]> de.git.xonotic.org Git - xonotic/netradiant.git/blobdiff - radiant/winding.cpp
reformat code! now the code is only ugly on the *inside*
[xonotic/netradiant.git] / radiant / winding.cpp
index 608451102c1eab8827889f7f3ff2395ffe764fab..d027f52dba2ab4a41ec968a655c4b27e39221a36 100644 (file)
@@ -1,5 +1,5 @@
 /*
-   Copyright (C) 1999-2007 id Software, Inc. and contributors.
+   Copyright (C) 1999-2006 Id Software, Inc. and contributors.
    For a list of contributors, see the accompanying CONTRIBUTORS file.
 
    This file is part of GtkRadiant.
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-
-
-#include "stdafx.h"
-#include <assert.h>
 #include "winding.h"
 
-#define BOGUS_RANGE ( g_MaxWorldCoord + 1 )
+#include <algorithm>
 
-/*
-   =============
-   Plane_Equal
-   =============
- */
-#define NORMAL_EPSILON  0.0001
-#define DIST_EPSILON    0.02
-
-int Plane_Equal( plane_t *a, plane_t *b, int flip ){
-       vec3_t normal;
-       float dist;
-
-       if ( flip ) {
-               normal[0] = -b->normal[0];
-               normal[1] = -b->normal[1];
-               normal[2] = -b->normal[2];
-               dist = -b->dist;
-       }
-       else {
-               normal[0] = b->normal[0];
-               normal[1] = b->normal[1];
-               normal[2] = b->normal[2];
-               dist = b->dist;
-       }
-       if (
-               fabs( a->normal[0] - normal[0] ) < NORMAL_EPSILON
-               && fabs( a->normal[1] - normal[1] ) < NORMAL_EPSILON
-               && fabs( a->normal[2] - normal[2] ) < NORMAL_EPSILON
-               && fabs( a->dist - dist ) < DIST_EPSILON ) {
-               return true;
-       }
-       return false;
-}
+#include "math/line.h"
 
-/*
-   ============
-   Plane_FromPoints
-   ============
- */
-int Plane_FromPoints( vec3_t p1, vec3_t p2, vec3_t p3, plane_t *plane ){
-       vec3_t v1, v2;
-
-       VectorSubtract( p2, p1, v1 );
-       VectorSubtract( p3, p1, v2 );
-       //CrossProduct(v2, v1, plane->normal);
-       CrossProduct( v1, v2, plane->normal );
-       if ( VectorNormalize( plane->normal, plane->normal ) < 0.1 ) {
-               return false;
-       }
-       plane->dist = DotProduct( p1, plane->normal );
-       return true;
-}
 
-/*
-   =================
-   Point_Equal
-   =================
- */
-int Point_Equal( vec3_t p1, vec3_t p2, float epsilon ){
-       int i;
-
-       for ( i = 0; i < 3; i++ )
-       {
-               if ( fabs( p1[i] - p2[i] ) > epsilon ) {
-                       return false;
-               }
-       }
-       return true;
+inline double plane3_distance_to_point(const Plane3 &plane, const DoubleVector3 &point)
+{
+    return vector3_dot(point, plane.normal()) - plane.dist();
 }
 
-
-/*
-   =================
-   Winding_BaseForPlane
-   =================
- */
-//#define DBG_WNDG
-winding_t *Winding_BaseForPlane( plane_t *p ){
-       int i, x;
-       vec_t max, v;
-       vec3_t org, vright, vup;
-       winding_t   *w;
-
-       // find the major axis
-#ifdef DBG_WNDG
-       Sys_Printf( "Winding_BaseForPlane %p\n",p );
-#endif
-
-       max = -BOGUS_RANGE;
-       x = -1;
-       for ( i = 0 ; i < 3; i++ )
-       {
-               v = fabs( p->normal[i] );
-               if ( v > max ) {
-                       x = i;
-                       max = v;
-               }
-       }
-       if ( x == -1 ) {
-               Error( "Winding_BaseForPlane: 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, p->normal );
-       VectorMA( vup, -v, p->normal, vup );
-       VectorNormalize( vup, vup );
-
-       VectorScale( p->normal, p->dist, org );
-
-       CrossProduct( vup, p->normal, vright );
-
-       VectorScale( vup, BOGUS_RANGE, vup );
-       VectorScale( vright, BOGUS_RANGE, vright );
-
-       // project a really big axis aligned box onto the plane
-       w = Winding_Alloc( 4 );
-
-       VectorSubtract( org, vright, w->points[0] );
-       VectorAdd( w->points[0], vup, w->points[0] );
-
-       VectorAdd( org, vright, w->points[1] );
-       VectorAdd( w->points[1], vup, w->points[1] );
-
-       VectorAdd( org, vright, w->points[2] );
-       VectorSubtract( w->points[2], vup, w->points[2] );
-
-       VectorSubtract( org, vright, w->points[3] );
-       VectorSubtract( w->points[3], vup, w->points[3] );
-
-       w->numpoints = 4;
-
-       return w;
+inline double plane3_distance_to_point(const Plane3 &plane, const Vector3 &point)
+{
+    return vector3_dot(point, plane.normal()) - plane.dist();
 }
 
