gtkradiant/tools/quake3/common/polylib.c

/*
   Copyright (C) 1999-2007 id Software, Inc. and contributors.
   For a list of contributors, see the accompanying CONTRIBUTORS file.

   This file is part of GtkRadiant.

   GtkRadiant 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.

   GtkRadiant 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 GtkRadiant; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */


#include "cmdlib.h"
#include "mathlib.h"
#include "inout.h"
#include "polylib.h"
#include "qfiles.h"


extern int numthreads;

// counters are only bumped when running single threaded,
// because they are an awefull coherence problem
int c_active_windings;
int c_peak_windings;
int c_winding_allocs;
int c_winding_points;

#define BOGUS_RANGE WORLD_SIZE

void pw( winding_t *w ){
	int i;
	for ( i = 0 ; i < w->numpoints ; i++ )
		Sys_Printf( "(%5.1f, %5.1f, %5.1f)\n",w->p[i][0], w->p[i][1],w->p[i][2] );
}


/*
   =============
   AllocWinding
   =============
 */
winding_t   *AllocWinding( int points ){
	winding_t   *w;
	int s;

	if ( points >= MAX_POINTS_ON_WINDING ) {
		Error( "AllocWinding failed: MAX_POINTS_ON_WINDING exceeded" );
	}

	if ( numthreads == 1 ) {
		c_winding_allocs++;
		c_winding_points += points;
		c_active_windings++;
		if ( c_active_windings > c_peak_windings ) {
			c_peak_windings = c_active_windings;
		}
	}
	s = sizeof( vec_t ) * 3 * points + sizeof( int );
	w = safe_malloc( s );
	memset( w, 0, s );
	return w;
}

/*
   =============
   AllocWindingAccu
   =============
 */
winding_accu_t *AllocWindingAccu( int points ){
	winding_accu_t  *w;
	int s;

	if ( points >= MAX_POINTS_ON_WINDING ) {
		Error( "AllocWindingAccu failed: MAX_POINTS_ON_WINDING exceeded" );
	}

	if ( numthreads == 1 ) {
		// At the time of this writing, these statistics were not used in any way.
		c_winding_allocs++;
		c_winding_points += points;
		c_active_windings++;
		if ( c_active_windings > c_peak_windings ) {
			c_peak_windings = c_active_windings;
		}
	}
	s = sizeof( vec_accu_t ) * 3 * points + sizeof( int );
	w = safe_malloc( s );
	memset( w, 0, s );
	return w;
}

/*
   =============
   FreeWinding
   =============
 */
void FreeWinding( winding_t *w ){
	if ( !w ) {
		Error( "FreeWinding: winding is NULL" );
	}

	if ( *(unsigned *)w == 0xdeaddead ) {
		Error( "FreeWinding: freed a freed winding" );
	}
	*(unsigned *)w = 0xdeaddead;

	if ( numthreads == 1 ) {
		c_active_windings--;
	}
	free( w );
}

/*
   =============
   FreeWindingAccu
   =============
 */
void FreeWindingAccu( winding_accu_t *w ){
	if ( !w ) {
		Error( "FreeWindingAccu: winding is NULL" );
	}

	if ( *( (unsigned *) w ) == 0xdeaddead ) {
		Error( "FreeWindingAccu: freed a freed winding" );
	}
	*( (unsigned *) w ) = 0xdeaddead;

	if ( numthreads == 1 ) {
		c_active_windings--;
	}
	free( w );
}

/*
   ============
   RemoveColinearPoints
   ============
 */
int c_removed;

void    RemoveColinearPoints( winding_t *w ){
	int i, j, k;
	vec3_t v1, v2;
	int nump;
	vec3_t p[MAX_POINTS_ON_WINDING];

	nump = 0;
	for ( i = 0 ; i < w->numpoints ; i++ )
	{
		j = ( i + 1 ) % w->numpoints;
		k = ( i + w->numpoints - 1 ) % w->numpoints;
		VectorSubtract( w->p[j], w->p[i], v1 );
		VectorSubtract( w->p[i], w->p[k], v2 );
		VectorNormalize( v1,v1 );
		VectorNormalize( v2,v2 );
		if ( DotProduct( v1, v2 ) < 0.999 ) {
			VectorCopy( w->p[i], p[nump] );
			nump++;
		}
	}

	if ( nump == w->numpoints ) {
		return;
	}

	if ( numthreads == 1 ) {
		c_removed += w->numpoints - nump;
	}
	w->numpoints = nump;
	memcpy( w->p, p, nump * sizeof( p[0] ) );
}

