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//--------------------------------------------------------------------------
//
// File: delaunay.c
//
// Created: 04/08/2000
//
// Author: Pavel Sakov
// CSIRO Marine Research
//
// Purpose: Delaunay triangulation - a wrapper to triangulate()
//
// Description: None
//
// Revisions: 10/06/2003 PS: delaunay_build(); delaunay_destroy();
// struct delaunay: from now on, only shallow copy of the
// input data is contained in struct delaunay. This saves
// memory and is consistent with libcsa.
//
// Modified: Joao Cardoso, 4/2/2003
// Adapted for use with Qhull instead of "triangle".
// Andrew Ross 20/10/2008
// Fix bug in delaunay_circles_find() when checking
// whether a circle has been found.
//
//--------------------------------------------------------------------------
#define USE_QHULL
#include <stdlib.h>
#include <stdio.h>
#include <assert.h>
#include <math.h>
#include <string.h>
#include <limits.h>
#include <float.h>
#ifdef USE_QHULL
#include <qhull/qhull_a.h>
#else
#include "triangle.h"
#endif
#include "istack.h"
#include "nan.h"
#include "delaunay.h"
int circle_build( circle* c, point* p0, point* p1, point* p2 );
int circle_contains( circle* c, point* p );
int delaunay_xytoi( delaunay* d, point* p, int id );
void delaunay_circles_find( delaunay* d, point* p, int* n, int** out );
#ifdef USE_QHULL
static int cw( delaunay *d, triangle *t );
#endif
#ifndef USE_QHULL
static void tio_init( struct triangulateio* tio )
{
tio->pointlist = NULL;
tio->pointattributelist = NULL;
tio->pointmarkerlist = NULL;
tio->numberofpoints = 0;
tio->numberofpointattributes = 0;
tio->trianglelist = NULL;
tio->triangleattributelist = NULL;
tio->trianglearealist = NULL;
tio->neighborlist = NULL;
tio->numberoftriangles = 0;
tio->numberofcorners = 0;
tio->numberoftriangleattributes = 0;
tio->segmentlist = 0;
tio->segmentmarkerlist = NULL;
tio->numberofsegments = 0;
tio->holelist = NULL;
tio->numberofholes = 0;
tio->regionlist = NULL;
tio->numberofregions = 0;
tio->edgelist = NULL;
tio->edgemarkerlist = NULL;
tio->normlist = NULL;
tio->numberofedges = 0;
}
static void tio_destroy( struct triangulateio* tio )
{
if ( tio->pointlist != NULL )
free( tio->pointlist );
if ( tio->pointattributelist != NULL )
free( tio->pointattributelist );
if ( tio->pointmarkerlist != NULL )
free( tio->pointmarkerlist );
if ( tio->trianglelist != NULL )
free( tio->trianglelist );
if ( tio->triangleattributelist != NULL )
free( tio->triangleattributelist );
if ( tio->trianglearealist != NULL )
free( tio->trianglearealist );
if ( tio->neighborlist != NULL )
free( tio->neighborlist );
if ( tio->segmentlist != NULL )
free( tio->segmentlist );
if ( tio->segmentmarkerlist != NULL )
free( tio->segmentmarkerlist );
if ( tio->holelist != NULL )
free( tio->holelist );
if ( tio->regionlist != NULL )
free( tio->regionlist );
if ( tio->edgelist != NULL )
free( tio->edgelist );
if ( tio->edgemarkerlist != NULL )
free( tio->edgemarkerlist );
if ( tio->normlist != NULL )
free( tio->normlist );
}
static delaunay* delaunay_create()
{
delaunay* d = malloc( sizeof ( delaunay ) );
d->npoints = 0;
d->points = NULL;
d->xmin = DBL_MAX;
d->xmax = -DBL_MAX;
d->ymin = DBL_MAX;
d->ymax = -DBL_MAX;
d->ntriangles = 0;
d->triangles = NULL;
d->circles = NULL;
d->neighbours = NULL;
d->n_point_triangles = NULL;
d->point_triangles = NULL;
d->nedges = 0;
d->edges = NULL;
d->flags = NULL;
d->first_id = -1;
d->t_in = NULL;
d->t_out = NULL;
return d;
}
static void tio2delaunay( struct triangulateio* tio_out, delaunay* d )
{
int i, j;
//
// I assume that all input points appear in tio_out in the same order as
// they were written to tio_in. I have seen no exceptions so far, even
// if duplicate points were presented. Just in case, let us make a couple
// of checks.