-// macro to compute winding size
-#define WINDING_SIZE( pt ) ( sizeof( int )*2 + sizeof( float )*5*( pt ) )
-
-/*
-   ==================
-   Winding_Alloc
-   ==================
- */
-winding_t *Winding_Alloc( int points ){
-       winding_t   *w;
-       int size;
-
-       if ( points > MAX_POINTS_ON_WINDING ) {
-               Error( "Winding_Alloc: %i points", points );
-       }
-
-//     size = (int)((winding_t *)0)->points[points];
-       size = WINDING_SIZE( points );
-       w = (winding_t*) malloc( size );
-       memset( w, 0, size );
-       w->maxpoints = points;
-
-       return w;
+/// \brief Returns the point at which \p line intersects \p plane, or an undefined value if there is no intersection.
+inline DoubleVector3 line_intersect_plane(const DoubleLine &line, const Plane3 &plane)
+{
+    return line.origin + vector3_scaled(
+            line.direction,
+            -plane3_distance_to_point(plane, line.origin)
+            / vector3_dot(line.direction, plane.normal())
+    );
 }
 
-void Winding_Free( winding_t *w ){
-       free( w );
+inline bool float_is_largest_absolute(double axis, double other)
+{
+    return fabs(axis) > fabs(other);
 }
 
-/*
-   ==================
-   Winding_Clone
-   ==================
- */
-winding_t *Winding_Clone( winding_t *w ){
-       int size;
-       winding_t   *c;
-
-//     size = (int)((winding_t *)0)->points[w->numpoints];
-       size = WINDING_SIZE( w->numpoints );
-       c = (winding_t*)qmalloc( size );
-       memcpy( c, w, size );
-       return c;
+/// \brief Returns the index of the component of \p v that has the largest absolute value.
+inline int vector3_largest_absolute_component_index(const DoubleVector3 &v)
+{
+    return (float_is_largest_absolute(v[1], v[0]))
+           ? (float_is_largest_absolute(v[1], v[2]))
+             ? 1
+             : 2
+           : (float_is_largest_absolute(v[0], v[2]))
+             ? 0
+             : 2;
 }
 
-/*
-   ==================
-   ReverseWinding
-   ==================
- */
-winding_t *Winding_Reverse( winding_t *w ){
-       int i;
-       winding_t   *c;
-
-       c = Winding_Alloc( w->numpoints );
-       for ( i = 0; i < w->numpoints; i++ )
-       {
-               VectorCopy( w->points[w->numpoints - 1 - i], c->points[i] );
-       }
-       c->numpoints = w->numpoints;
-       return c;
+/// \brief Returns the infinite line that is the intersection of \p plane and \p other.
+inline DoubleLine plane3_intersect_plane3(const Plane3 &plane, const Plane3 &other)
+{
+    DoubleLine line;
+    line.direction = vector3_cross(plane.normal(), other.normal());
+    switch (vector3_largest_absolute_component_index(line.direction)) {
+        case 0:
+            line.origin.x() = 0;
+            line.origin.y() =
+                    (-other.dist() * plane.normal().z() - -plane.dist() * other.normal().z()) / line.direction.x();
+            line.origin.z() =
+                    (-plane.dist() * other.normal().y() - -other.dist() * plane.normal().y()) / line.direction.x();
+            break;
+        case 1:
+            line.origin.x() =
+                    (-plane.dist() * other.normal().z() - -other.dist() * plane.normal().z()) / line.direction.y();
+            line.origin.y() = 0;
+            line.origin.z() =
+                    (-other.dist() * plane.normal().x() - -plane.dist() * other.normal().x()) / line.direction.y();
+            break;
+        case 2:
+            line.origin.x() =
+                    (-other.dist() * plane.normal().y() - -plane.dist() * other.normal().y()) / line.direction.z();
+            line.origin.y() =
+                    (-plane.dist() * other.normal().x() - -other.dist() * plane.normal().x()) / line.direction.z();
+            line.origin.z() = 0;
+            break;
+        default:
+            break;
+    }
+
+    return line;
 }
 
