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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.
+**
+*/
+/*
+ *monoPolyPart.C
+ *
+ *To partition a v-monotone polygon into some uv-monotone polygons.
+ *The algorithm is different from the general monotone partition algorithm.
+ *while the general monotone partition algorithm works for this special case,
+ *but it is more expensive (O(nlogn)). The algorithm implemented here takes
+ *advantage of the fact that the input is a v-monotone polygon and it is
+ *conceptually simpler and computationally cheaper (a linear time algorithm).
+ *The algorithm is described in Zicheng Liu's paper
+ * "Quality-Oriented Linear Time Tessellation".
+ */
+
+#include <stdlib.h>
+#include <stdio.h>
+#include "directedLine.h"
+#include "monoPolyPart.h"
+
+/*a vertex is u_maximal if both of its two neightbors are to the left of this
+ *vertex
+ */
+static Int is_u_maximal(directedLine* v)
+{
+ if (compV2InX(v->getPrev()->head(), v->head()) == -1 &&
+ compV2InX(v->getNext()->head(), v->head()) == -1)
+ return 1;
+ else
+ return 0;
+}
+
+/*a vertex is u_minimal if both of its two neightbors are to the right of this
+ *vertex
+ */
+static Int is_u_minimal(directedLine* v)
+{
+ if (compV2InX(v->getPrev()->head(), v->head()) == 1 &&
+ compV2InX(v->getNext()->head(), v->head()) == 1)
+ return 1;
+ else
+ return 0;
+}
+
+/*poly: a v-monotone polygon
+ *return: a linked list of uv-monotone polygons.
+ */
+directedLine* monoPolyPart(directedLine* polygon)
+{
+ //handle special cases:
+ if(polygon == NULL)
+ return NULL;
+ if(polygon->getPrev() == polygon)
+ return polygon;
+ if(polygon->getPrev() == polygon->getNext())
+ return polygon;
+ if(polygon->getPrev()->getPrev() == polygon->getNext())
+ return polygon;
+
+ //find the top and bottom vertexes
+ directedLine *tempV, *topV, *botV;
+ topV = botV = polygon;
+ for(tempV = polygon->getNext(); tempV != polygon; tempV = tempV->getNext())
+ {
+ if(compV2InY(topV->head(), tempV->head())<0) {
+ topV = tempV;
+ }
+ if(compV2InY(botV->head(), tempV->head())>0) {
+ botV = tempV;
+ }
+ }
+
+ //initilization
+ directedLine *A, *B, *C, *D, *G, *H;
+ //find A:the first u_maximal vertex on the left chain
+ //and C: the left most vertex between top and A
+ A = NULL;
+ C = topV;
+ for(tempV=topV->getNext(); tempV != botV; tempV = tempV->getNext())
+ {
+ if(tempV->head()[0] < C->head()[0])
+ C = tempV;
+
+ if(is_u_maximal(tempV))
+ {
+ A = tempV;
+ break;
+ }
+ }
+ if(A == NULL)
+ {
+ A = botV;
+ if(A->head()[0] < C->head()[0])
+ C = A;
+ }
+
+ //find B: the first u_minimal vertex on the right chain
+ //and D: the right most vertex between top and B
+ B = NULL;
+ D = topV;
+ for(tempV=topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
+ {
+ if(tempV->head()[0] > D->head()[0])
+ D = tempV;
+ if(is_u_minimal(tempV))
+ {
+ B = tempV;
+ break;
+ }
+ }
+ if(B == NULL)
+ {
+ B = botV;
+ if(B->head()[0] > D->head()[0])
+ D = B;
+ }
+
+ //error checking XXX
+ if(C->head()[0] >= D->head()[0])