//
assert( tio_out->numberofpoints == d->npoints );
assert( tio_out->pointlist[2 * d->npoints - 2] == d->points[d->npoints - 1].x && tio_out->pointlist[2 * d->npoints - 1] == d->points[d->npoints - 1].y );
for ( i = 0, j = 0; i < d->npoints; ++i )
{
point* p = &d->points[i];
if ( p->x < d->xmin )
d->xmin = p->x;
if ( p->x > d->xmax )
d->xmax = p->x;
if ( p->y < d->ymin )
d->ymin = p->y;
if ( p->y > d->ymax )
d->ymax = p->y;
}
if ( nn_verbose )
{
fprintf( stderr, "input:\n" );
for ( i = 0, j = 0; i < d->npoints; ++i )
{
point* p = &d->points[i];
fprintf( stderr, " %d: %15.7g %15.7g %15.7g\n", i, p->x, p->y, p->z );
}
}
d->ntriangles = tio_out->numberoftriangles;
if ( d->ntriangles > 0 )
{
d->triangles = malloc( d->ntriangles * sizeof ( triangle ) );
d->neighbours = malloc( d->ntriangles * sizeof ( triangle_neighbours ) );
d->circles = malloc( d->ntriangles * sizeof ( circle ) );
d->n_point_triangles = calloc( d->npoints, sizeof ( int ) );
d->point_triangles = malloc( d->npoints * sizeof ( int* ) );
d->flags = calloc( d->ntriangles, sizeof ( int ) );
}
if ( nn_verbose )
fprintf( stderr, "triangles:\n" );
for ( i = 0; i < d->ntriangles; ++i )
{
int offset = i * 3;
triangle * t = &d->triangles[i];
triangle_neighbours* n = &d->neighbours[i];
circle * c = &d->circles[i];
t->vids[0] = tio_out->trianglelist[offset];
t->vids[1] = tio_out->trianglelist[offset + 1];
t->vids[2] = tio_out->trianglelist[offset + 2];
n->tids[0] = tio_out->neighborlist[offset];
n->tids[1] = tio_out->neighborlist[offset + 1];
n->tids[2] = tio_out->neighborlist[offset + 2];
circle_build( c, &d->points[t->vids[0]], &d->points[t->vids[1]], &d->points[t->vids[2]] );
if ( nn_verbose )
fprintf( stderr, " %d: (%d,%d,%d)\n", i, t->vids[0], t->vids[1], t->vids[2] );
}
for ( i = 0; i < d->ntriangles; ++i )
{
triangle* t = &d->triangles[i];
for ( j = 0; j < 3; ++j )
d->n_point_triangles[t->vids[j]]++;
}
if ( d->ntriangles > 0 )
{
for ( i = 0; i < d->npoints; ++i )
{
if ( d->n_point_triangles[i] > 0 )
d->point_triangles[i] = malloc( d->n_point_triangles[i] * sizeof ( int ) );
else
d->point_triangles[i] = NULL;
d->n_point_triangles[i] = 0;
}
}
for ( i = 0; i < d->ntriangles; ++i )
{
triangle* t = &d->triangles[i];
for ( j = 0; j < 3; ++j )
{
int vid = t->vids[j];
d->point_triangles[vid][d->n_point_triangles[vid]] = i;
d->n_point_triangles[vid]++;
}
}
if ( tio_out->edgelist != NULL )
{
d->nedges = tio_out->numberofedges;
d->edges = malloc( d->nedges * 2 * sizeof ( int ) );
memcpy( d->edges, tio_out->edgelist, d->nedges * 2 * sizeof ( int ) );
}
}
#endif
// Builds Delaunay triangulation of the given array of points.
