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+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+**
+** http://oss.sgi.com/projects/FreeB
+**
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+**
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+**
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+**
+** $Date: 2001/11/29 16:16:55 $ $Revision: 1.2 $
+*/
+/*
+** $Header: /cvs/mesa/Mesa/src/glu/sgi/libnurbs/nurbtess/partitionY.cc,v 1.2 2001/11/29 16:16:55 kschultz Exp $
+*/
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <time.h>
+
+#include "zlassert.h"
+#include "partitionY.h"
+#include "searchTree.h"
+#include "quicksort.h"
+#include "polyUtil.h"
+
+
+#define max(a,b) ((a>b)? a:b)
+#define min(a,b) ((a>b)? b:a)
+
+
+/*retrurn
+ *-1: if A < B (Ya<Yb) || (Ya==Yb)
+ * 0: if A == B
+ * 1: if A>B
+ */
+static Int compVertInY(Real A[2], Real B[2])
+{
+ if( (A[1] < B[1]) || (A[1]==B[1] && A[0]<B[0]))
+ return -1;
+ else if
+ ( A[1] == B[1] && A[0] == B[0]) return 0;
+ else
+ return 1;
+}
+
+/*v is a vertex: the head of en edge,
+ *e is an edge,
+ *return 1 if e is below v: assume v1 and v2 are the two endpoints of e:
+ * v1<= v, v2<=v.
+ */
+Int isBelow(directedLine *v, directedLine *e)
+{
+ Real* vert = v->head();
+ if( compVertInY(e->head(), vert) != 1
+ && compVertInY(e->tail(), vert) != 1
+ )
+ return 1;
+ else
+ return 0;
+}
+
+/*v is a vertex: the head of en edge,
+ *e is an edge,
+ *return 1 if e is below v: assume v1 and v2 are the two endpoints of e:
+ * v1>= v, v2>=v.
+ */
+Int isAbove(directedLine *v, directedLine *e)
+{
+ Real* vert = v->head();
+ if( compVertInY(e->head(), vert) != -1
+ && compVertInY(e->tail(), vert) != -1
+ )
+ return 1;
+ else
+ return 0;
+}
+
+Int isCusp(directedLine *v)
+{
+ Real *A=v->getPrev()->head();
+ Real *B=v->head();
+ Real *C=v->tail();
+ if(A[1] < B[1] && B[1] < C[1])
+ return 0;
+ else if(A[1] > B[1] && B[1] > C[1])
+ return 0;
+ else if(A[1] < B[1] && C[1] < B[1])
+ return 1;
+ else if(A[1] > B[1] && C[1] > B[1])
+ return 1;
+
+ if(isAbove(v, v) && isAbove(v, v->getPrev()) ||
+ isBelow(v, v) && isBelow(v, v->getPrev()))
+ return 1;
+ else
+ return 0;
+}
+
+/*crossproduct is strictly less than 0*/
+Int isReflex(directedLine *v)
+{
+ Real* A = v->getPrev()->head();
+ Real* B = v->head();
+ Real* C = v->tail();
+ Real Bx,By, Cx, Cy;
+ Bx = B[0] - A[0];
+ By = B[1] - A[1];
+ Cx = C[0] - A[0];
+ Cy = C[1] - A[1];
+
+ if(Bx*Cy - Cx*By < 0) return 1;
+ else return 0;
+}
+
+ /*return
+ *0: not-cusp
