src/common/triangulate.c

#ifndef lint
static const char RCSid[] = "$Id: triangulate.c,v 2.6 2021/04/19 19:40:03 greg Exp $";
#endif
/*
 *  triangulate.c
 *  
 *  Adapted by Greg Ward on 1/23/14.
 *  Fixes for polygons with seams/holes and co-linear vertices added
 *  by Nathaniel Jones on 12/21/16.
 *  Copyright 2016 Anyhere Software. All rights reserved.
 *
 */

/* COTD Entry submitted by John W. Ratcliff [[email protected]]

// ** THIS IS A CODE SNIPPET WHICH WILL EFFICIEINTLY TRIANGULATE ANY
// ** POLYGON/CONTOUR (without holes) AS A STATIC CLASS.  THIS SNIPPET
// ** IS COMPRISED OF 3 FILES, TRIANGULATE.H, THE HEADER FILE FOR THE
// ** TRIANGULATE BASE CLASS, TRIANGULATE.CPP, THE IMPLEMENTATION OF
// ** THE TRIANGULATE BASE CLASS, AND TEST.CPP, A SMALL TEST PROGRAM
// ** DEMONSTRATING THE USAGE OF THE TRIANGULATOR.  THE TRIANGULATE
// ** BASE CLASS ALSO PROVIDES TWO USEFUL HELPER METHODS, ONE WHICH
// ** COMPUTES THE AREA OF A POLYGON, AND ANOTHER WHICH DOES AN EFFICENT
// ** POINT IN A TRIANGLE TEST.
// ** SUBMITTED BY JOHN W. RATCLIFF ([email protected]) July 22, 2000
*/

#include <stdio.h>
#include <stdlib.h>
#include "triangulate.h"

#ifndef true
#define true    1
#define false   0
#endif

#define EPSILON         0.0000000001

static int
polySnip(const Vert2_list *contour, int u, int v, int w, int n, int *V)
{
  int p;
  double Ax, Ay, Bx, By, Cx, Cy, Px, Py, cross;

  Ax = contour->v[V[u]].mX;
  Ay = contour->v[V[u]].mY;

  Bx = contour->v[V[v]].mX;
  By = contour->v[V[v]].mY;

  Cx = contour->v[V[w]].mX;
  Cy = contour->v[V[w]].mY;

  cross = ((Bx - Ax)*(Cy - Ay)) - ((By - Ay)*(Cx - Ax));
  if (cross < EPSILON)
        return cross > -EPSILON ? -1 : false; /* Negative if colinear points */

  for (p=0;p<n;p++)
  {
    if( (p == u) | (p == v) | (p == w) ) continue;
    Px = contour->v[V[p]].mX;
    Py = contour->v[V[p]].mY;
    if ((Px == Ax) & (Py == Ay) || (Px == Bx) & (Py == By) ||
                (Px == Cx) & (Py == Cy)) continue; /* Handle donuts */
    if (insideTriangle(Ax,Ay,Bx,By,Cx,Cy,Px,Py)) return false;
  }

  return true;
}

Vert2_list *
polyAlloc(int nv)
{
        Vert2_list      *pnew;

        if (nv < 3) return NULL;
        
        pnew = (Vert2_list *)malloc(sizeof(Vert2_list) + sizeof(Vert2)*(nv-3));
        if (pnew == NULL) return NULL;
        pnew->nv = nv;
        pnew->p = NULL;
        
        return pnew;
}

/*
  Area is positive if vertices listed counter-clockwise, negative if clockwise
 */
double
polyArea(const Vert2_list *contour)
{
  double A=0.0;
  int   p, q;

  for(p = contour->nv-1, q = 0; q < contour->nv; p=q++)
  {
    A += contour->v[p].mX*contour->v[q].mY - contour->v[q].mX*contour->v[p].mY;
  }
  return A*0.5;
}

/*
  InsideTriangle decides if a point P is Inside of the triangle
  defined by A, B, C.
*/
int
insideTriangle(double Ax, double Ay,
                      double Bx, double By,
                      double Cx, double Cy,
                      double Px, double Py)
{
  double ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
  double cCROSSap, bCROSScp, aCROSSbp;

  ax = Cx - Bx;  ay = Cy - By;
  bx = Ax - Cx;  by = Ay - Cy;
  cx = Bx - Ax;  cy = By - Ay;
  apx= Px - Ax;  apy= Py - Ay;
  bpx= Px - Bx;  bpy= Py - By;
  cpx= Px - Cx;  cpy= Py - Cy;

  aCROSSbp = ax*bpy - ay*bpx;
  cCROSSap = cx*apy - cy*apx;
  bCROSScp = bx*cpy - by*cpx;

  return ((aCROSSbp >= 0.0) & (bCROSScp >= 0.0) & (cCROSSap >= 0.0));
};

int
polyTriangulate(const Vert2_list *contour, tri_out_t *cb)
{
  /* allocate and initialize list of Vertices in polygon */

  int nv, u, v, w, count, result;
  int *V;

  if ( contour->nv < 3 ) return false;