//
// @param np Number of points
// @param points Array of points [np] (input)
// @param ns Number of forced segments
// @param segments Array of (forced) segment endpoint indices [2*ns]
// @param nh Number of holes
// @param holes Array of hole (x,y) coordinates [2*nh]
// @return Delaunay triangulation structure with triangulation results
//
delaunay* delaunay_build( int np, point points[], int ns, int segments[], int nh, double holes[] )
#ifndef USE_QHULL
{
delaunay * d = delaunay_create();
struct triangulateio tio_in;
struct triangulateio tio_out;
char cmd[64] = "eznC";
int i, j;
assert( sizeof ( REAL ) == sizeof ( double ) );
tio_init( &tio_in );
if ( np == 0 )
{
free( d );
return NULL;
}
tio_in.pointlist = malloc( np * 2 * sizeof ( double ) );
tio_in.numberofpoints = np;
for ( i = 0, j = 0; i < np; ++i )
{
tio_in.pointlist[j++] = points[i].x;
tio_in.pointlist[j++] = points[i].y;
}
if ( ns > 0 )
{
tio_in.segmentlist = malloc( ns * 2 * sizeof ( int ) );
tio_in.numberofsegments = ns;
memcpy( tio_in.segmentlist, segments, ns * 2 * sizeof ( int ) );
}
if ( nh > 0 )
{
tio_in.holelist = malloc( nh * 2 * sizeof ( double ) );
tio_in.numberofholes = nh;
memcpy( tio_in.holelist, holes, nh * 2 * sizeof ( double ) );
}
tio_init( &tio_out );
if ( !nn_verbose )
strcat( cmd, "Q" );
else if ( nn_verbose > 1 )
strcat( cmd, "VV" );
if ( ns != 0 )
strcat( cmd, "p" );
if ( nn_verbose )
fflush( stderr );
//
// climax
//
triangulate( cmd, &tio_in, &tio_out, NULL );
if ( nn_verbose )
fflush( stderr );
d->npoints = np;
d->points = points;
tio2delaunay( &tio_out, d );
tio_destroy( &tio_in );
tio_destroy( &tio_out );
return d;
}
#else // USE_QHULL
{
delaunay* d = malloc( sizeof ( delaunay ) );
coordT *qpoints; // array of coordinates for each point
boolT ismalloc = False; // True if qhull should free points
char flags[64] = "qhull d Qbb Qt"; // option flags for qhull
facetT *facet, *neighbor, **neighborp; // variables to walk through facets
vertexT *vertex, **vertexp; // variables to walk through vertex
int curlong, totlong; // memory remaining after qh_memfreeshort
FILE *outfile = stdout;
FILE *errfile = stderr; // error messages from qhull code
int i, j;
int exitcode;
int dim, ntriangles;
int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
(void) segments; // Cast to void to suppress compiler warnings about unused parameters
(void) holes;
dim = 2;
assert( sizeof ( realT ) == sizeof ( double ) ); // Qhull was compiled with doubles?
if ( np == 0 || ns > 0 || nh > 0 )
{
fprintf( stderr, "segments=%d holes=%d\n, aborting Qhull implementation, use 'triangle' instead.\n", ns, nh );
free( d );
return NULL;
}
qpoints = (coordT *) malloc( (size_t) ( np * ( dim + 1 ) ) * sizeof ( coordT ) );
for ( i = 0; i < np; i++ )
{
qpoints[i * dim] = points[i].x;
qpoints[i * dim + 1] = points[i].y;
}
if ( !nn_verbose )
outfile = NULL;
if ( nn_verbose )
strcat( flags, " s" );
if ( nn_verbose > 1 )
strcat( flags, " Ts" );
if ( nn_verbose )
fflush( stderr );
//
// climax
//
exitcode = qh_new_qhull( dim, np, qpoints, ismalloc,
flags, outfile, errfile );
if ( !exitcode )
{
if ( nn_verbose )
fflush( stderr );
d->xmin = DBL_MAX;
d->xmax = -DBL_MAX;
d->ymin = DBL_MAX;
d->ymax = -DBL_MAX;
d->npoints = np;
d->points = malloc( (size_t) np * sizeof ( point ) );
for ( i = 0; i < np; ++i )
{
point* p = &d->points[i];
p->x = points[i].x;
p->y = points[i].y;
p->z = points[i].z;
if ( p->x < d->xmin )
d->xmin = p->x;
if ( p->x > d->xmax )
d->xmax = p->x;
if ( p->y < d->ymin )
d->ymin = p->y;
if ( p->y > d->ymax )
d->ymax = p->y;
}
if ( nn_verbose )
{
fprintf( stderr, "input:\n" );
for ( i = 0; i < np; ++i )
{
point* p = &d->points[i];
fprintf( stderr, " %d: %15.7g %15.7g %15.7g\n",
i, p->x, p->y, p->z );
}
}
qh_findgood_all( qh facet_list );
qh_countfacets( qh facet_list, NULL, !qh_ALL, &numfacets,
&numsimplicial, &totneighbors, &numridges,
&numcoplanars, &numtricoplanars );
ntriangles = 0;
FORALLfacets {
if ( !facet->upperdelaunay && facet->simplicial )
ntriangles++;
}
d->ntriangles = ntriangles;
d->triangles = malloc( (size_t) d->ntriangles * sizeof ( triangle ) );
d->neighbours = malloc( (size_t) d->ntriangles * sizeof ( triangle_neighbours ) );
d->circles = malloc( (size_t) d->ntriangles * sizeof ( circle ) );
if ( nn_verbose )
fprintf( stderr, "triangles:\tneighbors:\n" );
i = 0;
FORALLfacets {
if ( !facet->upperdelaunay && facet->simplicial )
{
triangle * t = &d->triangles[i];
triangle_neighbours* n = &d->neighbours[i];
circle * c = &d->circles[i];
j = 0;
FOREACHvertex_( facet->vertices )
t->vids[j++] = qh_pointid( vertex->point );
j = 0;
FOREACHneighbor_( facet )
n->tids[j++] = ( neighbor->visitid > 0 ) ? (int) neighbor->visitid - 1 : -1;
// Put triangle vertices in counterclockwise order, as
// 'triangle' do.