+ *1: interior cusp
+ *2: exterior cusp
+ */
+Int cuspType(directedLine *v)
+{
+ if(! isCusp(v)) return 0;
+ else if(isReflex(v)) return 1;
+ else
+ return 2;
+}
+
+sweepRange* sweepRangeMake(directedLine* left, Int leftType,
+ directedLine* right, Int rightType)
+{
+ sweepRange* ret = (sweepRange*)malloc(sizeof(sweepRange));
+ assert(ret);
+ ret->left = left;
+ ret->leftType = leftType;
+ ret->right = right;
+ ret->rightType = rightType;
+ return ret;
+}
+
+void sweepRangeDelete(sweepRange* range)
+{
+ free(range);
+}
+
+Int sweepRangeEqual(sweepRange* src1, sweepRange* src2)
+{
+ Int leftEqual;
+ Int rightEqual;
+
+
+ /*The case when both are vertices should not happen*/
+ assert(! (src1->leftType == 0 && src2->leftType == 0));
+ if(src1->leftType == 0 && src2->leftType == 1){
+ if(src1->left == src2->left ||
+ src1->left->getPrev() == src2->left
+ )
+ leftEqual = 1;
+ else
+ leftEqual = 0;
+ }
+ else if(src1->leftType == 1 && src2->leftType == 1){
+ if(src1->left == src2->left)
+ leftEqual = 1;
+ else
+ leftEqual = 0;
+ }
+ else /*src1->leftType == 1 && src2->leftType == 0*/{
+ if(src1->left == src2->left ||
+ src1->left == src2->left->getPrev()
+ )
+ leftEqual = 1;
+ else
+ leftEqual = 0;
+ }
+
+ /*the same thing for right*/
+ /*The case when both are vertices should not happen*/
+ assert(! (src1->rightType == 0 && src2->rightType == 0));
+ if(src1->rightType == 0 && src2->rightType == 1){
+ if(src1->right == src2->right ||
+ src1->right->getPrev() == src2->right
+ )
+ rightEqual = 1;
+ else
+ rightEqual = 0;
+ }
+ else if(src1->rightType == 1 && src2->rightType == 1){
+ if(src1->right == src2->right)
+ rightEqual = 1;
+ else
+ rightEqual = 0;
+ }
+ else /*src1->rightType == 1 && src2->rightType == 0*/{
+ if(src1->right == src2->right ||
+ src1->right == src2->right->getPrev()
+ )
+ rightEqual = 1;
+ else
+ rightEqual = 0;
+ }
+
+ return (leftEqual == 1 || rightEqual == 1);
+}
+
+/*given (x_1, y_1) and (x_2, y_2), and y
+ *return x such that (x,y) is on the line
+ */
+inline/*static*/ Real intersectHoriz(Real x1, Real y1, Real x2, Real y2, Real y)
+{
+ return ((y2==y1)? (x1+x2)*Real(0.5) : x1 + ((y-y1)/(y2-y1)) * (x2-x1));
+/*
+ if(y2 == y1) return (x1+x2)*0.5;
+ else return x1 + ((y-y1)/(y2-y1)) * (x2-x1);
+*/
+}
+
+/*compare two edges of a polygon.
+ *edge A < edge B if there is a horizontal line so that the intersection
+ *with A is to the left of the intersection with B.
+ *This function is used in sweepY for the dynamic search tree insertion to
+ *order the edges.