/*
   ============
   WindingPlane
   ============
 */
void WindingPlane( winding_t *w, vec3_t normal, vec_t *dist ){
	vec3_t v1, v2;

	VectorSubtract( w->p[1], w->p[0], v1 );
	VectorSubtract( w->p[2], w->p[0], v2 );
	CrossProduct( v2, v1, normal );
	VectorNormalize( normal, normal );
	*dist = DotProduct( w->p[0], normal );

}

/*
   =============
   WindingArea
   =============
 */
vec_t   WindingArea( winding_t *w ){
	int i;
	vec3_t d1, d2, cross;
	vec_t total;

	total = 0;
	for ( i = 2 ; i < w->numpoints ; i++ )
	{
		VectorSubtract( w->p[i - 1], w->p[0], d1 );
		VectorSubtract( w->p[i], w->p[0], d2 );
		CrossProduct( d1, d2, cross );
		total += 0.5 * VectorLength( cross );
	}
	return total;
}

void    WindingBounds( winding_t *w, vec3_t mins, vec3_t maxs ){
	vec_t v;
	int i,j;

	mins[0] = mins[1] = mins[2] = 99999;
	maxs[0] = maxs[1] = maxs[2] = -99999;

	for ( i = 0 ; i < w->numpoints ; i++ )
	{
		for ( j = 0 ; j < 3 ; j++ )
		{
			v = w->p[i][j];
			if ( v < mins[j] ) {
				mins[j] = v;
			}
			if ( v > maxs[j] ) {
				maxs[j] = v;
			}
		}
	}
}

/*
   =============
   WindingCenter
   =============
 */
void    WindingCenter( winding_t *w, vec3_t center ){
	int i;
	float scale;

	VectorCopy( vec3_origin, center );
	for ( i = 0 ; i < w->numpoints ; i++ )
		VectorAdd( w->p[i], center, center );

	scale = 1.0 / w->numpoints;
	VectorScale( center, scale, center );
}

/*
   =================
   BaseWindingForPlaneAccu
   =================
 */
winding_accu_t *BaseWindingForPlaneAccu( vec3_t normal, vec_t dist ){
	// The goal in this function is to replicate the behavior of the original BaseWindingForPlane()
	// function (see below) but at the same time increasing accuracy substantially.

	// The original code gave a preference for the vup vector to start out as (0, 0, 1), unless the
	// normal had a dominant Z value, in which case vup started out as (1, 0, 0).  After that, vup
	// was "bent" [along the plane defined by normal and vup] to become perpendicular to normal.
	// After that the vright vector was computed as the cross product of vup and normal.

	// I'm constructing the winding polygon points in a fashion similar to the method used in the
	// original function.  Orientation is the same.  The size of the winding polygon, however, is
	// variable in this function (depending on the angle of normal), and is larger (by about a factor
	// of 2) than the winding polygon in the original function.

	int x, i;
	vec_t max, v;
	vec3_accu_t vright, vup, org, normalAccu;
	winding_accu_t  *w;

	// One of the components of normal must have a magnitiude greater than this value,
	// otherwise normal is not a unit vector.  This is a little bit of inexpensive
	// partial error checking we can do.
	max = 0.56; // 1 / sqrt(1^2 + 1^2 + 1^2) = 0.577350269

	x = -1;
	for ( i = 0; i < 3; i++ ) {
		v = (vec_t) fabs( normal[i] );
		if ( v > max ) {
			x = i;
			max = v;
		}
	}
	if ( x == -1 ) {
		Error( "BaseWindingForPlaneAccu: no dominant axis found because normal is too short" );
	}

	switch ( x ) {
	case 0:     // Fall through to next case.
	case 1:
		vright[0] = (vec_accu_t) -normal[1];
		vright[1] = (vec_accu_t) normal[0];
		vright[2] = 0;
		break;
	case 2:
		vright[0] = 0;
		vright[1] = (vec_accu_t) -normal[2];
		vright[2] = (vec_accu_t) normal[1];
		break;
	}

	// vright and normal are now perpendicular; you can prove this by taking their
	// dot product and seeing that it's always exactly 0 (with no error).

	// NOTE: vright is NOT a unit vector at this point.  vright will have length
	// not exceeding 1.0.  The minimum length that vright can achieve happens when,
	// for example, the Z and X components of the normal input vector are equal,
	// and when normal's Y component is zero.  In that case Z and X of the normal
	// vector are both approximately 0.70711.  The resulting vright vector in this
	// case will have a length of 0.70711.

