static GtsSurface * happrox_list (GSList * points,
gboolean keep_enclosing,
gboolean closed,
CostFunc cost_func,
gpointer cost_data,
GtsStopFunc stop_func,
gpointer stop_data)
{
GtsSurface * s = gts_surface_new (gts_surface_class (),
GTS_FACE_CLASS (list_face_class ()),
gts_edge_class (),
gts_vertex_class ());
GtsTriangle * t;
GtsVertex * w1, * w2, * w3;
GtsListFace * f;
/* creates enclosing triangle */
t = gts_triangle_enclosing (gts_triangle_class (), points, 10.);
gts_triangle_vertices (t, &w1, &w2, &w3);
GTS_POINT (w1)->z = GTS_POINT (w2)->z = GTS_POINT (w3)->z =
keep_enclosing ? -10. : -1e30;
f = GTS_LIST_FACE (gts_face_new (s->face_class, t->e1, t->e2, t->e3));
gts_surface_add_face (s, GTS_FACE (f));
f->points = points;
/* refine surface */
surface_hf_refine (s, cost_func, cost_data, stop_func, stop_data);
/* destroy unused vertices */
gts_surface_foreach_face (s, (GtsFunc) destroy_unused, NULL);
/* destroy enclosing triangle */
if (!keep_enclosing) {
gts_allow_floating_vertices = TRUE;
gts_object_destroy (GTS_OBJECT (w1));
gts_object_destroy (GTS_OBJECT (w2));
gts_object_destroy (GTS_OBJECT (w3));
gts_allow_floating_vertices = FALSE;
}
else if (closed) {
GSList * l = gts_surface_boundary (s);
GtsFace * f;
g_assert (g_slist_length (l) == 3);
f = gts_face_new (s->face_class, l->data, l->next->data, l->next->next->data);
gts_surface_add_face (s, f);
if (!gts_face_is_compatible (f, s))
gts_triangle_revert (GTS_TRIANGLE (f));
g_slist_free (l);
gts_object_destroy (GTS_OBJECT (t));
}
else
gts_object_destroy (GTS_OBJECT (t));
return s;
}
/**
* gts_triangle_enclosing:
* @klass: the class of the new triangle.
* @points: a list of #GtsPoint.
* @scale: a scaling factor (must be larger than one).
*
* Builds a new triangle (including new vertices and edges) enclosing
* the plane projection of all the points in @points. This triangle is
* equilateral and encloses a rectangle defined by the maximum and
* minimum x and y coordinates of the points. @scale is an homothetic
* scaling factor. If equal to one, the triangle encloses exactly the
* enclosing rectangle.
*
* Returns: a new #GtsTriangle.
*/
GtsTriangle * gts_triangle_enclosing (GtsTriangleClass * klass,
GSList * points, gdouble scale)
{
gdouble xmax, xmin, ymax, ymin;
gdouble xo, yo, r;
GtsVertex * v1, * v2, * v3;
GtsEdge * e1, * e2, * e3;
if (points == NULL)
return NULL;
xmax = xmin = GTS_POINT (points->data)->x;
ymax = ymin = GTS_POINT (points->data)->y;
points = points->next;
while (points) {
GtsPoint * p = points->data;
if (p->x > xmax) xmax = p->x;
else if (p->x < xmin) xmin = p->x;
if (p->y > ymax) ymax = p->y;
else if (p->y < ymin) ymin = p->y;
points = points->next;
}
xo = (xmax + xmin)/2.;
yo = (ymax + ymin)/2.;
r = scale*sqrt((xmax - xo)*(xmax - xo) + (ymax - yo)*(ymax - yo));
if (r == 0.0) r = scale;
v1 = gts_vertex_new (gts_vertex_class (),
xo + r*SQRT3, yo - r, 0.0);
v2 = gts_vertex_new (gts_vertex_class (),
xo, yo + 2.*r, 0.0);
v3 = gts_vertex_new (gts_vertex_class (),
xo - r*SQRT3, yo - r, 0.0);
e1 = gts_edge_new (gts_edge_class (), v1, v2);
e2 = gts_edge_new (gts_edge_class (), v2, v3);
e3 = gts_edge_new (gts_edge_class (), v3, v1);
return gts_triangle_new (gts_triangle_class (), e1, e2, e3);
}
static void triangle_destroy (GtsObject * object)
{
GtsTriangle * triangle = GTS_TRIANGLE (object);
GtsEdge * e1 = triangle->e1;
GtsEdge * e2 = triangle->e2;
GtsEdge * e3 = triangle->e3;
e1->triangles = g_slist_remove (e1->triangles, triangle);
if (!GTS_OBJECT_DESTROYED (e1) &&
!gts_allow_floating_edges && e1->triangles == NULL)
gts_object_destroy (GTS_OBJECT (e1));
e2->triangles = g_slist_remove (e2->triangles, triangle);
if (!GTS_OBJECT_DESTROYED (e2) &&
!gts_allow_floating_edges && e2->triangles == NULL)
gts_object_destroy (GTS_OBJECT (e2));
e3->triangles = g_slist_remove (e3->triangles, triangle);
if (!GTS_OBJECT_DESTROYED (e3) &&
!gts_allow_floating_edges && e3->triangles == NULL)
gts_object_destroy (GTS_OBJECT (e3));
(* GTS_OBJECT_CLASS (gts_triangle_class ())->parent_class->destroy) (object);
}
static GtsSurface * happrox (gray ** g, gint width, gint height,
CostFunc cost_func,
gpointer cost_data,
GtsStopFunc stop_func,