+ * Implementation: (x_1,y_1) and (x_2, y_2)
+ */
+static Int compEdges(directedLine *e1, directedLine *e2)
+{
+ Real* head1 = e1->head();
+ Real* tail1 = e1->tail();
+ Real* head2 = e2->head();
+ Real* tail2 = e2->tail();
+/*
+ Real h10 = head1[0];
+ Real h11 = head1[1];
+ Real t10 = tail1[0];
+ Real t11 = tail1[1];
+ Real h20 = head2[0];
+ Real h21 = head2[1];
+ Real t20 = tail2[0];
+ Real t21 = tail2[1];
+*/
+ Real e1_Ymax, e1_Ymin, e2_Ymax, e2_Ymin;
+/*
+ if(h11>t11) {
+ e1_Ymax= h11;
+ e1_Ymin= t11;
+ }
+ else{
+ e1_Ymax = t11;
+ e1_Ymin = h11;
+ }
+
+ if(h21>t21) {
+ e2_Ymax= h21;
+ e2_Ymin= t21;
+ }
+ else{
+ e2_Ymax = t21;
+ e2_Ymin = h21;
+ }
+*/
+
+ if(head1[1]>tail1[1]) {
+ e1_Ymax= head1[1];
+ e1_Ymin= tail1[1];
+ }
+ else{
+ e1_Ymax = tail1[1];
+ e1_Ymin = head1[1];
+ }
+
+ if(head2[1]>tail2[1]) {
+ e2_Ymax= head2[1];
+ e2_Ymin= tail2[1];
+ }
+ else{
+ e2_Ymax = tail2[1];
+ e2_Ymin = head2[1];
+ }
+
+
+ /*Real e1_Ymax = max(head1[1], tail1[1]);*/ /*max(e1->head()[1], e1->tail()[1]);*/
+ /*Real e1_Ymin = min(head1[1], tail1[1]);*/ /*min(e1->head()[1], e1->tail()[1]);*/
+ /*Real e2_Ymax = max(head2[1], tail2[1]);*/ /*max(e2->head()[1], e2->tail()[1]);*/
+ /*Real e2_Ymin = min(head2[1], tail2[1]);*/ /*min(e2->head()[1], e2->tail()[1]);*/
+
+ Real Ymax = min(e1_Ymax, e2_Ymax);
+ Real Ymin = max(e1_Ymin, e2_Ymin);
+
+ Real y = Real(0.5)*(Ymax + Ymin);
+
+/* Real x1 = intersectHoriz(e1->head()[0], e1->head()[1], e1->tail()[0], e1->tail()[1], y);
+ Real x2 = intersectHoriz(e2->head()[0], e2->head()[1], e2->tail()[0], e2->tail()[1], y);
+*/
+/*
+ Real x1 = intersectHoriz(h10, h11, t10, t11, y);
+ Real x2 = intersectHoriz(h20, h21, t20, t21, y);
+*/
+ Real x1 = intersectHoriz(head1[0], head1[1], tail1[0], tail1[1], y);
+ Real x2 = intersectHoriz(head2[0], head2[1], tail2[0], tail2[1], y);
+
+ if(x1<= x2) return -1;
+ else return 1;
+}
+
+/*used by sort precedures
+ */
+static Int compInY(directedLine* v1, directedLine* v2)
+{
+ return v1->compInY(v2);
+}
+
+void findDiagonals(Int total_num_edges, directedLine** sortedVertices, sweepRange** ranges, Int& num_diagonals, directedLine** diagonal_vertices)
+{
+ Int i,j,k;
+
+ k=0;
+
+ for(i=0; i<total_num_edges; i++)
+ {
+ directedLine* vert =sortedVertices[i];
+ directedLine* thisEdge = vert;
+ directedLine* prevEdge = vert->getPrev();
+/*
+printf("find i=%i\n", i);
+printf("the vertex is\n");
+vert->printSingle();
+*/
+ if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge) && compEdges(prevEdge, thisEdge)<0)
+ {
+ /*this is an upward interior cusp*/
+ diagonal_vertices[k++] = vert;
+
+ for(j=i+1; j<total_num_edges; j++)
+ if(sweepRangeEqual(ranges[i], ranges[j]))
+ {
+ diagonal_vertices[k++] = sortedVertices[j];
+ break;
+ }
+ assert(j<total_num_edges);
+
+
+ }
+ else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge) && compEdges(prevEdge, thisEdge)>0)
+ {
+ /*this is an downward interior cusp*/
+ diagonal_vertices[k++] = vert;
+ for(j=i-1; j>=0; j--)
+ if(sweepRangeEqual(ranges[i], ranges[j]))
+ {
+ diagonal_vertices[k++] = sortedVertices[j];
+ break;
+ }
+/* printf("j=%i\n", j);*/
+ assert(j>=0);
+