	// We're relying on the fact that MAX_WORLD_COORD is a power of 2 to keep
	// our calculation precise and relatively free of floating point error.
	// [However, the code will still work fine if that's not the case.]
	VectorScaleAccu( vright, ( (vec_accu_t) MAX_WORLD_COORD ) * 4.0, vright );

	// At time time of this writing, MAX_WORLD_COORD was 65536 (2^16).  Therefore
	// the length of vright at this point is at least 185364.  In comparison, a
	// corner of the world at location (65536, 65536, 65536) is distance 113512
	// away from the origin.

	VectorCopyRegularToAccu( normal, normalAccu );
	CrossProductAccu( normalAccu, vright, vup );

	// vup now has length equal to that of vright.

	VectorScaleAccu( normalAccu, (vec_accu_t) dist, org );

	// org is now a point on the plane defined by normal and dist.  Furthermore,
	// org, vright, and vup are pairwise perpendicular.  Now, the 4 vectors
	// { (+-)vright + (+-)vup } have length that is at least sqrt(185364^2 + 185364^2),
	// which is about 262144.  That length lies outside the world, since the furthest
	// point in the world has distance 113512 from the origin as mentioned above.
	// Also, these 4 vectors are perpendicular to the org vector.  So adding them
	// to org will only increase their length.  Therefore the 4 points defined below
	// all lie outside of the world.  Furthermore, it can be easily seen that the
	// edges connecting these 4 points (in the winding_accu_t below) lie completely
	// outside the world.  sqrt(262144^2 + 262144^2)/2 = 185363, which is greater than
	// 113512.

	w = AllocWindingAccu( 4 );

	VectorSubtractAccu( org, vright, w->p[0] );
	VectorAddAccu( w->p[0], vup, w->p[0] );

	VectorAddAccu( org, vright, w->p[1] );
	VectorAddAccu( w->p[1], vup, w->p[1] );

	VectorAddAccu( org, vright, w->p[2] );
	VectorSubtractAccu( w->p[2], vup, w->p[2] );

	VectorSubtractAccu( org, vright, w->p[3] );
	VectorSubtractAccu( w->p[3], vup, w->p[3] );

	w->numpoints = 4;

	return w;
}

/*
   =================
   BaseWindingForPlane

   Original BaseWindingForPlane() function that has serious accuracy problems.  Here is why.
   The base winding is computed as a rectangle with very large coordinates.  These coordinates
   are in the range 2^17 or 2^18.  "Epsilon" (meaning the distance between two adjacent numbers)
   at these magnitudes in 32 bit floating point world is about 0.02.  So for example, if things
   go badly (by bad luck), then the whole plane could be shifted by 0.02 units (its distance could
   be off by that much).  Then if we were to compute the winding of this plane and another of
   the brush's planes met this winding at a very acute angle, that error could multiply to around
   0.1 or more when computing the final vertex coordinates of the winding.  0.1 is a very large
   error, and can lead to all sorts of disappearing triangle problems.
   =================
 */
winding_t *BaseWindingForPlane( vec3_t normal, vec_t dist ){
	int i, x;
	vec_t max, v;
	vec3_t org, vright, vup;
	winding_t   *w;

// find the major axis

	max = -BOGUS_RANGE;
	x = -1;
	for ( i = 0 ; i < 3; i++ )
	{
		v = fabs( normal[i] );
		if ( v > max ) {
			x = i;
			max = v;
		}
	}
	if ( x == -1 ) {
		Error( "BaseWindingForPlane: no axis found" );
	}

	VectorCopy( vec3_origin, vup );
	switch ( x )
	{
	case 0:
	case 1:
		vup[2] = 1;
		break;
	case 2:
		vup[0] = 1;
		break;
	}

	v = DotProduct( vup, normal );
	VectorMA( vup, -v, normal, vup );
	VectorNormalize( vup, vup );

	VectorScale( normal, dist, org );

	CrossProduct( vup, normal, vright );

	// LordHavoc: this has to use *2 because otherwise some created points may
	// be inside the world (think of a diagonal case), and any brush with such
	// points should be removed, failure to detect such cases is disasterous
	VectorScale( vup, MAX_WORLD_COORD * 2, vup );
	VectorScale( vright, MAX_WORLD_COORD * 2, vright );

	// project a really big	axis aligned box onto the plane
	w = AllocWinding( 4 );