+ return polygon;
+
+ //find G on the left chain that is right above B
+ for(tempV=topV; compV2InY(tempV->head(), B->head()) == 1; tempV=tempV->getNext());
+ G = tempV->getPrev();
+ //find H on the right chain that is right above A
+ for(tempV=topV; compV2InY(tempV->head(), A->head()) == 1; tempV = tempV->getPrev());
+ H = tempV->getNext();
+
+ //Main Loop
+ directedLine* ret = NULL;
+ directedLine* currentPolygon = polygon;
+ while(1)
+ {
+ //if both B and D are equal to botV, then this polygon is already
+ //u-monotone
+ if(A == botV && B == botV)
+ {
+ ret = currentPolygon->insertPolygon(ret);
+ return ret;
+ }
+ else //not u-monotone
+ {
+ directedLine *ret_p1, *ret_p2;
+ if(compV2InY(A->head(),B->head()) == 1) //A is above B
+ {
+ directedLine* E = NULL;
+ for(tempV = C; tempV != D; tempV = tempV->getPrev())
+ {
+ if(tempV->head()[0] >= A->head()[0])
+ {
+ E = tempV;
+ break;
+ }
+ }
+
+ if(E == NULL)
+ E = D;
+ if(E->head()[0]> H->head()[0])
+ E = H;
+ //connect AE and output polygon ECA
+ polygon->connectDiagonal_2slines(A, E,
+ &ret_p1,
+ &ret_p2,
+ NULL);
+ ret = ret_p2->insertPolygon(ret);
+ currentPolygon = ret_p1;
+
+ if(E == D)
+ D = ret_p1;
+ if(E == H)
+ H = ret_p1;
+ if(G->head()[1] >= A->head()[1])
+ G = A;
+ //update A to be the next u-maxiaml vertex on left chain
+ //and C the leftmost vertex between the old A and the new A
+ C = A;
+ for(tempV = A->getNext(); tempV != botV; tempV = tempV->getNext())
+ {
+
+ if(tempV->head()[0] < C->head()[0])
+ C = tempV;
+ if(is_u_maximal(tempV))
+ {
+ A = tempV;
+ break;
+ }
+ }
+
+ if(tempV == botV)
+ {
+ A = botV;
+ if(botV->head()[0] < C->head()[0])
+ C = botV;
+ }
+ //update H
+
+ if(A == botV)
+ H = botV;
+ else
+ {
+ for(tempV = H; compV2InY(tempV->head(), A->head()) == 1; tempV = tempV->getPrev());
+ H = tempV->getNext();
+ }
+
+ }
+ else //A is below B
+ {
+
+ directedLine* F = NULL;
+ for(tempV = D; tempV != C; tempV = tempV->getNext())
+ {
+ if(tempV->head()[0] <= B->head()[0])
+ {
+ F = tempV;
+ break;
+ }
+ }
+ if(F == NULL)
+ F = C;
+ if(F->head()[0] < G->head()[0])
+ F = G;
+
+ //connect FB
+ polygon->connectDiagonal_2slines(F, B,
+ &ret_p1,
+ &ret_p2,
+ NULL);
+ ret = ret_p2->insertPolygon(ret);
+ currentPolygon = ret_p1;
+ B = ret_p1;
+ if(H ->head()[1] >= B->head()[1])
+ H = ret_p1;
+
+ //update B to be the next u-minimal vertex on right chain
+ //and D the rightmost vertex between the old B and the new B
+ D = B;
+ for(tempV = B->getPrev(); tempV != botV; tempV = tempV->getPrev())
+ {
+ if(tempV->head()[0] > D->head()[0])
+ D = tempV;
+ if(is_u_minimal(tempV))
+ {
+ B = tempV;
+ break;
+ }
+ }
+ if(tempV == botV)
+ {
+ B = botV;
+ if(botV->head()[0] > D->head()[0])
+ D = botV;
+ }
+ //update G
+ if(B == botV)
+ G = botV;
+ else
+ {
+ for(tempV = G; compV2InY(tempV->head(), B->head()) == 1; tempV = tempV->getNext());
+ G = tempV->getPrev();
+ }
+ } //end of A is below B
+ } //end not u-monotone
+ } //end of main loop
+}
+
+
+
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