+
+
+ }
+ }
+ num_diagonals = k/2;
+}
+
+/*get rid of repeated diagonlas so that each diagonal appears only once in the array
+ */
+Int deleteRepeatDiagonals(Int num_diagonals, directedLine** diagonal_vertices, directedLine** new_vertices)
+{
+ Int i,k;
+ Int j,l;
+ Int index;
+ index=0;
+ for(i=0,k=0; i<num_diagonals; i++, k+=2)
+ {
+ Int isRepeated=0;
+ /*check the diagonla (diagonal_vertice[k], diagonal_vertices[k+1])
+ *is repeated or not
+ */
+ for(j=0,l=0; j<index; j++, l+=2)
+ {
+ if(
+ (diagonal_vertices[k] == new_vertices[l] &&
+ diagonal_vertices[k+1] == new_vertices[l+1]
+ )
+ ||
+ (
+ diagonal_vertices[k] == new_vertices[l+1] &&
+ diagonal_vertices[k+1] == new_vertices[l]
+ )
+ )
+ {
+ isRepeated=1;
+ break;
+ }
+ }
+ if(! isRepeated)
+ {
+ new_vertices[index+index] = diagonal_vertices[k];
+ new_vertices[index+index+1] = diagonal_vertices[k+1];
+ index++;
+ }
+ }
+ return index;
+}
+
+/*for debug only*/
+directedLine** DBGfindDiagonals(directedLine *polygons, Int& num_diagonals)
+{
+ Int total_num_edges = 0;
+ directedLine** array = polygons->toArrayAllPolygons(total_num_edges);
+ quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void*, void*)) compInY);
+ sweepRange** ranges = (sweepRange**) malloc(sizeof(sweepRange*) * total_num_edges);
+ assert(ranges);
+
+ sweepY(total_num_edges, array, ranges);
+
+ directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges);
+ assert(diagonal_vertices);
+ findDiagonals(total_num_edges, array, ranges, num_diagonals, diagonal_vertices);
+
+ num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);
+ return diagonal_vertices;
+
+}
+
+
+/*partition into Y-monotone polygons*/
+directedLine* partitionY(directedLine *polygons, sampledLine **retSampledLines)
+{
+ Int total_num_edges = 0;
+ directedLine** array = polygons->toArrayAllPolygons(total_num_edges);
+
+ quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void*, void*)) compInY);
+
+ sweepRange** ranges = (sweepRange**) malloc(sizeof(sweepRange*) * (total_num_edges));
+ assert(ranges);
+
+
+
+ sweepY(total_num_edges, array, ranges);
+
+
+
+ /*the diagonal vertices are stored as:
+ *v0-v1: 1st diagonal
+ *v2-v3: 2nd diagonal
+ *v5-v5: 3rd diagonal
+ *...
+ */
+
+
+ Int num_diagonals;
+ /*number diagonals is < total_num_edges*total_num_edges*/
+ directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges*2/*total_num_edges*/);
+ assert(diagonal_vertices);
+
+
+
+ findDiagonals(total_num_edges, array, ranges, num_diagonals, diagonal_vertices);
+
+
+
+ directedLine* ret_polygons = polygons;
+ sampledLine* newSampledLines = NULL;
+ Int i,k;
+
+num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);
+
+
+
+ Int *removedDiagonals=(Int*)malloc(sizeof(Int) * num_diagonals);
+ for(i=0; i<num_diagonals; i++)
+ removedDiagonals[i] = 0;
+
+
+
+
+
+ for(i=0,k=0; i<num_diagonals; i++,k+=2)
+ {
+
+
+ directedLine* v1=diagonal_vertices[k];
+ directedLine* v2=diagonal_vertices[k+1];
+ directedLine* ret_p1;
+ directedLine* ret_p2;
+
+ /*we ahve to determine whether v1 and v2 belong to the same polygon before
+ *their structure are modified by connectDiagonal().