-/*
-   ==============
-   Winding_RemovePoint
-   ==============
- */
-void Winding_RemovePoint( winding_t *w, int point ){
-       if ( point < 0 || point >= w->numpoints ) {
-               Error( "Winding_RemovePoint: point out of range" );
-       }
-
-       if ( point < w->numpoints - 1 ) {
-               memmove( &w->points[point], &w->points[point + 1], (size_t)( (winding_t *)0 )->points[w->numpoints - point - 1] );
-       }
-       w->numpoints--;
-}
 
-/*
-   =============
-   Winding_InsertPoint
-   =============
- */
-winding_t *Winding_InsertPoint( winding_t *w, vec3_t point, int spot ){
-       int i, j;
-       winding_t *neww;
-
-       if ( spot > w->numpoints ) {
-               Error( "Winding_InsertPoint: spot > w->numpoints" );
-       } //end if
-       if ( spot < 0 ) {
-               Error( "Winding_InsertPoint: spot < 0" );
-       } //end if
-       neww = Winding_Alloc( w->numpoints + 1 );
-       neww->numpoints = w->numpoints + 1;
-       for ( i = 0, j = 0; i < neww->numpoints; i++ )
-       {
-               if ( i == spot ) {
-                       VectorCopy( point, neww->points[i] );
-               }
-               else
-               {
-                       VectorCopy( w->points[j], neww->points[i] );
-                       j++;
-               }
-       }
-       return neww;
+/// \brief Keep the value of \p infinity as small as possible to improve precision in Winding_Clip.
+void Winding_createInfinite(FixedWinding &winding, const Plane3 &plane, double infinity)
+{
+    double max = -infinity;
+    int x = -1;
+    for (int i = 0; i < 3; i++) {
+        double d = fabs(plane.normal()[i]);
+        if (d > max) {
+            x = i;
+            max = d;
+        }
+    }
+    if (x == -1) {
+        globalErrorStream() << "invalid plane\n";
+        return;
+    }
+
+    DoubleVector3 vup = g_vector3_identity;
+    switch (x) {
+        case 0:
+        case 1:
+            vup[2] = 1;
+            break;
+        case 2:
+            vup[0] = 1;
+            break;
+    }
+
+
+    vector3_add(vup, vector3_scaled(plane.normal(), -vector3_dot(vup, plane.normal())));
+    vector3_normalise(vup);
+
+    DoubleVector3 org = vector3_scaled(plane.normal(), plane.dist());
+
+    DoubleVector3 vright = vector3_cross(vup, plane.normal());
+
+    vector3_scale(vup, infinity);
+    vector3_scale(vright, infinity);
+
+    // project a really big  axis aligned box onto the plane
+
+    DoubleLine r1, r2, r3, r4;
+    r1.origin = vector3_added(vector3_subtracted(org, vright), vup);
+    r1.direction = vector3_normalised(vright);
+    winding.push_back(FixedWindingVertex(r1.origin, r1, c_brush_maxFaces));
+    r2.origin = vector3_added(vector3_added(org, vright), vup);
+    r2.direction = vector3_normalised(vector3_negated(vup));
+    winding.push_back(FixedWindingVertex(r2.origin, r2, c_brush_maxFaces));
+    r3.origin = vector3_subtracted(vector3_added(org, vright), vup);
+    r3.direction = vector3_normalised(vector3_negated(vright));
+    winding.push_back(FixedWindingVertex(r3.origin, r3, c_brush_maxFaces));
+    r4.origin = vector3_subtracted(vector3_subtracted(org, vright), vup);
+    r4.direction = vector3_normalised(vup);
+    winding.push_back(FixedWindingVertex(r4.origin, r4, c_brush_maxFaces));
 }
 