	VectorSubtract( org, vright, w->p[0] );
	VectorAdd( w->p[0], vup, w->p[0] );

	VectorAdd( org, vright, w->p[1] );
	VectorAdd( w->p[1], vup, w->p[1] );

	VectorAdd( org, vright, w->p[2] );
	VectorSubtract( w->p[2], vup, w->p[2] );

	VectorSubtract( org, vright, w->p[3] );
	VectorSubtract( w->p[3], vup, w->p[3] );

	w->numpoints = 4;

	return w;
}

/*
   ==================
   CopyWinding
   ==================
 */
winding_t   *CopyWinding( winding_t *w ){
	int size;
	winding_t   *c;

	if ( !w ) {
		Error( "CopyWinding: winding is NULL" );
	}

	c = AllocWinding( w->numpoints );
	size = (int)( (size_t)( (winding_t *)0 )->p[w->numpoints] );
	memcpy( c, w, size );
	return c;
}

/*
   ==================
   CopyWindingAccuIncreaseSizeAndFreeOld
   ==================
 */
winding_accu_t *CopyWindingAccuIncreaseSizeAndFreeOld( winding_accu_t *w ){
	int i;
	winding_accu_t  *c;

	if ( !w ) {
		Error( "CopyWindingAccuIncreaseSizeAndFreeOld: winding is NULL" );
	}

	c = AllocWindingAccu( w->numpoints + 1 );
	c->numpoints = w->numpoints;
	for ( i = 0; i < c->numpoints; i++ )
	{
		VectorCopyAccu( w->p[i], c->p[i] );
	}
	FreeWindingAccu( w );
	return c;
}

/*
   ==================
   CopyWindingAccuToRegular
   ==================
 */
winding_t   *CopyWindingAccuToRegular( winding_accu_t *w ){
	int i;
	winding_t   *c;

	if ( !w ) {
		Error( "CopyWindingAccuToRegular: winding is NULL" );
	}

	c = AllocWinding( w->numpoints );
	c->numpoints = w->numpoints;
	for ( i = 0; i < c->numpoints; i++ )
	{
		VectorCopyAccuToRegular( w->p[i], c->p[i] );
	}
	return c;
}

/*
   ==================
   ReverseWinding
   ==================
 */
winding_t   *ReverseWinding( winding_t *w ){
	int i;
	winding_t   *c;

	c = AllocWinding( w->numpoints );
	for ( i = 0 ; i < w->numpoints ; i++ )
	{
		VectorCopy( w->p[w->numpoints - 1 - i], c->p[i] );
	}
	c->numpoints = w->numpoints;
	return c;
}


/*
   =============
   ClipWindingEpsilon
   =============
 */
void    ClipWindingEpsilon( winding_t *in, vec3_t normal, vec_t dist,
							vec_t epsilon, winding_t **front, winding_t **back ){
	vec_t dists[MAX_POINTS_ON_WINDING + 4];
	int sides[MAX_POINTS_ON_WINDING + 4];
	int counts[3];
	static vec_t dot;           // VC 4.2 optimizer bug if not static
	int i, j;
	vec_t   *p1, *p2;
	vec3_t mid;
	winding_t   *f, *b;
	int maxpts;

	counts[0] = counts[1] = counts[2] = 0;

// determine sides for each point
	for ( i = 0 ; i < in->numpoints ; i++ )
	{

		dot = DotProduct( in->p[i], normal );
		dot -= dist;
		dists[i] = dot;
		if ( dot > epsilon ) {
			sides[i] = SIDE_FRONT;
		}
		else if ( dot < -epsilon ) {
			sides[i] = SIDE_BACK;
		}
		else
		{
			sides[i] = SIDE_ON;
		}
		counts[sides[i]]++;
	}
	sides[i] = sides[0];
	dists[i] = dists[0];

	*front = *back = NULL;

	if ( !counts[0] ) {
		*back = CopyWinding( in );
		return;
	}
	if ( !counts[1] ) {
		*front = CopyWinding( in );
		return;
	}

	maxpts = in->numpoints + 4;   // cant use counts[0]+2 because
	                              // of fp grouping errors