+ */
+/*
+ directedLine *root1 = v1->findRoot();
+ directedLine *root2 = v2->findRoot();
+ assert(root1);
+ assert(root2);
+*/
+
+directedLine* root1 = v1->rootLinkFindRoot();
+directedLine* root2 = v2->rootLinkFindRoot();
+
+ if(root1 != root2)
+ {
+
+ removedDiagonals[i] = 1;
+ sampledLine* generatedLine;
+
+
+
+ v1->connectDiagonal(v1,v2, &ret_p1, &ret_p2, &generatedLine, ret_polygons);
+
+
+
+ newSampledLines = generatedLine->insert(newSampledLines);
+/*
+ ret_polygons = ret_polygons->cutoffPolygon(root1);
+
+ ret_polygons = ret_polygons->cutoffPolygon(root2);
+ ret_polygons = ret_p1->insertPolygon(ret_polygons);
+root1->rootLinkSet(ret_p1);
+root2->rootLinkSet(ret_p1);
+ret_p1->rootLinkSet(NULL);
+ret_p2->rootLinkSet(ret_p1);
+*/
+ ret_polygons = ret_polygons->cutoffPolygon(root2);
+
+
+
+root2->rootLinkSet(root1);
+ret_p1->rootLinkSet(root1);
+ret_p2->rootLinkSet(root1);
+
+ /*now that we have connected the diagonal v1 and v2,
+ *we have to check those unprocessed diagonals which
+ *have v1 or v2 as an end point. Notice that the head of v1
+ *has the same coodinates as the head of v2->prev, and the head of
+ *v2 has the same coordinate as the head of v1->prev.
+ *Suppose these is a diagonal (v1, x). If (v1,x) is still a valid
+ *diagonal, then x should be on the left hand side of the directed line: *v1->prev->head -- v1->head -- v1->tail. Otherwise, (v1,x) should be
+ *replaced by (v2->prev, x), that is, x is on the left of
+ * v2->prev->prev->head, v2->prev->head, v2->prev->tail.
+ */
+ Int ii, kk;
+ for(ii=0, kk=0; ii<num_diagonals; ii++, kk+=2)
+ if( removedDiagonals[ii]==0)
+ {
+ directedLine* d1=diagonal_vertices[kk];
+ directedLine* d2=diagonal_vertices[kk+1];
+ /*check d1, and replace diagonal_vertices[kk] if necessary*/
+ if(d1 == v1) {
+ /*check if d2 is to left of v1->prev->head:v1->head:v1->tail*/
+ if(! pointLeft2Lines(v1->getPrev()->head(),
+ v1->head(), v1->tail(), d2->head()))
+ {
+/*
+ assert(pointLeft2Lines(v2->getPrev()->getPrev()->head(),
+ v2->getPrev()->head(),
+ v2->getPrev()->tail(), d2->head()));
+*/
+ diagonal_vertices[kk] = v2->getPrev();
+ }
+ }
+ if(d1 == v2) {
+ /*check if d2 is to left of v2->prev->head:v2->head:v2->tail*/
+ if(! pointLeft2Lines(v2->getPrev()->head(),
+ v2->head(), v2->tail(), d2->head()))
+ {
+/*
+ assert(pointLeft2Lines(v1->getPrev()->getPrev()->head(),
+ v1->getPrev()->head(),
+ v1->getPrev()->tail(), d2->head()));
+*/
+ diagonal_vertices[kk] = v1->getPrev();
+ }
+ }
+ /*check d2 and replace diagonal_vertices[k+1] if necessary*/
+ if(d2 == v1) {
+ /*check if d1 is to left of v1->prev->head:v1->head:v1->tail*/
+ if(! pointLeft2Lines(v1->getPrev()->head(),
+ v1->head(), v1->tail(), d1->head()))
+ {
+/* assert(pointLeft2Lines(v2->getPrev()->getPrev()->head(),
+ v2->getPrev()->head(),
+ v2->getPrev()->tail(), d1->head()));
+*/
+ diagonal_vertices[kk+1] = v2->getPrev();
+ }
+ }
+ if(d2 == v2) {
+ /*check if d1 is to left of v2->prev->head:v2->head:v2->tail*/
+ if(! pointLeft2Lines(v2->getPrev()->head(),
+ v2->head(), v2->tail(), d1->head()))
+ {
+/* assert(pointLeft2Lines(v1->getPrev()->getPrev()->head(),
+ v1->getPrev()->head(),
+ v1->getPrev()->tail(), d1->head()));
+*/
+ diagonal_vertices[kk+1] = v1->getPrev();
+ }
+ }
+ }
+}/*end if (root1 not equal to root 2)*/
+}
+
+ /*second pass, now all diagoals should belong to the same polygon*/
+
+
+
+ for(i=0,k=0; i<num_diagonals; i++, k += 2)
+ if(removedDiagonals[i] == 0)
+ {
+
+
+ directedLine* v1=diagonal_vertices[k];
+ directedLine* v2=diagonal_vertices[k+1];
+
+
+
+ directedLine* ret_p1;
+ directedLine* ret_p2;
+
+ /*we ahve to determine whether v1 and v2 belong to the same polygon before
+ *their structure are modified by connectDiagonal().