-/*
-   ==============
-   Winding_IsTiny
-   ==============
- */
-#define EDGE_LENGTH 0.2
-
-int Winding_IsTiny( winding_t *w ){
-       int i, j;
-       vec_t len;
-       vec3_t delta;
-       int edges;
-
-       edges = 0;
-       for ( i = 0 ; i < w->numpoints ; i++ )
-       {
-               j = i == w->numpoints - 1 ? 0 : i + 1;
-               VectorSubtract( w->points[j], w->points[i], delta );
-               len = VectorLength( delta );
-               if ( len > EDGE_LENGTH ) {
-                       if ( ++edges == 3 ) {
-                               return false;
-                       }
-               }
-       }
-       return true;
+
+inline PlaneClassification Winding_ClassifyDistance(const double distance, const double epsilon)
+{
+    if (distance > epsilon) {
+        return ePlaneFront;
+    }
+    if (distance < -epsilon) {
+        return ePlaneBack;
+    }
+    return ePlaneOn;
 }
 
-/*
-   ==============
-   Winding_IsHuge
-   ==============
- */
-int Winding_IsHuge( winding_t *w ){
-       int i, j;
-
-       for ( i = 0 ; i < w->numpoints ; i++ )
-       {
-               for ( j = 0 ; j < 3 ; j++ )
-                       if ( w->points[i][j] < -BOGUS_RANGE + 1 || w->points[i][j] > BOGUS_RANGE - 1 ) {
-                               return true;
-                       }
-       }
-       return false;
+/// \brief Returns true if
+/// !flipped && winding is completely BACK or ON
+/// or flipped && winding is completely FRONT or ON
+bool Winding_TestPlane(const Winding &winding, const Plane3 &plane, bool flipped)
+{
+    const int test = (flipped) ? ePlaneBack : ePlaneFront;
+    for (Winding::const_iterator i = winding.begin(); i != winding.end(); ++i) {
+        if (test == Winding_ClassifyDistance(plane3_distance_to_point(plane, (*i).vertex), ON_EPSILON)) {
+            return false;
+        }
+    }
+    return true;
 }
 
-/*
-   =============
-   Winding_PlanesConcave
-   =============
- */
-#define WCONVEX_EPSILON     0.2
-
-int Winding_PlanesConcave( winding_t *w1, winding_t *w2,
-                                                  vec3_t normal1, vec3_t normal2,
-                                                  float dist1, float dist2 ){
-       int i;
-
-       if ( !w1 || !w2 ) {
-               return false;
-       }
-
-       // check if one of the points of winding 1 is at the back of the plane of winding 2
-       for ( i = 0; i < w1->numpoints; i++ )
-       {
-               if ( DotProduct( normal2, w1->points[i] ) - dist2 > WCONVEX_EPSILON ) {
-                       return true;
-               }
-       }
-       // check if one of the points of winding 2 is at the back of the plane of winding 1
-       for ( i = 0; i < w2->numpoints; i++ )
-       {
-               if ( DotProduct( normal1, w2->points[i] ) - dist1 > WCONVEX_EPSILON ) {
-                       return true;
-               }
-       }
-
-       return false;
+/// \brief Returns true if any point in \p w1 is in front of plane2, or any point in \p w2 is in front of plane1
+bool Winding_PlanesConcave(const Winding &w1, const Winding &w2, const Plane3 &plane1, const Plane3 &plane2)
+{
+    return !Winding_TestPlane(w1, plane2, false) || !Winding_TestPlane(w2, plane1, false);
 }
 
