fc0, fc1;
		GF_Vec v1, v2;
		fc0 = gf_divfix(gf_mulfix(fn11, -plane->d) + gf_mulfix(fn01, with->d), det);
		fc1 = gf_divfix(gf_mulfix(fn00, -with->d) + gf_mulfix(fn01, plane->d), det);
		*linevec = gf_vec_cross(plane->normal, with->normal);
		v1 = gf_vec_scale(plane->normal, fc0);
		v2 = gf_vec_scale(with->normal, fc1);
		gf_vec_add(*linepoint, v1, v2);
		return GF_TRUE;
	}
	return GF_FALSE;
}

GF_EXPORT
Bool gf_plane_intersect_planes(GF_Plane *plane, GF_Plane *p1, GF_Plane *p2, GF_Vec *outPoint)
{
	GF_Vec lp, lv;
	if (gf_plane_intersect_plane(plane, p1, &lp, &lv))
		return gf_plane_intersect_line(p2, &lp, &lv, outPoint);
	return GF_FALSE;
}


GF_EXPORT
GF_Ray gf_ray(GF_Vec start, GF_Vec end)
{
	GF_Ray r;
	r.orig = start;
	gf_vec_diff(r.dir, end, start);
	gf_vec_norm(&r.dir);
	return r;
}

GF_EXPORT
void gf_mx_apply_ray(GF_Matrix *mx, GF_Ray *r)
{
	gf_vec_add(r->dir, r->orig, r->dir);
	gf_mx_apply_vec(mx, &r->orig);
	gf_mx_apply_vec(mx, &r->dir);
	gf_vec_diff(r->dir, r->dir, r->orig);
	gf_vec_norm(&r->dir);
}

#define XPLANE 0
#define YPLANE 1
#define ZPLANE 2


GF_EXPORT
Bool gf_ray_hit_box(GF_Ray *ray, GF_Vec box_min, GF_Vec box_max, GF_Vec *outPoint)
{
	Fixed t1, t2, tNEAR = FIX_MIN, tFAR = FIX_MAX;
	Fixed temp;
	//s8 xyorz, sign;

	if (ray->dir.x == 0) {
		if ((ray->orig.x < box_min.x) || (ray->orig.x > box_max.x))
			return GF_FALSE;
	}
	else {
		t1 = gf_divfix(box_min.x - ray->orig.x, ray->dir.x);
		t2 = gf_divfix(box_max.x - ray->orig.x, ray->dir.x);
		if (t1 > t2) {
			temp = t1;
			t1 = t2;
			t2 = temp;
		}
		if (t1 > tNEAR) {
			tNEAR = t1;
			//xyorz = XPLANE;
			//sign = (ray->dir.x < 0) ? 1 : -1;
		}
		if (t2 < tFAR) tFAR = t2;
		if (tNEAR > tFAR) return GF_FALSE; // box missed
		if (tFAR < 0) return GF_FALSE; // box behind the ray
	}

	if (ray->dir.y == 0) {
		if ((ray->orig.y < box_min.y) || (ray->orig.y > box_max.y))
			return GF_FALSE;
	}
	else {
		tNEAR = FIX_MIN;
		tFAR = FIX_MAX;
		t1 = gf_divfix(box_min.y - ray->orig.y, ray->dir.y);
		t2 = gf_divfix(box_max.y - ray->orig.y, ray->dir.y);
		if (t1 > t2) {
			temp = t1;
			t1 = t2;
			t2 = temp;
		}
		if (t1 > tNEAR) {
			tNEAR = t1;
			//xyorz = YPLANE;
			//sign = (ray->dir.y < 0) ? 1 : -1;
		}
		if (t2 < tFAR) tFAR = t2;
		if (tNEAR > tFAR) return GF_FALSE; // box missed
		if (tFAR < 0) return GF_FALSE; // box behind the ray
	}