+ */
+ directedLine *root1 = v1->findRoot();
+/*
+ directedLine *root2 = v2->findRoot();
+
+
+
+ assert(root1);
+ assert(root2);
+ assert(root1 == root2);
+ */
+ sampledLine* generatedLine;
+
+
+
+ v1->connectDiagonal(v1,v2, &ret_p1, &ret_p2, &generatedLine, ret_polygons);
+ newSampledLines = generatedLine->insert(newSampledLines);
+
+ ret_polygons = ret_polygons->cutoffPolygon(root1);
+
+ ret_polygons = ret_p1->insertPolygon(ret_polygons);
+
+ ret_polygons = ret_p2->insertPolygon(ret_polygons);
+
+
+
+ for(Int j=i+1; j<num_diagonals; j++)
+ {
+ if(removedDiagonals[j] ==0)
+ {
+
+ directedLine* temp1=diagonal_vertices[2*j];
+ directedLine* temp2=diagonal_vertices[2*j+1];
+ if(temp1==v1 || temp1==v2 || temp2==v1 || temp2==v2)
+ if(! temp1->samePolygon(temp1, temp2))
+ {
+ /*if temp1 and temp2 are in different polygons,
+ *then one of them must be v1 or v2.
+ */
+
+
+
+ assert(temp1==v1 || temp1 == v2 || temp2==v1 || temp2 ==v2);
+ if(temp1==v1)
+ {
+ diagonal_vertices[2*j] = v2->getPrev();
+ }
+ if(temp2==v1)
+ {
+ diagonal_vertices[2*j+1] = v2->getPrev();
+ }
+ if(temp1==v2)
+ {
+ diagonal_vertices[2*j] = v1->getPrev();
+ }
+ if(temp2==v2)
+ {
+ diagonal_vertices[2*j+1] = v1->getPrev();
+ }
+ }
+ }
+ }
+
+ }
+
+ /*clean up spaces*/
+ free(array);
+ free(ranges);
+ free(diagonal_vertices);
+ free(removedDiagonals);
+
+ *retSampledLines = newSampledLines;
+ return ret_polygons;
+}
+
+/*given a set of simple polygons where the interior
+ *is decided by left-hand principle,
+ *return a range (sight) for each vertex. This is called
+ *Trapezoidalization.
+ */
+void sweepY(Int nVertices, directedLine** sortedVertices, sweepRange** ret_ranges)
+{
+ Int i;
+ /*for each vertex in the sorted list, update the binary search tree.
+ *and store the range information for each vertex.
+ */
+ treeNode* searchTree = NULL;
+ for(i=0; i<nVertices;i++)
+ {
+
+ directedLine* vert = sortedVertices[i];
+
+ directedLine* thisEdge = vert;
+ directedLine* prevEdge = vert->getPrev();
+
+ if(isBelow(vert, thisEdge) && isAbove(vert, prevEdge))
+ {
+
+ /*case 1: this < v < prev
+ *the polygon is going down at v, the interior is to
+ *the right hand side.