	*front = f = AllocWinding( maxpts );
	*back = b = AllocWinding( maxpts );

	for ( i = 0 ; i < in->numpoints ; i++ )
	{
		p1 = in->p[i];

		if ( sides[i] == SIDE_ON ) {
			VectorCopy( p1, f->p[f->numpoints] );
			f->numpoints++;
			VectorCopy( p1, b->p[b->numpoints] );
			b->numpoints++;
			continue;
		}

		if ( sides[i] == SIDE_FRONT ) {
			VectorCopy( p1, f->p[f->numpoints] );
			f->numpoints++;
		}
		if ( sides[i] == SIDE_BACK ) {
			VectorCopy( p1, b->p[b->numpoints] );
			b->numpoints++;
		}

		if ( sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i] ) {
			continue;
		}

		// generate a split point
		p2 = in->p[( i + 1 ) % in->numpoints];

		dot = dists[i] / ( dists[i] - dists[i + 1] );
		for ( j = 0 ; j < 3 ; j++ )
		{   // avoid round off error when possible
			if ( normal[j] == 1 ) {
				mid[j] = dist;
			}
			else if ( normal[j] == -1 ) {
				mid[j] = -dist;
			}
			else{
				mid[j] = p1[j] + dot * ( p2[j] - p1[j] );
			}
		}

		VectorCopy( mid, f->p[f->numpoints] );
		f->numpoints++;
		VectorCopy( mid, b->p[b->numpoints] );
		b->numpoints++;
	}

	if ( f->numpoints > maxpts || b->numpoints > maxpts ) {
		Error( "ClipWinding: points exceeded estimate" );
	}
	if ( f->numpoints > MAX_POINTS_ON_WINDING || b->numpoints > MAX_POINTS_ON_WINDING ) {
		Error( "ClipWinding: MAX_POINTS_ON_WINDING" );
	}
}


/*
   =============
   ChopWindingInPlaceAccu
   =============
 */
void ChopWindingInPlaceAccu( winding_accu_t **inout, vec3_t normal, vec_t dist, vec_t crudeEpsilon ){
	vec_accu_t fineEpsilon;
	winding_accu_t  *in;
	int counts[3];
	int i, j;
	vec_accu_t dists[MAX_POINTS_ON_WINDING + 1];
	int sides[MAX_POINTS_ON_WINDING + 1];
	int maxpts;
	winding_accu_t  *f;
	vec_accu_t  *p1, *p2;
	vec_accu_t w;
	vec3_accu_t mid, normalAccu;

	// We require at least a very small epsilon.  It's a good idea for several reasons.
	// First, we will be dividing by a potentially very small distance below.  We don't
	// want that distance to be too small; otherwise, things "blow up" with little accuracy
	// due to the division.  (After a second look, the value w below is in range (0,1), but
	// graininess problem remains.)  Second, Having minimum epsilon also prevents the following
	// situation.  Say for example we have a perfect octagon defined by the input winding.
	// Say our chopping plane (defined by normal and dist) is essentially the same plane
	// that the octagon is sitting on.  Well, due to rounding errors, it may be that point
	// 1 of the octagon might be in front, point 2 might be in back, point 3 might be in
	// front, point 4 might be in back, and so on.  So we could end up with a very ugly-
	// looking chopped winding, and this might be undesirable, and would at least lead to
	// a possible exhaustion of MAX_POINTS_ON_WINDING.  It's better to assume that points
	// very very close to the plane are on the plane, using an infinitesimal epsilon amount.

	// Now, the original ChopWindingInPlace() function used a vec_t-based winding_t.
	// So this minimum epsilon is quite similar to casting the higher resolution numbers to
	// the lower resolution and comparing them in the lower resolution mode.  We explicitly
	// choose the minimum epsilon as something around the vec_t epsilon of one because we
	// want the resolution of vec_accu_t to have a large resolution around the epsilon.
	// Some of that leftover resolution even goes away after we scale to points far away.

	// Here is a further discussion regarding the choice of smallestEpsilonAllowed.
	// In the 32 float world (we can assume vec_t is that), the "epsilon around 1.0" is
	// 0.00000011921.  In the 64 bit float world (we can assume vec_accu_t is that), the
	// "epsilon around 1.0" is 0.00000000000000022204.  (By the way these two epsilons
	// are defined as VEC_SMALLEST_EPSILON_AROUND_ONE VEC_ACCU_SMALLEST_EPSILON_AROUND_ONE
	// respectively.)  If you divide the first by the second, you get approximately
	// 536,885,246.  Dividing that number by 200,000 (a typical base winding coordinate)
	// gives 2684.  So in other words, if our smallestEpsilonAllowed was chosen as exactly
	// VEC_SMALLEST_EPSILON_AROUND_ONE, you would be guaranteed at least 2000 "ticks" in
	// 64-bit land inside of the epsilon for all numbers we're dealing with.