	// Check the Z plane
	if (ray->dir.z == 0) {
		if ((ray->orig.z < box_min.z) || (ray->orig.z > box_max.z))
			return GF_FALSE;
	}
	else {
		tNEAR = FIX_MIN;
		tFAR = FIX_MAX;
		t1 = gf_divfix(box_min.z - ray->orig.z, ray->dir.z);
		t2 = gf_divfix(box_max.z - ray->orig.z, ray->dir.z);
		if (t1 > t2) {
			temp = t1;
			t1 = t2;
			t2 = temp;
		}
		if (t1 > tNEAR) {
			tNEAR = t1;
			//xyorz = ZPLANE;
			//sign = (ray->dir.z < 0) ? 1 : -1;
		}
		if (t2 < tFAR) tFAR = t2;
		if (tNEAR>tFAR) return GF_FALSE; // box missed
		if (tFAR < 0) return GF_FALSE;  // box behind the ray
	}
	if (outPoint) {
		*outPoint = gf_vec_scale(ray->dir, tNEAR);
		gf_vec_add(*outPoint, *outPoint, ray->orig);
	}
	return GF_TRUE;
}


GF_EXPORT
Bool gf_ray_hit_sphere(GF_Ray *ray, GF_Vec *center, Fixed radius, GF_Vec *outPoint)
{
	GF_Vec radv;
	Fixed dist, center_proj, center_proj_sq, hcord;
	if (center) {
		gf_vec_diff(radv, *center, ray->orig);
	}
	else {
		radv = ray->orig;
		gf_vec_rev(radv);
	}
	dist = gf_vec_len(radv);
	center_proj = gf_vec_dot(radv, ray->dir);
	if (radius + ABS(center_proj) < dist) return GF_FALSE;

	center_proj_sq = gf_mulfix(center_proj, center_proj);
	hcord = center_proj_sq - gf_mulfix(dist, dist) + gf_mulfix(radius, radius);
	if (hcord < 0) return GF_FALSE;
	if (center_proj_sq < hcord) return GF_FALSE;
	if (outPoint) {
		center_proj -= gf_sqrt(hcord);
		radv = gf_vec_scale(ray->dir, center_proj);
		gf_vec_add(*outPoint, ray->orig, radv);
	}
	return GF_TRUE;
}

/*
*		Tomas M�ller and Ben Trumbore.
*	 Fast, minimum storage ray-triangle intersection.
*		Journal of graphics tools, 2(1):21-28, 1997
*
*/
GF_EXPORT
Bool gf_ray_hit_triangle(GF_Ray *ray, GF_Vec *v0, GF_Vec *v1, GF_Vec *v2, Fixed *dist)
{
	Fixed u, v, det;
	GF_Vec edge1, edge2, tvec, pvec, qvec;
	/* find vectors for two edges sharing vert0 */
	gf_vec_diff(edge1, *v1, *v0);
	gf_vec_diff(edge2, *v2, *v0);
	/* begin calculating determinant - also used to calculate U parameter */
	pvec = gf_vec_cross(ray->dir, edge2);
	/* if determinant is near zero, ray lies in plane of triangle */
	det = gf_vec_dot(edge1, pvec);
	if (ABS(det) < FIX_EPSILON) return GF_FALSE;
	/* calculate distance from vert0 to ray origin */
	gf_vec_diff(tvec, ray->orig, *v0);
	/* calculate U parameter and test bounds */
	u = gf_divfix(gf_vec_dot(tvec, pvec), det);
	if ((u < 0) || (u > FIX_ONE)) return GF_FALSE;
	/* prepare to test V parameter */
	qvec = gf_vec_cross(tvec, edge1);
	/* calculate V parameter and test bounds */
	v = gf_divfix(gf_vec_dot(ray->dir, qvec), det);
	if ((v < 0) || (u + v > FIX_ONE)) return GF_FALSE;
#ifdef GPAC_FIXED_POINT
#define VSCALE	4096
	det /= VSCALE;
	qvec.x /= VSCALE;
	qvec.y /= VSCALE;
	qvec.z /= VSCALE;
#undef VSCALE
#endif
	/* calculate t, ray intersects triangle */
	*dist = gf_divfix(gf_vec_dot(edge2, qvec), det);
	return GF_TRUE;
}