-/*
-   ==================
-   Winding_Clip
-
-   Clips the winding to the plane, returning the new winding on the positive side
-   Frees the input winding.
-   If keepon is true, an exactly on-plane winding will be saved, otherwise
-   it will be clipped away.
-   ==================
- */
-winding_t *Winding_Clip( winding_t *in, plane_t *split, qboolean keepon ){
-       vec_t dists[MAX_POINTS_ON_WINDING];
-       int sides[MAX_POINTS_ON_WINDING];
-       int counts[3];
-       vec_t dot;
-       int i, j;
-       vec_t   *p1, *p2;
-       vec3_t mid;
-       winding_t   *neww;
-       int maxpts;
-
-       counts[0] = counts[1] = counts[2] = 0;
-
-       // determine sides for each point
-       for ( i = 0 ; i < in->numpoints ; i++ )
-       {
-               dot = DotProduct( in->points[i], split->normal );
-               dot -= split->dist;
-               dists[i] = dot;
-               if ( dot > ON_EPSILON ) {
-                       sides[i] = SIDE_FRONT;
-               }
-               else if ( dot < -ON_EPSILON ) {
-                       sides[i] = SIDE_BACK;
-               }
-               else
-               {
-                       sides[i] = SIDE_ON;
-               }
-               counts[sides[i]]++;
-       }
-       sides[i] = sides[0];
-       dists[i] = dists[0];
-
-       if ( keepon && !counts[0] && !counts[1] ) {
-               return in;
-       }
-
-       if ( !counts[0] ) {
-               Winding_Free( in );
-               return NULL;
-       }
-       if ( !counts[1] ) {
-               return in;
-       }
-
-       maxpts = in->numpoints + 4;   // can't use counts[0]+2 because
-                                     // of fp grouping errors
-       neww = Winding_Alloc( maxpts );
-
-       for ( i = 0 ; i < in->numpoints ; i++ )
-       {
-               p1 = in->points[i];
-
-               if ( sides[i] == SIDE_ON ) {
-                       VectorCopy( p1, neww->points[neww->numpoints] );
-                       neww->numpoints++;
-                       continue;
-               }
-
-               if ( sides[i] == SIDE_FRONT ) {
-                       VectorCopy( p1, neww->points[neww->numpoints] );
-                       neww->numpoints++;
-               }
-
-               if ( sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i] ) {
-                       continue;
-               }
-
-               // generate a split point
-               p2 = in->points[( 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 ( split->normal[j] == 1 ) {
-                               mid[j] = split->dist;
-                       }
-                       else if ( split->normal[j] == -1 ) {
-                               mid[j] = -split->dist;
-                       }
-                       else{
-                               mid[j] = p1[j] + dot * ( p2[j] - p1[j] );
-                       }
-               }
-
-               VectorCopy( mid, neww->points[neww->numpoints] );
-               neww->numpoints++;
-       }
-
-       if ( neww->numpoints > maxpts ) {
-               Error( "Winding_Clip: points exceeded estimate" );
-       }
-
-       // free the original winding
-       Winding_Free( in );
-
-       return neww;
+brushsplit_t Winding_ClassifyPlane(const Winding &winding, const Plane3 &plane)
+{
+    brushsplit_t split;
+    for (Winding::const_iterator i = winding.begin(); i != winding.end(); ++i) {
+        ++split.counts[Winding_ClassifyDistance(plane3_distance_to_point(plane, (*i).vertex), ON_EPSILON)];
+    }
+    return split;
 }
 