	static const vec_accu_t smallestEpsilonAllowed = ( (vec_accu_t) VEC_SMALLEST_EPSILON_AROUND_ONE ) * 0.5;
	if ( crudeEpsilon < smallestEpsilonAllowed ) {
		fineEpsilon = smallestEpsilonAllowed;
	}
	else{fineEpsilon = (vec_accu_t) crudeEpsilon; }

	in = *inout;
	counts[0] = counts[1] = counts[2] = 0;
	VectorCopyRegularToAccu( normal, normalAccu );

	for ( i = 0; i < in->numpoints; i++ )
	{
		dists[i] = DotProductAccu( in->p[i], normalAccu ) - dist;
		if ( dists[i] > fineEpsilon ) {
			sides[i] = SIDE_FRONT;
		}
		else if ( dists[i] < -fineEpsilon ) {
			sides[i] = SIDE_BACK;
		}
		else{sides[i] = SIDE_ON; }
		counts[sides[i]]++;
	}
	sides[i] = sides[0];
	dists[i] = dists[0];

	// I'm wondering if whatever code that handles duplicate planes is robust enough
	// that we never get a case where two nearly equal planes result in 2 NULL windings
	// due to the 'if' statement below.  TODO: Investigate this.
	if ( !counts[SIDE_FRONT] ) {
		FreeWindingAccu( in );
		*inout = NULL;
		return;
	}
	if ( !counts[SIDE_BACK] ) {
		return; // Winding is unmodified.
	}

	// NOTE: The least number of points that a winding can have at this point is 2.
	// In that case, one point is SIDE_FRONT and the other is SIDE_BACK.

	maxpts = counts[SIDE_FRONT] + 2; // We dynamically expand if this is too small.
	f = AllocWindingAccu( maxpts );

	for ( i = 0; i < in->numpoints; i++ )
	{
		p1 = in->p[i];

		if ( sides[i] == SIDE_ON || sides[i] == SIDE_FRONT ) {
			if ( f->numpoints >= MAX_POINTS_ON_WINDING ) {
				Error( "ChopWindingInPlaceAccu: MAX_POINTS_ON_WINDING" );
			}
			if ( f->numpoints >= maxpts ) { // This will probably never happen.
				Sys_FPrintf( SYS_VRB, "WARNING: estimate on chopped winding size incorrect (no problem)\n" );
				f = CopyWindingAccuIncreaseSizeAndFreeOld( f );
				maxpts++;
			}
			VectorCopyAccu( p1, f->p[f->numpoints] );
			f->numpoints++;
			if ( sides[i] == SIDE_ON ) {
				continue;
			}
		}
		if ( sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i] ) {
			continue;
		}

		// Generate a split point.
		p2 = in->p[( ( i + 1 ) == in->numpoints ) ? 0 : ( i + 1 )];

		// The divisor's absolute value is greater than the dividend's absolute value.
		// w is in the range (0,1).
		w = dists[i] / ( dists[i] - dists[i + 1] );

		for ( j = 0; j < 3; j++ )
		{
			// Avoid round-off error when possible.  Check axis-aligned normal.
			if ( normal[j] == 1 ) {
				mid[j] = dist;
			}
			else if ( normal[j] == -1 ) {
				mid[j] = -dist;
			}
			else{mid[j] = p1[j] + ( w * ( p2[j] - p1[j] ) ); }
		}
		if ( f->numpoints >= MAX_POINTS_ON_WINDING ) {
			Error( "ChopWindingInPlaceAccu: MAX_POINTS_ON_WINDING" );
		}
		if ( f->numpoints >= maxpts ) { // This will probably never happen.
			Sys_FPrintf( SYS_VRB, "WARNING: estimate on chopped winding size incorrect (no problem)\n" );
			f = CopyWindingAccuIncreaseSizeAndFreeOld( f );
			maxpts++;
		}
		VectorCopyAccu( mid, f->p[f->numpoints] );
		f->numpoints++;
	}

	FreeWindingAccu( in );
	*inout = f;
}

/*
   =============
   ChopWindingInPlace
   =============
 */
void ChopWindingInPlace( winding_t **inout, vec3_t normal, vec_t dist, vec_t epsilon ){
	winding_t   *in;
	vec_t dists[MAX_POINTS_ON_WINDING + 4];
	int sides[MAX_POINTS_ON_WINDING + 4];
	int counts[3];
	static vec_t dot;           // VC 4.2 optimizer bug if not static
	int i, j;
	vec_t   *p1, *p2;
	vec3_t mid;
	winding_t   *f;
	int maxpts;

	in = *inout;
	counts[0] = counts[1] = counts[2] = 0;