GF_EXPORT
Bool gf_ray_hit_triangle_backcull(GF_Ray *ray, GF_Vec *v0, GF_Vec *v1, GF_Vec *v2, Fixed *dist)
{
	Fixed u, v, det;
	GF_Vec edge1, edge2, tvec, pvec, qvec;
	/* find vectors for two edges sharing vert0 */
	gf_vec_diff(edge1, *v1, *v0);
	gf_vec_diff(edge2, *v2, *v0);
	/* begin calculating determinant - also used to calculate U parameter */
	pvec = gf_vec_cross(ray->dir, edge2);
	/* if determinant is near zero, ray lies in plane of triangle */
	det = gf_vec_dot(edge1, pvec);
	if (det < FIX_EPSILON) return GF_FALSE;
	/* calculate distance from vert0 to ray origin */
	gf_vec_diff(tvec, ray->orig, *v0);
	/* calculate U parameter and test bounds */
	u = gf_vec_dot(tvec, pvec);
	if ((u < 0) || (u > det)) return GF_FALSE;
	/* prepare to test V parameter */
	qvec = gf_vec_cross(tvec, edge1);
	/* calculate V parameter and test bounds */
	v = gf_vec_dot(ray->dir, qvec);
	if ((v < 0) || (u + v > det)) return GF_FALSE;
	/* calculate t, scale parameters, ray intersects triangle */
	*dist = gf_divfix(gf_vec_dot(edge2, qvec), det);
	return GF_TRUE;
}

GF_EXPORT
GF_Vec gf_closest_point_to_line(GF_Vec line_pt, GF_Vec line_vec, GF_Vec pt)
{
	GF_Vec c;
	Fixed t;
	gf_vec_diff(c, pt, line_pt);
	t = gf_vec_dot(line_vec, c);
	c = gf_vec_scale(line_vec, t);
	gf_vec_add(c, c, line_pt);
	return c;
}


GF_EXPORT
GF_Vec4 gf_quat_from_matrix(GF_Matrix *mx)
{
	GF_Vec4 res;
	Fixed diagonal, s;
	diagonal = mx->m[0] + mx->m[5] + mx->m[10];

	if (diagonal > 0) {
		s = gf_sqrt(diagonal + FIX_ONE);
		res.q = s / 2;
		s = gf_invfix(2 * s);
		res.x = gf_mulfix(mx->m[6] - mx->m[9], s);
		res.y = gf_mulfix(mx->m[8] - mx->m[2], s);
		res.z = gf_mulfix(mx->m[1] - mx->m[4], s);
	}
	else {
		Fixed q[4];
		u32 i, j, k;
		static const u32 next[3] = { 1, 2, 0 };
		i = 0;
		if (mx->m[5] > mx->m[0]) {
			i = 1;
		}
		if (mx->m[10] > mx->m[4 * i + i]) {
			i = 2;
		}
		j = next[i];
		k = next[j];
		s = gf_sqrt(FIX_ONE + mx->m[4 * i + i] - (mx->m[4 * j + j] + mx->m[4 * k + k]));
		q[i] = s / 2;
		if (s != 0) {
			s = gf_invfix(2 * s);
		}
		q[3] = gf_mulfix(mx->m[4 * j + k] - mx->m[4 * k + j], s);
		q[j] = gf_mulfix(mx->m[4 * i + j] + mx->m[4 * j + i], s);
		q[k] = gf_mulfix(mx->m[4 * i + k] + mx->m[4 * k + i], s);
		res.x = q[0];
		res.y = q[1];
		res.z = q[2];
		res.q = q[3];
	}
	return res;
}

GF_EXPORT
GF_Vec4 gf_quat_to_rotation(GF_Vec4 *quat)
{
	GF_Vec4 r;
	Fixed val = gf_acos(quat->q);
	if (val == 0) {
		r.x = r.y = 0;
		r.z = FIX_ONE;
		r.q = 0;
	}
	else {
		GF_Vec axis;
		Fixed sin_val = gf_sin(val);
		axis.x = gf_divfix(quat->x, sin_val);
		axis.y = gf_divfix(quat->y, sin_val);
		axis.z = gf_divfix(quat->z, sin_val);
		gf_vec_norm(&axis);
		r.x = axis.x;
		r.y = axis.y;
		r.z = axis.z;
		r.q = 2 * val;
	}
	return r;
}