-/*
-   =============
-   Winding_SplitEpsilon
 
-   split the input winding with the plane
-   the input winding stays untouched
-   =============
- */
-void Winding_SplitEpsilon( winding_t *in, vec3_t normal, double 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];
-       vec_t dot;
-       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->points[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 = Winding_Clone( in );
-               return;
-       }
-       if ( !counts[1] ) {
-               *front = Winding_Clone( in );
-               return;
-       }
-
-       maxpts = in->numpoints + 4;   // cant use counts[0]+2 because
-                                     // of fp grouping errors
-
-       *front = f = Winding_Alloc( maxpts );
-       *back = b = Winding_Alloc( maxpts );
-
-       for ( i = 0; i < in->numpoints; i++ )
-       {
-               p1 = in->points[i];
-
-               if ( sides[i] == SIDE_ON ) {
-                       VectorCopy( p1, f->points[f->numpoints] );
-                       f->numpoints++;
-                       VectorCopy( p1, b->points[b->numpoints] );
-                       b->numpoints++;
-                       continue;
-               }
-
-               if ( sides[i] == SIDE_FRONT ) {
-                       VectorCopy( p1, f->points[f->numpoints] );
-                       f->numpoints++;
-               }
-               if ( sides[i] == SIDE_BACK ) {
-                       VectorCopy( p1, b->points[b->numpoints] );
-                       b->numpoints++;
-               }
-
-               if ( sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i] ) {
-                       continue;
-               }
-
-               // generate a split point
-               p2 = in->points[( 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->points[f->numpoints] );
-               f->numpoints++;
-               VectorCopy( mid, b->points[b->numpoints] );
-               b->numpoints++;
-       }
-
-       if ( f->numpoints > maxpts || b->numpoints > maxpts ) {
-               Error( "Winding_Clip: points exceeded estimate" );
-       }
-       if ( f->numpoints > MAX_POINTS_ON_WINDING || b->numpoints > MAX_POINTS_ON_WINDING ) {
-               Error( "Winding_Clip: MAX_POINTS_ON_WINDING" );
-       }
+#define DEBUG_EPSILON ON_EPSILON
+const double DEBUG_EPSILON_SQUARED = DEBUG_EPSILON * DEBUG_EPSILON;
+
+#define WINDING_DEBUG 0
+
+/// \brief Clip \p winding which lies on \p plane by \p clipPlane, resulting in \p clipped.
+/// If \p winding is completely in front of the plane, \p clipped will be identical to \p winding.
+/// If \p winding is completely in back of the plane, \p clipped will be empty.
+/// If \p winding intersects the plane, the edge of \p clipped which lies on \p clipPlane will store the value of \p adjacent.
+void Winding_Clip(const FixedWinding &winding, const Plane3 &plane, const Plane3 &clipPlane, std::size_t adjacent,
+                  FixedWinding &clipped)
+{
+    PlaneClassification classification = Winding_ClassifyDistance(
+            plane3_distance_to_point(clipPlane, winding.back().vertex), ON_EPSILON);
+    PlaneClassification nextClassification;
+    // for each edge
+    for (std::size_t next = 0, i = winding.size() - 1;
+         next != winding.size(); i = next, ++next, classification = nextClassification) {
+        nextClassification = Winding_ClassifyDistance(plane3_distance_to_point(clipPlane, winding[next].vertex),
+                                                      ON_EPSILON);
+        const FixedWindingVertex &vertex = winding[i];
+
+        // if first vertex of edge is ON
+        if (classification == ePlaneOn) {
+            // append first vertex to output winding
+            if (nextClassification == ePlaneBack) {
+                // this edge lies on the clip plane
+                clipped.push_back(
+                        FixedWindingVertex(vertex.vertex, plane3_intersect_plane3(plane, clipPlane), adjacent));
+            } else {
+                clipped.push_back(vertex);
+            }
+            continue;
+        }
+
+        // if first vertex of edge is FRONT
+        if (classification == ePlaneFront) {
+            // add first vertex to output winding
+            clipped.push_back(vertex);
+        }
+        // if second vertex of edge is ON
+        if (nextClassification == ePlaneOn) {
+            continue;
+        }
+            // else if second vertex of edge is same as first
+        else if (nextClassification == classification) {
+            continue;
+        }
+            // else if first vertex of edge is FRONT and there are only two edges
+        else if (classification == ePlaneFront && winding.size() == 2) {
+            continue;
+        }
+            // else first vertex is FRONT and second is BACK or vice versa
+        else {
+            // append intersection point of line and plane to output winding
+            DoubleVector3 mid(line_intersect_plane(vertex.edge, clipPlane));
+
+            if (classification == ePlaneFront) {
+                // this edge lies on the clip plane
+                clipped.push_back(FixedWindingVertex(mid, plane3_intersect_plane3(plane, clipPlane), adjacent));
+            } else {
+                clipped.push_back(FixedWindingVertex(mid, vertex.edge, vertex.adjacent));
+            }
+        }
+    }
 }
 
-/*
-   =============
-   Winding_TryMerge
+std::size_t Winding_FindAdjacent(const Winding &winding, std::size_t face)
+{
+    for (std::size_t i = 0; i < winding.numpoints; ++i) {
+        ASSERT_MESSAGE(winding[i].adjacent != c_brush_maxFaces, "edge connectivity data is invalid");
+        if (winding[i].adjacent == face) {
+            return i;
+        }
+    }
+    return c_brush_maxFaces;
+}
 
-   If two windings share a common edge and the edges that meet at the
-   common points are both inside the other polygons, merge them
+std::size_t Winding_Opposite(const Winding &winding, const std::size_t index, const std::size_t other)
+{
+    ASSERT_MESSAGE(index < winding.numpoints && other < winding.numpoints, "Winding_Opposite: index out of range");
 
-   Returns NULL if the windings couldn't be merged, or the new winding.
-   The originals will NOT be freed.
+    double dist_best = 0;
+    std::size_t index_best = c_brush_maxFaces;
 