// determine sides for each point
	for ( i = 0 ; i < in->numpoints ; i++ )
	{
		dot = DotProduct( in->p[i], normal );
		dot -= dist;
		dists[i] = dot;
		if ( dot > epsilon ) {
			sides[i] = SIDE_FRONT;
		}
		else if ( dot < -epsilon ) {
			sides[i] = SIDE_BACK;
		}
		else
		{
			sides[i] = SIDE_ON;
		}
		counts[sides[i]]++;
	}
	sides[i] = sides[0];
	dists[i] = dists[0];

	if ( !counts[0] ) {
		FreeWinding( in );
		*inout = NULL;
		return;
	}
	if ( !counts[1] ) {
		return;     // inout stays the same

	}
	maxpts = in->numpoints + 4;   // cant use counts[0]+2 because
	                              // of fp grouping errors

	f = AllocWinding( maxpts );

	for ( i = 0 ; i < in->numpoints ; i++ )
	{
		p1 = in->p[i];

		if ( sides[i] == SIDE_ON ) {
			VectorCopy( p1, f->p[f->numpoints] );
			f->numpoints++;
			continue;
		}

		if ( sides[i] == SIDE_FRONT ) {
			VectorCopy( p1, f->p[f->numpoints] );
			f->numpoints++;
		}

		if ( sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i] ) {
			continue;
		}

		// generate a split point
		p2 = in->p[( i + 1 ) % in->numpoints];

		dot = dists[i] / ( dists[i] - dists[i + 1] );
		for ( j = 0 ; j < 3 ; j++ )
		{   // avoid round off error when possible
			if ( normal[j] == 1 ) {
				mid[j] = dist;
			}
			else if ( normal[j] == -1 ) {
				mid[j] = -dist;
			}
			else{
				mid[j] = p1[j] + dot * ( p2[j] - p1[j] );
			}
		}

		VectorCopy( mid, f->p[f->numpoints] );
		f->numpoints++;
	}

	if ( f->numpoints > maxpts ) {
		Error( "ClipWinding: points exceeded estimate" );
	}
	if ( f->numpoints > MAX_POINTS_ON_WINDING ) {
		Error( "ClipWinding: MAX_POINTS_ON_WINDING" );
	}

	FreeWinding( in );
	*inout = f;
}


/*
   =================
   ChopWinding

   Returns the fragment of in that is on the front side
   of the cliping plane.  The original is freed.
   =================
 */
winding_t   *ChopWinding( winding_t *in, vec3_t normal, vec_t dist ){
	winding_t   *f, *b;

	ClipWindingEpsilon( in, normal, dist, ON_EPSILON, &f, &b );
	FreeWinding( in );
	if ( b ) {
		FreeWinding( b );
	}
	return f;
}


/*
   =================
   CheckWinding

   =================
 */
void CheckWinding( winding_t *w ){
	int i, j;
	vec_t   *p1, *p2;
	vec_t d, edgedist;
	vec3_t dir, edgenormal, facenormal;
	vec_t area;
	vec_t facedist;

	if ( w->numpoints < 3 ) {
		Error( "CheckWinding: %i points",w->numpoints );
	}

	area = WindingArea( w );
	if ( area < 1 ) {
		Error( "CheckWinding: %f area", area );
	}

	WindingPlane( w, facenormal, &facedist );

	for ( i = 0 ; i < w->numpoints ; i++ )
	{
		p1 = w->p[i];

		for ( j = 0 ; j < 3 ; j++ )
			if ( p1[j] > MAX_WORLD_COORD || p1[j] < MIN_WORLD_COORD ) {
				Error( "CheckFace: MAX_WORLD_COORD exceeded: %f",p1[j] );
			}

		j = i + 1 == w->numpoints ? 0 : i + 1;

		// check the point is on the face plane
		d = DotProduct( p1, facenormal ) - facedist;
		if ( d < -ON_EPSILON || d > ON_EPSILON ) {
			Error( "CheckWinding: point off plane" );
		}

		// check the edge isnt degenerate
		p2 = w->p[j];
		VectorSubtract( p2, p1, dir );

		if ( VectorLength( dir ) < ON_EPSILON ) {
			Error( "CheckWinding: degenerate edge" );
		}