GF_EXPORT
GF_Vec4 gf_quat_from_rotation(GF_Vec4 rot)
{
	GF_Vec4 res;
	Fixed s;
	Fixed scale = gf_sqrt(gf_mulfix(rot.x, rot.x) + gf_mulfix(rot.y, rot.y) + gf_mulfix(rot.z, rot.z));

	/* no rotation - use (multiplication ???) identity quaternion */
	if (scale == 0) {
		res.q = FIX_ONE;
		res.x = 0;
		res.y = 0;
		res.z = 0;
	}
	else {
		s = gf_sin(rot.q / 2);
		res.q = gf_cos(rot.q / 2);
		res.x = gf_muldiv(s, rot.x, scale);
		res.y = gf_muldiv(s, rot.y, scale);
		res.z = gf_muldiv(s, rot.z, scale);
		gf_quat_norm(res);
	}
	return res;
}

GF_EXPORT
GF_Vec4 gf_quat_from_axis_cos(GF_Vec axis, Fixed cos_a)
{
	GF_Vec4 r;
	if (cos_a < -FIX_ONE) cos_a = -FIX_ONE;
	else if (cos_a > FIX_ONE) cos_a = FIX_ONE;
	r.x = axis.x;
	r.y = axis.y;
	r.z = axis.z;
	r.q = gf_acos(cos_a);
	return gf_quat_from_rotation(r);
}

static void gf_quat_conjugate(GF_Vec4 *quat)
{
	quat->x *= -1;
	quat->y *= -1;
	quat->z *= -1;
}

GF_EXPORT
GF_Vec4 gf_quat_get_inv(GF_Vec4 *quat)
{
	GF_Vec4 ret = *quat;
	gf_quat_conjugate(&ret);
	gf_quat_norm(ret);
	return ret;
}


GF_EXPORT
GF_Vec4 gf_quat_multiply(GF_Vec4 *q1, GF_Vec4 *q2)
{
	GF_Vec4 ret;
	ret.q = gf_mulfix(q1->q, q2->q) - gf_mulfix(q1->x, q2->x) - gf_mulfix(q1->y, q2->y) - gf_mulfix(q1->z, q2->z);
	ret.x = gf_mulfix(q1->q, q2->x) + gf_mulfix(q1->x, q2->q) + gf_mulfix(q1->y, q2->z) - gf_mulfix(q1->z, q2->y);
	ret.y = gf_mulfix(q1->q, q2->y) + gf_mulfix(q1->y, q2->q) - gf_mulfix(q1->x, q2->z) + gf_mulfix(q1->z, q2->x);
	ret.z = gf_mulfix(q1->q, q2->z) + gf_mulfix(q1->z, q2->q) + gf_mulfix(q1->x, q2->y) - gf_mulfix(q1->y, q2->x);
	return ret;
}

GF_EXPORT
GF_Vec gf_quat_rotate(GF_Vec4 *quat, GF_Vec *vec)
{
	GF_Vec ret;
	GF_Vec4 q_v, q_i, q_r1, q_r2;
	q_v.q = 0;
	q_v.x = vec->x;
	q_v.y = vec->y;
	q_v.z = vec->z;
	q_i = gf_quat_get_inv(quat);
	q_r1 = gf_quat_multiply(&q_v, &q_i);
	q_r2 = gf_quat_multiply(quat, &q_r1);
	ret.x = q_r2.x;
	ret.y = q_r2.y;
	ret.z = q_r2.z;
	return ret;
}