+ * find the edge to the right of thisEdge for right range.
+ * delete thisEdge
+ * insert prevEdge
+ */
+ treeNode* thisNode = TreeNodeFind(searchTree, thisEdge, ( Int (*) (void *, void *))compEdges);
+ assert(thisNode);
+
+ treeNode* succ = TreeNodeSuccessor(thisNode);
+ assert(succ);
+ searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
+ searchTree = TreeNodeInsert(searchTree, TreeNodeMake(prevEdge), ( Int (*) (void *, void *))compEdges);
+
+
+ ret_ranges[i] = sweepRangeMake(vert, 0, (directedLine*) (succ->key), 1);
+
+ }
+ else if(isAbove(vert, thisEdge) && isBelow(vert, prevEdge))
+ {
+
+ /*case 2: this > v > prev
+ *the polygon is going up at v, the interior is to
+ *the left hand side.
+ * find the edge to the left of thisEdge for left range.
+ * delete prevEdge
+ * insert thisEdge
+ */
+ treeNode* prevNode = TreeNodeFind(searchTree, prevEdge, ( Int (*) (void *, void *))compEdges);
+ assert(prevNode);
+ treeNode* pred = TreeNodePredecessor(prevNode);
+ searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);
+ searchTree = TreeNodeInsert(searchTree, TreeNodeMake(thisEdge), ( Int (*) (void *, void *))compEdges);
+ ret_ranges[i] = sweepRangeMake((directedLine*)(pred->key), 1, vert, 0);
+ }
+ else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge))
+ {
+
+ /*case 3: insert both edges*/
+ treeNode* thisNode = TreeNodeMake(thisEdge);
+ treeNode* prevNode = TreeNodeMake(prevEdge);
+ searchTree = TreeNodeInsert(searchTree, thisNode, ( Int (*) (void *, void *))compEdges);
+ searchTree = TreeNodeInsert(searchTree, prevNode, ( Int (*) (void *, void *))compEdges);
+ if(compEdges(thisEdge, prevEdge)<0) /*interior cusp*/
+ {
+
+ treeNode* leftEdge = TreeNodePredecessor(thisNode);
+ treeNode* rightEdge = TreeNodeSuccessor(prevNode);
+ ret_ranges[i] = sweepRangeMake( (directedLine*) leftEdge->key, 1,
+ (directedLine*) rightEdge->key, 1
+ );
+ }
+ else /*exterior cusp*/
+ {
+
+ ret_ranges[i] = sweepRangeMake( prevEdge, 1, thisEdge, 1);
+ }
+ }
+ else if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge))
+ {
+
+ /*case 4: delete both edges*/
+ treeNode* thisNode = TreeNodeFind(searchTree, thisEdge, ( Int (*) (void *, void *))compEdges);
+ treeNode* prevNode = TreeNodeFind(searchTree, prevEdge, ( Int (*) (void *, void *))compEdges);
+ if(compEdges(thisEdge, prevEdge)>0) /*interior cusp*/
+ {
+ treeNode* leftEdge = TreeNodePredecessor(prevNode);
+ treeNode* rightEdge = TreeNodeSuccessor(thisNode);
+ ret_ranges[i] = sweepRangeMake( (directedLine*) leftEdge->key, 1,
+ (directedLine*) rightEdge->key, 1
+ );
+ }
+ else /*exterior cusp*/
+ {
+ ret_ranges[i] = sweepRangeMake( thisEdge, 1, prevEdge, 1);
+ }
+ searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
+ searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);
+ }
+ else
+ {
+ fprintf(stderr,"error in partitionY.C, invalid case\n");
+ printf("vert is\n");
+ vert->printSingle();
+ printf("thisEdge is\n");
+ thisEdge->printSingle();
+ printf("prevEdge is\n");
+ prevEdge->printSingle();
+
+ exit(1);
+ }
+ }
+
+ /*finaly clean up space: delete the search tree*/
+ TreeNodeDeleteWholeTree(searchTree);
+}