		CrossProduct( facenormal, dir, edgenormal );
		VectorNormalize( edgenormal, edgenormal );
		edgedist = DotProduct( p1, edgenormal );
		edgedist += ON_EPSILON;

		// all other points must be on front side
		for ( j = 0 ; j < w->numpoints ; j++ )
		{
			if ( j == i ) {
				continue;
			}
			d = DotProduct( w->p[j], edgenormal );
			if ( d > edgedist ) {
				Error( "CheckWinding: non-convex" );
			}
		}
	}
}


/*
   ============
   WindingOnPlaneSide
   ============
 */
int     WindingOnPlaneSide( winding_t *w, vec3_t normal, vec_t dist ){
	qboolean front, back;
	int i;
	vec_t d;

	front = qfalse;
	back = qfalse;
	for ( i = 0 ; i < w->numpoints ; i++ )
	{
		d = DotProduct( w->p[i], normal ) - dist;
		if ( d < -ON_EPSILON ) {
			if ( front ) {
				return SIDE_CROSS;
			}
			back = qtrue;
			continue;
		}
		if ( d > ON_EPSILON ) {
			if ( back ) {
				return SIDE_CROSS;
			}
			front = qtrue;
			continue;
		}
	}

	if ( back ) {
		return SIDE_BACK;
	}
	if ( front ) {
		return SIDE_FRONT;
	}
	return SIDE_ON;
}


/*
   =================
   AddWindingToConvexHull

   Both w and *hull are on the same plane
   =================
 */
#define MAX_HULL_POINTS     128
void    AddWindingToConvexHull( winding_t *w, winding_t **hull, vec3_t normal ) {
	int i, j, k;
	float       *p, *copy;
	vec3_t dir;
	float d;
	int numHullPoints, numNew;
	vec3_t hullPoints[MAX_HULL_POINTS];
	vec3_t newHullPoints[MAX_HULL_POINTS];
	vec3_t hullDirs[MAX_HULL_POINTS];
	qboolean hullSide[MAX_HULL_POINTS];
	qboolean outside;

	if ( !*hull ) {
		*hull = CopyWinding( w );
		return;
	}

	numHullPoints = ( *hull )->numpoints;
	memcpy( hullPoints, ( *hull )->p, numHullPoints * sizeof( vec3_t ) );

	for ( i = 0 ; i < w->numpoints ; i++ ) {
		p = w->p[i];

		// calculate hull side vectors
		for ( j = 0 ; j < numHullPoints ; j++ ) {
			k = ( j + 1 ) % numHullPoints;

			VectorSubtract( hullPoints[k], hullPoints[j], dir );
			VectorNormalize( dir, dir );
			CrossProduct( normal, dir, hullDirs[j] );
		}

		outside = qfalse;
		for ( j = 0 ; j < numHullPoints ; j++ ) {
			VectorSubtract( p, hullPoints[j], dir );
			d = DotProduct( dir, hullDirs[j] );
			if ( d >= ON_EPSILON ) {
				outside = qtrue;
			}
			if ( d >= -ON_EPSILON ) {
				hullSide[j] = qtrue;
			}
			else {
				hullSide[j] = qfalse;
			}
		}

		// if the point is effectively inside, do nothing
		if ( !outside ) {
			continue;
		}

		// find the back side to front side transition
		for ( j = 0 ; j < numHullPoints ; j++ ) {
			if ( !hullSide[ j % numHullPoints ] && hullSide[ ( j + 1 ) % numHullPoints ] ) {
				break;
			}
		}
		if ( j == numHullPoints ) {
			continue;
		}

		// insert the point here
		VectorCopy( p, newHullPoints[0] );
		numNew = 1;

		// copy over all points that aren't double fronts
		j = ( j + 1 ) % numHullPoints;
		for ( k = 0 ; k < numHullPoints ; k++ ) {
			if ( hullSide[ ( j + k ) % numHullPoints ] && hullSide[ ( j + k + 1 ) % numHullPoints ] ) {
				continue;
			}
			copy = hullPoints[ ( j + k + 1 ) % numHullPoints ];
			VectorCopy( copy, newHullPoints[numNew] );
			numNew++;
		}

		numHullPoints = numNew;
		memcpy( hullPoints, newHullPoints, numHullPoints * sizeof( vec3_t ) );
	}

	FreeWinding( *hull );
	w = AllocWinding( numHullPoints );
	w->numpoints = numHullPoints;
	*hull = w;
	memcpy( w->p, hullPoints, numHullPoints * sizeof( vec3_t ) );
}