/*
* Code from www.gamasutra.com/features/19980703/quaternions_01.htm,
* Listing 5.
*
* SLERP(p, q, t) = [p sin((1 - t)a) + q sin(ta)] / sin(a)
*
* where a is the arc angle, quaternions pq = cos(q) and 0 <= t <= 1
*/
GF_EXPORT
GF_Vec4 gf_quat_slerp(GF_Vec4 q1, GF_Vec4 q2, Fixed frac)
{
	GF_Vec4 res;
	Fixed omega, cosom, sinom, scale0, scale1, q2_array[4];

	cosom = gf_mulfix(q1.x, q2.x) + gf_mulfix(q1.y, q2.y) + gf_mulfix(q1.z, q2.z) + gf_mulfix(q1.q, q2.q);
	if (cosom < 0) {
		cosom = -cosom;
		q2_array[0] = -q2.x;
		q2_array[1] = -q2.y;
		q2_array[2] = -q2.z;
		q2_array[3] = -q2.q;
	}
	else {
		q2_array[0] = q2.x;
		q2_array[1] = q2.y;
		q2_array[2] = q2.z;
		q2_array[3] = q2.q;
	}

	/* calculate coefficients */
	if ((FIX_ONE - cosom) > FIX_EPSILON) {
		omega = gf_acos(cosom);
		sinom = gf_sin(omega);
		scale0 = gf_divfix(gf_sin(gf_mulfix(FIX_ONE - frac, omega)), sinom);
		scale1 = gf_divfix(gf_sin(gf_mulfix(frac, omega)), sinom);
	}
	else {
		/* q1 & q2 are very close, so do linear interpolation */
		scale0 = FIX_ONE - frac;
		scale1 = frac;
	}
	res.x = gf_mulfix(scale0, q1.x) + gf_mulfix(scale1, q2_array[0]);
	res.y = gf_mulfix(scale0, q1.y) + gf_mulfix(scale1, q2_array[1]);
	res.z = gf_mulfix(scale0, q1.z) + gf_mulfix(scale1, q2_array[2]);
	res.q = gf_mulfix(scale0, q1.q) + gf_mulfix(scale1, q2_array[3]);
	return res;
}


/*update center & radius & is_set flag*/
GF_EXPORT
void gf_bbox_refresh(GF_BBox *b)
{
	GF_Vec v;
	gf_vec_add(v, b->min_edge, b->max_edge);
	b->center = gf_vec_scale(v, FIX_ONE / 2);
	gf_vec_diff(v, b->max_edge, b->min_edge);
	b->radius = gf_vec_len(v) / 2;
	b->is_set = GF_TRUE;
}

GF_EXPORT
void gf_bbox_from_rect(GF_BBox *box, GF_Rect *rc)
{
	box->min_edge.x = rc->x;
	box->min_edge.y = rc->y - rc->height;
	box->min_edge.z = 0;
	box->max_edge.x = rc->x + rc->width;
	box->max_edge.y = rc->y;
	box->max_edge.z = 0;
	gf_bbox_refresh(box);
}

GF_EXPORT
void gf_rect_from_bbox(GF_Rect *rc, GF_BBox *box)
{
	rc->x = box->min_edge.x;
	rc->y = box->max_edge.y;
	rc->width = box->max_edge.x - box->min_edge.x;
	rc->height = box->max_edge.y - box->min_edge.y;
}

GF_EXPORT
void gf_bbox_grow_point(GF_BBox *box, GF_Vec pt)
{
	if (pt.x > box->max_edge.x) box->max_edge.x = pt.x;
	if (pt.y > box->max_edge.y) box->max_edge.y = pt.y;
	if (pt.z > box->max_edge.z) box->max_edge.z = pt.z;
	if (pt.x < box->min_edge.x) box->min_edge.x = pt.x;
	if (pt.y < box->min_edge.y) box->min_edge.y = pt.y;
	if (pt.z < box->min_edge.z) box->min_edge.z = pt.z;
}

GF_EXPORT
void gf_bbox_union(GF_BBox *b1, GF_BBox *b2)
{
	if (b2->is_set) {
		if (!b1->is_set) {
			*b1 = *b2;
		}
		else {
			gf_bbox_grow_point(b1, b2->min_edge);
			gf_bbox_grow_point(b1, b2->max_edge);
			gf_bbox_refresh(b1);
		}
	}
}