  V = (int *)malloc(sizeof(int)*contour->nv);
  if (V == NULL) return false;

  /* we want a counter-clockwise polygon in V */

  if ( polyArea(contour) > 0.0 )
    for (v=0; v<contour->nv; v++) V[v] = v;
  else
    for (v=0; v<contour->nv; v++) V[v] = (contour->nv-1)-v;

  nv = contour->nv;

  /*  remove nv-2 Vertices, creating 1 triangle every time */
  count = 2*nv;   /* error detection */

  v = nv-1;
  while (nv > 2)
  {
    /* if we loop, it is probably a non-simple polygon */
    if (count-- <= 0)
    {
      /* Triangulate: ERROR - probable bad polygon */
      free(V);
      return false;
    }

    /* three consecutive vertices in current polygon, <u,v,w> */
    u = v  ; u *= (nv > u);     /* previous */
    v = u+1; v *= (nv > v);     /* new v    */
    w = v+1; w *= (nv > w);     /* next     */

    result = polySnip(contour, u, v, w, nv, V);
    if (result > 0) /* successfully found a triangle */
    {
      /* output Triangle */
      if (!(*cb)(contour, V[u], V[v], V[w])) {
        free(V);
        return false;
      }
    }
    if (result) /* successfully found a triangle or three consecutive colinear points */
    {
      int s,t;

      /* remove v from remaining polygon */
      for(s=v,t=v+1;t<nv;s++,t++) V[s] = V[t]; nv--;

      /* reset error detection counter */
      count = 2*nv;
    }
  }

  free(V);