-   if keep is true no points are ever removed
-   =============
- */
-#define CONTINUOUS_EPSILON  0.005
-
-winding_t *Winding_TryMerge( winding_t *f1, winding_t *f2, vec3_t planenormal, int keep ){
-       vec_t       *p1, *p2, *p3, *p4, *back;
-       winding_t   *newf;
-       int i, j, k, l;
-       vec3_t normal, delta;
-       vec_t dot;
-       qboolean keep1, keep2;
-
-
-       //
-       // find a common edge
-       //
-       p1 = p2 = NULL; // stop compiler warning
-       j = 0;          //
-
-       for ( i = 0; i < f1->numpoints; i++ )
-       {
-               p1 = f1->points[i];
-               p2 = f1->points[( i + 1 ) % f1->numpoints];
-               for ( j = 0; j < f2->numpoints; j++ )
-               {
-                       p3 = f2->points[j];
-                       p4 = f2->points[( j + 1 ) % f2->numpoints];
-                       for ( k = 0; k < 3; k++ )
-                       {
-                               if ( fabs( p1[k] - p4[k] ) > 0.1 ) { //EQUAL_EPSILON) //ME
-                                       break;
-                               }
-                               if ( fabs( p2[k] - p3[k] ) > 0.1 ) { //EQUAL_EPSILON) //ME
-                                       break;
-                               }
-                       } //end for
-                       if ( k == 3 ) {
-                               break;
-                       }
-               } //end for
-               if ( j < f2->numpoints ) {
-                       break;
-               }
-       } //end for
-
-       if ( i == f1->numpoints ) {
-               return NULL;            // no matching edges
-
-       }
-       //
-       // check slope of connected lines
-       // if the slopes are colinear, the point can be removed
-       //
-       back = f1->points[( i + f1->numpoints - 1 ) % f1->numpoints];
-       VectorSubtract( p1, back, delta );
-       CrossProduct( planenormal, delta, normal );
-       VectorNormalize( normal, normal );
-
-       back = f2->points[( j + 2 ) % f2->numpoints];
-       VectorSubtract( back, p1, delta );
-       dot = DotProduct( delta, normal );
-       if ( dot > CONTINUOUS_EPSILON ) {
-               return NULL;            // not a convex polygon
-       }
-       keep1 = (qboolean)( dot < -CONTINUOUS_EPSILON );
-
-       back = f1->points[( i + 2 ) % f1->numpoints];
-       VectorSubtract( back, p2, delta );
-       CrossProduct( planenormal, delta, normal );
-       VectorNormalize( normal, normal );
-
-       back = f2->points[( j + f2->numpoints - 1 ) % f2->numpoints];
-       VectorSubtract( back, p2, delta );
-       dot = DotProduct( delta, normal );
-       if ( dot > CONTINUOUS_EPSILON ) {
-               return NULL;            // not a convex polygon
-       }
-       keep2 = (qboolean)( dot < -CONTINUOUS_EPSILON );
-
-       //
-       // build the new polygon
-       //
-       newf = Winding_Alloc( f1->numpoints + f2->numpoints );
-
-       // copy first polygon
-       for ( k = ( i + 1 ) % f1->numpoints ; k != i ; k = ( k + 1 ) % f1->numpoints )
-       {
-               if ( !keep && k == ( i + 1 ) % f1->numpoints && !keep2 ) {
-                       continue;
-               }
-
-               VectorCopy( f1->points[k], newf->points[newf->numpoints] );
-               newf->numpoints++;
-       }
-
-       // copy second polygon
-       for ( l = ( j + 1 ) % f2->numpoints ; l != j ; l = ( l + 1 ) % f2->numpoints )
-       {
-               if ( !keep && l == ( j + 1 ) % f2->numpoints && !keep1 ) {
-                       continue;
-               }
-               VectorCopy( f2->points[l], newf->points[newf->numpoints] );
-               newf->numpoints++;
-       }
-
-       return newf;
-}
+    Ray edge(ray_for_points(winding[index].vertex, winding[other].vertex));
 
-/*
-   ============
-   Winding_Plane
-   ============
- */
-void Winding_Plane( winding_t *w, vec3_t normal, double *dist ){
-       vec3_t v1, v2;
-       int i;
-
-       //find two vectors each longer than 0.5 units
-       for ( i = 0; i < w->numpoints; i++ )
-       {
-               VectorSubtract( w->points[( i + 1 ) % w->numpoints], w->points[i], v1 );
-               VectorSubtract( w->points[( i + 2 ) % w->numpoints], w->points[i], v2 );
-               if ( VectorLength( v1 ) > 0.5 && VectorLength( v2 ) > 0.5 ) {
-                       break;
-               }
-       }
-       CrossProduct( v2, v1, normal );
-       VectorNormalize( normal, normal );
-       *dist = DotProduct( w->points[0], normal );
-}
+    for (std::size_t i = 0; i < winding.numpoints; ++i) {
+        if (i == index || i == other) {
+            continue;
+        }
 
