src/common/triangulate.c

#ifndef lint
static const char RCSid[] = "$Id: triangulate.c,v 2.4 2016/12/22 18:48:36 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

static const double 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 (EPSILON > cross) return EPSILON > -cross ? -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;
}

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, m, 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 ( 0.0 < polyArea(contour) )
    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 */

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

    /* three consecutive vertices in current polygon, <u,v,w> */
    u = v  ; if (nv <= u) u = 0;     /* previous */
    v = u+1; if (nv <= v) v = 0;     /* new v    */
    w = v+1; if (nv <= w) w = 0;     /* next     */

    result = polySnip(contour, u, v, w, nv, V);
    if (result > 0) /* successfully found a triangle */
    {
      int a,b,c;

      /* true names of the vertices */
      a = V[u]; b = V[v]; c = V[w];

      /* output Triangle */
      if (!(*cb)(contour, a, b, c)) return false;
 
      m++;
    }
    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:	2.5
Committed:	Thu Dec 22 18:50:48 2016 UTC (7 years, 4 months ago) by greg
Content type:	text/plain
Branch:	MAIN
CVS Tags:	rad5R2, rad5R1, rad5R3
Changes since 2.4:	+4 -2 lines
Log Message:	Added comment regarding last change.
#	User	Rev	Content
1	greg	2.1	#ifndef lint
2	greg	2.5	static const char RCSid[] = "$Id: triangulate.c,v 2.4 2016/12/22 18:48:36 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			static const double EPSILON = 0.0000000001;
38
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			if (EPSILON > cross) return EPSILON > -cross ? -1 : false; /* Negative if colinear points */
56	greg	2.1
57			for (p=0;p<n;p++)
58			{
59	greg	2.3	if( (p == u) \| (p == v) \| (p == w) ) continue;
60	greg	2.1	Px = contour->v[V[p]].mX;
61			Py = contour->v[V[p]].mY;
62	greg	2.4	if ((Px == Ax && Py == Ay) \|\| (Px == Bx && Py == By) \|\|
63			(Px == Cx && Py == Cy)) continue; /* Handle donuts */
64	greg	2.1	if (insideTriangle(Ax,Ay,Bx,By,Cx,Cy,Px,Py)) return false;
65			}
66
67			return true;
68			}
69
70			Vert2_list *
71			polyAlloc(int nv)
72			{
73			Vert2_list *pnew;
74
75			if (nv < 3) return NULL;
76
77			pnew = (Vert2_list )malloc(sizeof(Vert2_list) + sizeof(Vert2)(nv-3));
78			if (pnew == NULL) return NULL;
79			pnew->nv = nv;
80			pnew->p = NULL;
81
82			return pnew;
83			}
84
85			double
86			polyArea(const Vert2_list *contour)
87			{
88			double A=0.0;
89			int p, q;
90
91			for(p = contour->nv-1, q = 0; q < contour->nv; p=q++)
92			{
93			A += contour->v[p].mXcontour->v[q].mY - contour->v[q].mXcontour->v[p].mY;
94			}
95			return A*0.5;
96			}
97
98			/*
99			InsideTriangle decides if a point P is Inside of the triangle
100			defined by A, B, C.
101			*/
102			int
103			insideTriangle(double Ax, double Ay,
104			double Bx, double By,
105			double Cx, double Cy,
106			double Px, double Py)
107
108			{
109			double ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
110			double cCROSSap, bCROSScp, aCROSSbp;
111
112			ax = Cx - Bx; ay = Cy - By;
113			bx = Ax - Cx; by = Ay - Cy;
114			cx = Bx - Ax; cy = By - Ay;
115			apx= Px - Ax; apy= Py - Ay;
116			bpx= Px - Bx; bpy= Py - By;
117			cpx= Px - Cx; cpy= Py - Cy;
118
119			aCROSSbp = axbpy - aybpx;
120			cCROSSap = cxapy - cyapx;
121			bCROSScp = bxcpy - bycpx;
122
123			return ((aCROSSbp >= 0.0) && (bCROSScp >= 0.0) && (cCROSSap >= 0.0));
124			};
125
126			int
127			polyTriangulate(const Vert2_list contour, tri_out_t cb)
128			{
129			/* allocate and initialize list of Vertices in polygon */
130
131	greg	2.4	int nv, m, u, v, w, count, result;
132	greg	2.1	int *V;
133
134			if ( contour->nv < 3 ) return false;
135
136			V = (int )malloc(sizeof(int)contour->nv);
137			if (V == NULL) return false;
138
139			/* we want a counter-clockwise polygon in V */
140
141	greg	2.2	if ( 0.0 < polyArea(contour) )
142	greg	2.1	for (v=0; v<contour->nv; v++) V[v] = v;
143			else
144			for(v=0; v<contour->nv; v++) V[v] = (contour->nv-1)-v;
145
146			nv = contour->nv;
147
148			/* remove nv-2 Vertices, creating 1 triangle every time */
149			count = 2nv; / error detection */
150
151			for(m=0, v=nv-1; nv>2; )
152			{
153			/* if we loop, it is probably a non-simple polygon */
154	greg	2.3	if (0 >= count--)
155	greg	2.1	{
156	greg	2.3	/* Triangulate: ERROR - probable bad polygon */
157	greg	2.1	return false;
158			}
159
160			/* three consecutive vertices in current polygon, <u,v,w> */
161			u = v ; if (nv <= u) u = 0; /* previous */
162			v = u+1; if (nv <= v) v = 0; /* new v */
163			w = v+1; if (nv <= w) w = 0; /* next */
164
165	greg	2.4	result = polySnip(contour, u, v, w, nv, V);
166			if (result > 0) /* successfully found a triangle */
167	greg	2.1	{
168	greg	2.4	int a,b,c;
169	greg	2.1
170			/* true names of the vertices */
171			a = V[u]; b = V[v]; c = V[w];
172
173			/* output Triangle */
174	greg	2.2	if (!(*cb)(contour, a, b, c)) return false;
175	greg	2.1
176			m++;
177	greg	2.4	}
178			if (result) /* successfully found a triangle or three consecutive colinear points */
179			{
180			int s,t;
181	greg	2.1
182			/* remove v from remaining polygon */
183			for(s=v,t=v+1;t<nv;s++,t++) V[s] = V[t]; nv--;
184
185	greg	2.3	/* reset error detection counter */
186	greg	2.1	count = 2*nv;
187			}
188			}
189
190			free(V);
191
192			return true;
193			}