  return true;
}
Revision:	2.7
Committed:	Mon Apr 19 20:37:04 2021 UTC (4 years, 6 months ago) by greg
Content type:	text/plain
Branch:	MAIN
CVS Tags:	rad5R4, rad6R0, HEAD
Changes since 2.6:	+2 -2 lines
Log Message:	fix: Repaired issue in last change with colinear vertices
#	User	Rev	Content
1	greg	2.1	#ifndef lint
2	greg	2.7	static const char RCSid[] = "$Id: triangulate.c,v 2.6 2021/04/19 19:40:03 greg Exp $";
3	greg	2.1	#endif
4			/*
5			* triangulate.c
6			*
7			* Adapted by Greg Ward on 1/23/14.
8	greg	2.5	* Fixes for polygons with seams/holes and co-linear vertices added
9			* by Nathaniel Jones on 12/21/16.
10			* Copyright 2016 Anyhere Software. All rights reserved.
11	greg	2.1	*
12			*/
13
14			/* COTD Entry submitted by John W. Ratcliff [[email protected]]
15
16			// ** THIS IS A CODE SNIPPET WHICH WILL EFFICIEINTLY TRIANGULATE ANY
17			// ** POLYGON/CONTOUR (without holes) AS A STATIC CLASS. THIS SNIPPET
18			// ** IS COMPRISED OF 3 FILES, TRIANGULATE.H, THE HEADER FILE FOR THE
19			// ** TRIANGULATE BASE CLASS, TRIANGULATE.CPP, THE IMPLEMENTATION OF
20			// ** THE TRIANGULATE BASE CLASS, AND TEST.CPP, A SMALL TEST PROGRAM
21			// ** DEMONSTRATING THE USAGE OF THE TRIANGULATOR. THE TRIANGULATE
22			// ** BASE CLASS ALSO PROVIDES TWO USEFUL HELPER METHODS, ONE WHICH
23			// ** COMPUTES THE AREA OF A POLYGON, AND ANOTHER WHICH DOES AN EFFICENT
24			// ** POINT IN A TRIANGLE TEST.
25			// ** SUBMITTED BY JOHN W. RATCLIFF ([email protected]) July 22, 2000
26			*/
27
28			#include <stdio.h>
29			#include <stdlib.h>
30			#include "triangulate.h"
31
32			#ifndef true
33			#define true 1
34			#define false 0
35			#endif
36
37	greg	2.6	#define EPSILON 0.0000000001
38	greg	2.1
39			static int
40			polySnip(const Vert2_list contour, int u, int v, int w, int n, int V)
41			{
42			int p;
43	greg	2.4	double Ax, Ay, Bx, By, Cx, Cy, Px, Py, cross;
44	greg	2.1
45			Ax = contour->v[V[u]].mX;
46			Ay = contour->v[V[u]].mY;
47
48			Bx = contour->v[V[v]].mX;
49			By = contour->v[V[v]].mY;
50
51			Cx = contour->v[V[w]].mX;
52			Cy = contour->v[V[w]].mY;
53
54	greg	2.4	cross = ((Bx - Ax)(Cy - Ay)) - ((By - Ay)(Cx - Ax));
55	greg	2.6	if (cross < EPSILON)
56	greg	2.7	return cross > -EPSILON ? -1 : false; /* Negative if colinear points */
57	greg	2.1
58			for (p=0;p<n;p++)
59			{
60	greg	2.3	if( (p == u) \| (p == v) \| (p == w) ) continue;
61	greg	2.1	Px = contour->v[V[p]].mX;
62			Py = contour->v[V[p]].mY;
63	greg	2.6	if ((Px == Ax) & (Py == Ay) \|\| (Px == Bx) & (Py == By) \|\|
64			(Px == Cx) & (Py == Cy)) continue; /* Handle donuts */
65	greg	2.1	if (insideTriangle(Ax,Ay,Bx,By,Cx,Cy,Px,Py)) return false;
66			}
67
68			return true;
69			}
70
71			Vert2_list *
72			polyAlloc(int nv)
73			{
74			Vert2_list *pnew;
75
76			if (nv < 3) return NULL;
77
78			pnew = (Vert2_list )malloc(sizeof(Vert2_list) + sizeof(Vert2)(nv-3));
79			if (pnew == NULL) return NULL;
80			pnew->nv = nv;
81			pnew->p = NULL;
82
83			return pnew;
84			}
85
86	greg	2.6	/*
87			Area is positive if vertices listed counter-clockwise, negative if clockwise
88			*/
89	greg	2.1	double
90			polyArea(const Vert2_list *contour)
91			{
92			double A=0.0;
93			int p, q;
94
95			for(p = contour->nv-1, q = 0; q < contour->nv; p=q++)
96			{
97			A += contour->v[p].mXcontour->v[q].mY - contour->v[q].mXcontour->v[p].mY;
98			}
99			return A*0.5;
100			}
101
102			/*
103			InsideTriangle decides if a point P is Inside of the triangle
104			defined by A, B, C.
105			*/
106			int
107			insideTriangle(double Ax, double Ay,
108			double Bx, double By,
109			double Cx, double Cy,
110			double Px, double Py)
111			{
112			double ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
113			double cCROSSap, bCROSScp, aCROSSbp;
114
115			ax = Cx - Bx; ay = Cy - By;
116			bx = Ax - Cx; by = Ay - Cy;
117			cx = Bx - Ax; cy = By - Ay;
118			apx= Px - Ax; apy= Py - Ay;
119			bpx= Px - Bx; bpy= Py - By;
120			cpx= Px - Cx; cpy= Py - Cy;
121
122			aCROSSbp = axbpy - aybpx;
123			cCROSSap = cxapy - cyapx;
124			bCROSScp = bxcpy - bycpx;
125
126	greg	2.6	return ((aCROSSbp >= 0.0) & (bCROSScp >= 0.0) & (cCROSSap >= 0.0));
127	greg	2.1	};
128
129			int
130			polyTriangulate(const Vert2_list contour, tri_out_t cb)
131			{
132			/* allocate and initialize list of Vertices in polygon */
133
134	greg	2.6	int nv, u, v, w, count, result;
135	greg	2.1	int *V;
136
137			if ( contour->nv < 3 ) return false;
138
139			V = (int )malloc(sizeof(int)contour->nv);
140			if (V == NULL) return false;
141
142			/* we want a counter-clockwise polygon in V */
143
144	greg	2.6	if ( polyArea(contour) > 0.0 )
145	greg	2.1	for (v=0; v<contour->nv; v++) V[v] = v;
146			else
147	greg	2.6	for (v=0; v<contour->nv; v++) V[v] = (contour->nv-1)-v;
148	greg	2.1
149			nv = contour->nv;
150
151			/* remove nv-2 Vertices, creating 1 triangle every time */
152			count = 2nv; / error detection */
153
154	greg	2.6	v = nv-1;
155			while (nv > 2)
156	greg	2.1	{
157			/* if we loop, it is probably a non-simple polygon */
158	greg	2.6	if (count-- <= 0)
159	greg	2.1	{
160	greg	2.3	/* Triangulate: ERROR - probable bad polygon */
161	greg	2.6	free(V);
162	greg	2.1	return false;
163			}
164
165			/* three consecutive vertices in current polygon, <u,v,w> */
166	greg	2.6	u = v ; u = (nv > u); / previous */
167			v = u+1; v = (nv > v); / new v */
168			w = v+1; w = (nv > w); / next */
169	greg	2.1
170	greg	2.4	result = polySnip(contour, u, v, w, nv, V);
171			if (result > 0) /* successfully found a triangle */
172	greg	2.1	{
173			/* output Triangle */
174	greg	2.6	if (!(*cb)(contour, V[u], V[v], V[w])) {
175			free(V);
176			return false;
177			}
178	greg	2.4	}
179			if (result) /* successfully found a triangle or three consecutive colinear points */
180			{
181			int s,t;
182	greg	2.1
183			/* remove v from remaining polygon */
184			for(s=v,t=v+1;t<nv;s++,t++) V[s] = V[t]; nv--;
185
186	greg	2.3	/* reset error detection counter */
187	greg	2.1	count = 2*nv;
188			}
189			}
190
191			free(V);
192
193			return true;
194			}