GF_EXPORT
Bool gf_bbox_equal(GF_BBox *b1, GF_BBox *b2)
{
	return (gf_vec_equal(b1->min_edge, b2->min_edge) && gf_vec_equal(b1->max_edge, b2->max_edge));
}

GF_EXPORT
Bool gf_bbox_point_inside(GF_BBox *box, GF_Vec *p)
{
	return (p->x >= box->min_edge.x && p->x <= box->max_edge.x &&
		p->y >= box->min_edge.y && p->y <= box->max_edge.y &&
		p->z >= box->min_edge.z && p->z <= box->max_edge.z);
}

/*vertices are ordered to respect p vertex indexes (vertex from bbox closer to plane)
and so that n-vertex (vertex from bbox farther from plane) is 7-p_vx_idx*/
GF_EXPORT
void gf_bbox_get_vertices(GF_Vec bmin, GF_Vec bmax, GF_Vec *vecs)
{
	vecs[0].x = vecs[1].x = vecs[2].x = vecs[3].x = bmax.x;
	vecs[4].x = vecs[5].x = vecs[6].x = vecs[7].x = bmin.x;
	vecs[0].y = vecs[1].y = vecs[4].y = vecs[5].y = bmax.y;
	vecs[2].y = vecs[3].y = vecs[6].y = vecs[7].y = bmin.y;
	vecs[0].z = vecs[2].z = vecs[4].z = vecs[6].z = bmax.z;
	vecs[1].z = vecs[3].z = vecs[5].z = vecs[7].z = bmin.z;
}


GF_EXPORT
void gf_mx_apply_plane(GF_Matrix *mx, GF_Plane *plane)
{
	GF_Vec pt, end;
	/*get pt*/
	pt = gf_vec_scale(plane->normal, -plane->d);
	gf_vec_add(end, pt, plane->normal);
	gf_mx_apply_vec(mx, &pt);
	gf_mx_apply_vec(mx, &end);
	gf_vec_diff(plane->normal, end, pt);
	gf_vec_norm(&plane->normal);
	plane->d = -gf_vec_dot(pt, plane->normal);
}

GF_EXPORT
Fixed gf_plane_get_distance(GF_Plane *plane, GF_Vec *p)
{
	return gf_vec_dot(*p, plane->normal) + plane->d;
}


/*return p-vertex index (vertex from bbox closer to plane) - index range from 0 to 8*/
GF_EXPORT
u32 gf_plane_get_p_vertex_idx(GF_Plane *p)
{
	if (p->normal.x >= 0) {
		if (p->normal.y >= 0) return (p->normal.z >= 0) ? 0 : 1;
		return (p->normal.z >= 0) ? 2 : 3;
	}
	else {
		if (p->normal.y >= 0) return (p->normal.z >= 0) ? 4 : 5;
		return (p->normal.z >= 0) ? 6 : 7;
	}
}


GF_EXPORT
u32 gf_bbox_plane_relation(GF_BBox *box, GF_Plane *p)
{
	GF_Vec nearv, farv;
	nearv = box->max_edge;
	farv = box->min_edge;
	if (p->normal.x > 0) {
		nearv.x = box->min_edge.x;
		farv.x = box->max_edge.x;
	}
	if (p->normal.y > 0) {
		nearv.y = box->min_edge.y;
		farv.y = box->max_edge.y;
	}
	if (p->normal.z > 0) {
		nearv.z = box->min_edge.z;
		farv.z = box->max_edge.z;
	}
	if (gf_vec_dot(p->normal, nearv) + p->d > 0) return GF_BBOX_FRONT;
	if (gf_vec_dot(p->normal, farv) + p->d > 0) return GF_BBOX_INTER;
	return GF_BBOX_BACK;
}


GF_EXPORT
u32 gf_get_next_pow2(u32 s)
{
	u32 res = 1;
	while (s > res) {
		res <<= 1;
	}
	return res;
}