-/*
-   =============
-   Winding_Area
-   =============
- */
-float Winding_Area( winding_t *w ){
-       int i;
-       vec3_t d1, d2, cross;
-       float total;
-
-       total = 0;
-       for ( i = 2 ; i < w->numpoints ; i++ )
-       {
-               VectorSubtract( w->points[i - 1], w->points[0], d1 );
-               VectorSubtract( w->points[i], w->points[0], d2 );
-               CrossProduct( d1, d2, cross );
-               total += 0.5 * VectorLength( cross );
-       }
-       return total;
-}
+        double dist_squared = ray_squared_distance_to_point(edge, winding[i].vertex);
 
-/*
-   =============
-   Winding_Bounds
-   =============
- */
-void Winding_Bounds( 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->points[i][j];
-                       if ( v < mins[j] ) {
-                               mins[j] = v;
-                       }
-                       if ( v > maxs[j] ) {
-                               maxs[j] = v;
-                       }
-               }
-       }
+        if (dist_squared > dist_best) {
+            dist_best = dist_squared;
+            index_best = i;
+        }
+    }
+    return index_best;
 }
 
-
-/*
-   =================
-   Winding_PointInside
-   =================
- */
-int Winding_PointInside( winding_t *w, plane_t *plane, vec3_t point, float epsilon ){
-       int i;
-       vec3_t dir, normal, pointvec;
-
-       for ( i = 0; i < w->numpoints; i++ )
-       {
-               VectorSubtract( w->points[( i + 1 ) % w->numpoints], w->points[i], dir );
-               VectorSubtract( point, w->points[i], pointvec );
-               //
-               CrossProduct( dir, plane->normal, normal );
-               //
-               if ( DotProduct( pointvec, normal ) < -epsilon ) {
-                       return false;
-               }
-       }
-       return true;
+std::size_t Winding_Opposite(const Winding &winding, const std::size_t index)
+{
+    return Winding_Opposite(winding, index, Winding_next(winding, index));
 }
 
-/*
-   =================
-   Winding_VectorIntersect
-   =================
- */
-int Winding_VectorIntersect( winding_t *w, plane_t *plane, vec3_t p1, vec3_t p2, float epsilon ){
-       float front, back, frac;
-       vec3_t mid;
-
-       front = DotProduct( p1, plane->normal ) - plane->dist;
-       back = DotProduct( p2, plane->normal ) - plane->dist;
-       //if both points at the same side of the plane
-       if ( front < -epsilon && back < -epsilon ) {
-               return false;
-       }
-       if ( front > epsilon && back > epsilon ) {
-               return false;
-       }
-       //get point of intersection with winding plane
-       if ( fabs( front - back ) < 0.001 ) {
-               VectorCopy( p2, mid );
-       }
-       else
-       {
-               frac = front / ( front - back );
-               mid[0] = p1[0] + ( p2[0] - p1[0] ) * frac;
-               mid[1] = p1[1] + ( p2[1] - p1[1] ) * frac;
-               mid[2] = p1[2] + ( p2[2] - p1[2] ) * frac;
-       }
-       return Winding_PointInside( w, plane, mid, epsilon );
+/// \brief Calculate the \p centroid of the polygon defined by \p winding which lies on plane \p plane.
+void Winding_Centroid(const Winding &winding, const Plane3 &plane, Vector3 &centroid)
+{
+    double area2 = 0, x_sum = 0, y_sum = 0;
+    const ProjectionAxis axis = projectionaxis_for_normal(plane.normal());
+    const indexremap_t remap = indexremap_for_projectionaxis(axis);
+    for (std::size_t i = winding.numpoints - 1, j = 0; j < winding.numpoints; i = j, ++j) {
+        const double ai = winding[i].vertex[remap.x] * winding[j].vertex[remap.y] -
+                          winding[j].vertex[remap.x] * winding[i].vertex[remap.y];
+        area2 += ai;
+        x_sum += (winding[j].vertex[remap.x] + winding[i].vertex[remap.x]) * ai;
+        y_sum += (winding[j].vertex[remap.y] + winding[i].vertex[remap.y]) * ai;
+    }
+
+    centroid[remap.x] = static_cast<float>( x_sum / (3 * area2));
+    centroid[remap.y] = static_cast<float>( y_sum / (3 * area2));
+    {
+        Ray ray(Vector3(0, 0, 0), Vector3(0, 0, 0));
+        ray.origin[remap.x] = centroid[remap.x];
+        ray.origin[remap.y] = centroid[remap.y];
+        ray.direction[remap.z] = 1;
+        centroid[remap.z] = static_cast<float>( ray_distance_to_plane(ray, plane));
+    }
 }