// The same needs to be done with the neighbors.
//
// The following works, i.e., it seems that Qhull maintains a
// relationship between the vertices and the neighbors
// triangles, but that is not said anywhere, so if this stop
// working in a future Qhull release, you know what you have
// to do, reorder the neighbors.
//
if ( cw( d, t ) )
{
int tmp = t->vids[1];
t->vids[1] = t->vids[2];
t->vids[2] = tmp;
tmp = n->tids[1];
n->tids[1] = n->tids[2];
n->tids[2] = tmp;
}
circle_build( c, &d->points[t->vids[0]], &d->points[t->vids[1]],
&d->points[t->vids[2]] );
if ( nn_verbose )
fprintf( stderr, " %d: (%d,%d,%d)\t(%d,%d,%d)\n",
i, t->vids[0], t->vids[1], t->vids[2], n->tids[0],
n->tids[1], n->tids[2] );
i++;
}
}
d->flags = calloc( (size_t) ( d->ntriangles ), sizeof ( int ) );
d->n_point_triangles = calloc( (size_t) ( d->npoints ), sizeof ( int ) );
for ( i = 0; i < d->ntriangles; ++i )
{
triangle* t = &d->triangles[i];
for ( j = 0; j < 3; ++j )
d->n_point_triangles[t->vids[j]]++;
}
d->point_triangles = malloc( (size_t) ( d->npoints ) * sizeof ( int* ) );
for ( i = 0; i < d->npoints; ++i )
{
if ( d->n_point_triangles[i] > 0 )
d->point_triangles[i] = malloc( (size_t) ( d->n_point_triangles[i] ) * sizeof ( int ) );
else
d->point_triangles[i] = NULL;
d->n_point_triangles[i] = 0;
}
for ( i = 0; i < d->ntriangles; ++i )
{
triangle* t = &d->triangles[i];
for ( j = 0; j < 3; ++j )
{
int vid = t->vids[j];
d->point_triangles[vid][d->n_point_triangles[vid]] = i;
d->n_point_triangles[vid]++;
}
}
d->nedges = 0;
d->edges = NULL;
d->t_in = NULL;
d->t_out = NULL;
d->first_id = -1;
}
else
{
free( d );
d = NULL;
}
free( qpoints );
qh_freeqhull( !qh_ALL ); // free long memory
qh_memfreeshort( &curlong, &totlong ); // free short memory and memory allocator
if ( curlong || totlong )
fprintf( errfile,
"qhull: did not free %d bytes of long memory (%d pieces)\n",
totlong, curlong );
return d;
}
// returns 1 if a,b,c are clockwise ordered
static int cw( delaunay *d, triangle *t )
{
point* pa = &d->points[t->vids[0]];
point* pb = &d->points[t->vids[1]];
point* pc = &d->points[t->vids[2]];
return ( ( pb->x - pa->x ) * ( pc->y - pa->y ) <
( pc->x - pa->x ) * ( pb->y - pa->y ) );
}
#endif
// Releases memory engaged in the Delaunay triangulation structure.
//
// @param d Structure to be destroyed
//
void delaunay_destroy( delaunay* d )
{
if ( d == NULL )
return;
if ( d->point_triangles != NULL )
{
int i;
for ( i = 0; i < d->npoints; ++i )
if ( d->point_triangles[i] != NULL )
free( d->point_triangles[i] );
free( d->point_triangles );
}
if ( d->nedges > 0 )
free( d->edges );
#ifdef USE_QHULL
// This is a shallow copy if we're not using qhull so we don't
// need to free it
if ( d->points != NULL )
free( d->points );
#endif
if ( d->n_point_triangles != NULL )
free( d->n_point_triangles );
if ( d->flags != NULL )
free( d->flags );
if ( d->circles != NULL )
free( d->circles );
if ( d->neighbours != NULL )
free( d->neighbours );
if ( d->triangles != NULL )
free( d->triangles );
if ( d->t_in != NULL )
istack_destroy( d->t_in );
if ( d->t_out != NULL )
istack_destroy( d->t_out );
free( d );
}
// Returns whether the point p is on the right side of the vector (p0, p1).
//
static int on_right_side( point* p, point* p0, point* p1 )
{
return ( p1->x - p->x ) * ( p0->y - p->y ) > ( p0->x - p->x ) * ( p1->y - p->y );
}
// Finds triangle specified point belongs to (if any).
//
// @param d Delaunay triangulation
// @param p Point to be mapped
// @param seed Triangle index to start with
// @return Triangle id if successful, -1 otherwhile
//
int delaunay_xytoi( delaunay* d, point* p, int id )
{
triangle* t;
int i;
if ( p->x < d->xmin || p->x > d->xmax || p->y < d->ymin || p->y > d->ymax )
return -1;
if ( id < 0 || id > d->ntriangles )
id = 0;
t = &d->triangles[id];
do
{
for ( i = 0; i < 3; ++i )
{
int i1 = ( i + 1 ) % 3;
if ( on_right_side( p, &d->points[t->vids[i]], &d->points[t->vids[i1]] ) )
{
id = d->neighbours[id].tids[( i + 2 ) % 3];
if ( id < 0 )
return id;
t = &d->triangles[id];
break;
}
}
} while ( i < 3 );
return id;
}
// Finds all tricircles specified point belongs to.
//
// @param d Delaunay triangulation
// @param p Point to be mapped
// @param n Pointer to the number of tricircles within `d' containing `p'
// (output)
// @param out Pointer to an array of indices of the corresponding triangles
// [n] (output)
//
// There is a standard search procedure involving search through triangle
// neighbours (not through vertex neighbours). It must be a bit faster due to
// the smaller number of triangle neighbours (3 per triangle) but can fail
// for a point outside convex hall.
//
// We may wish to modify this procedure in future: first check if the point
// is inside the convex hall, and depending on that use one of the two
// search algorithms. It not 100% clear though whether this will lead to a
// substantial speed gains because of the check on convex hall involved.
//
void delaunay_circles_find( delaunay* d, point* p, int* n, int** out )
{
int i;
if ( d->t_in == NULL )
{
d->t_in = istack_create();
d->t_out = istack_create();
}
//
// It is important to have a reasonable seed here. If the last search
// was successful -- start with the last found tricircle, otherwhile (i)
// try to find a triangle containing (x,y); if fails then (ii) check
// tricircles from the last search; if fails then (iii) make linear
// search through all tricircles
//
if ( d->first_id < 0 || !circle_contains( &d->circles[d->first_id], p ) )
{
//
// if any triangle contains (x,y) -- start with this triangle
//
d->first_id = delaunay_xytoi( d, p, d->first_id );
//
// if no triangle contains (x,y), there still is a chance that it is
// inside some of circumcircles
//
if ( d->first_id < 0 )
{
int nn = d->t_out->n;
int tid = -1;
//
// first check results of the last search
//
for ( i = 0; i < nn; ++i )
{
tid = d->t_out->v[i];
if ( circle_contains( &d->circles[tid], p ) )
break;
}
//
// if unsuccessful, search through all circles
//
if ( tid < 0 || i == nn )
{
double nt = d->ntriangles;
for ( tid = 0; tid < nt; ++tid )
{
if ( circle_contains( &d->circles[tid], p ) )
break;
}
if ( tid == nt )
{
istack_reset( d->t_out );
*n = 0;
*out = NULL;
return; // failed
}
}
d->first_id = tid;
}
}
istack_reset( d->t_in );
istack_reset( d->t_out );
istack_push( d->t_in, d->first_id );
d->flags[d->first_id] = 1;
//
// main cycle
//
while ( d->t_in->n > 0 )
{
int tid = istack_pop( d->t_in );
triangle* t = &d->triangles[tid];
if ( circle_contains( &d->circles[tid], p ) )
{
istack_push( d->t_out, tid );
for ( i = 0; i < 3; ++i )
{
int vid = t->vids[i];
int nt = d->n_point_triangles[vid];
int j;
for ( j = 0; j < nt; ++j )
{
int ntid = d->point_triangles[vid][j];
if ( d->flags[ntid] == 0 )
{
istack_push( d->t_in, ntid );
d->flags[ntid] = 1;
}
}
}
}
}
*n = d->t_out->n;
*out = d->t_out->v;
}
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