gpointer stop_data)
{
GtsSurface * s = gts_surface_new (gts_surface_class (),
GTS_FACE_CLASS (list_face_class ()),
gts_edge_class (),
gts_vertex_class ());
GtsVertex * v1 = gts_vertex_new (s->vertex_class, 0., 0., g[0][0]);
GtsVertex * v2 = gts_vertex_new (s->vertex_class,
0., height - 1, g[height - 1][0]);
GtsVertex * v3 = gts_vertex_new (s->vertex_class,
width - 1, 0., g[0][width - 1]);
GtsVertex * v4 = gts_vertex_new (s->vertex_class,
width - 1, height - 1,
g[height - 1][width - 1]);
guint i, j;
GSList * corners = NULL;
GtsTriangle * t;
GtsVertex * w1, * w2, * w3;
GtsListFace * f;
/* creates enclosing triangle */
corners = g_slist_prepend (corners, v1);
corners = g_slist_prepend (corners, v2);
corners = g_slist_prepend (corners, v3);
corners = g_slist_prepend (corners, v4);
t = gts_triangle_enclosing (gts_triangle_class (), corners, 100.);
g_slist_free (corners);
gts_triangle_vertices (t, &w1, &w2, &w3);
f = GTS_LIST_FACE (gts_face_new (s->face_class, t->e1, t->e2, t->e3));
gts_surface_add_face (s, GTS_FACE (f));
/* add PGM vertices (corners excepted) to point list of f */
for (i = 1; i < width - 1; i++) {
for (j = 1; j < height - 1; j++)
prepend (f, g, i, j);
prepend (f, g, i, 0);
prepend (f, g, i, height - 1);
}
for (j = 1; j < height - 1; j++) {
prepend (f, g, 0, j);
prepend (f, g, width - 1, j);
}
pgm_freearray (g, height);
/* add four corners to initial triangulation */
g_assert (gts_delaunay_add_vertex_to_face (s, v1, GTS_FACE (f)) == NULL);
f = GTS_LIST_FACE (gts_point_locate (GTS_POINT (v2), s, NULL));
g_assert (gts_delaunay_add_vertex_to_face (s, v2, GTS_FACE (f)) == NULL);
f = GTS_LIST_FACE (gts_point_locate (GTS_POINT (v3), s, NULL));
g_assert (gts_delaunay_add_vertex_to_face (s, v3, GTS_FACE (f)) == NULL);
f = GTS_LIST_FACE (gts_point_locate (GTS_POINT (v4), s, NULL));
g_assert (gts_delaunay_add_vertex_to_face (s, v4, GTS_FACE (f)) == NULL);
/* refine surface */
surface_hf_refine (s, cost_func, cost_data, stop_func, stop_data);
/* destroy unused vertices */
gts_surface_foreach_face (s, (GtsFunc) destroy_unused, NULL);
/* destroy enclosing triangle */
gts_allow_floating_vertices = TRUE;
gts_object_destroy (GTS_OBJECT (w1));
gts_object_destroy (GTS_OBJECT (w2));
gts_object_destroy (GTS_OBJECT (w3));
gts_allow_floating_vertices = FALSE;
return s;
}
int main (int argc, char * argv[])
{
guint i, j, nx, ny;
gdouble cosa, sina;
GtsSurface * surface;
GSList * l, * vertices = NULL;
GtsTriangle * t;
GtsVertex * v1, * v2, * v3;
GTimer * timer;
if (argc != 4) {
fprintf (stderr, "usage: cartesian nx ny angle\n");
return 0;
}
nx = strtol (argv[1], NULL, 0);
ny = strtol (argv[2], NULL, 0);
cosa = cos (strtod (argv[3], NULL));
sina = sin (strtod (argv[3], NULL));
timer = g_timer_new ();
g_timer_start (timer);
for (i = 0; i < nx; i++) {
gdouble x = (gdouble) i/(gdouble) (nx - 1);
for (j = 0; j < ny; j++) {
gdouble y = (gdouble) j/(gdouble) (nx - 1);
vertices = g_slist_prepend (vertices,
gts_vertex_new (gts_vertex_class (),
cosa*x - sina*y, sina*x + cosa*y, 0.));
}
}
t = gts_triangle_enclosing (gts_triangle_class (), vertices, 100.);
gts_triangle_vertices (t, &v1, &v2, &v3);
surface = gts_surface_new (gts_surface_class (),
gts_face_class (),
gts_edge_class (),
gts_vertex_class ());
gts_surface_add_face (surface, gts_face_new (gts_face_class (),
t->e1, t->e2, t->e3));
g_timer_stop (timer);
fprintf (stderr, "Input: %g s\n", g_timer_elapsed (timer, NULL));
g_timer_reset (timer);
g_timer_start (timer);
l = vertices;
while (l) {
g_assert (gts_delaunay_add_vertex (surface, l->data, NULL) == NULL);
l = l->next;
}
gts_allow_floating_vertices = TRUE;
gts_object_destroy (GTS_OBJECT (v1));
gts_object_destroy (GTS_OBJECT (v2));
gts_object_destroy (GTS_OBJECT (v3));
gts_allow_floating_vertices = FALSE;
g_timer_stop (timer);
fprintf (stderr, "Triangulation: %g s speed: %.0f vertex/s\n",
g_timer_elapsed (timer, NULL),
g_slist_length (vertices)/g_timer_elapsed (timer, NULL));
g_timer_reset (timer);
g_timer_start (timer);
gts_surface_write (surface, stdout);
g_timer_stop (timer);
fprintf (stderr, "Output: %g s\n", g_timer_elapsed (timer, NULL));
if (gts_delaunay_check (surface)) {
fprintf (stderr, "WARNING: surface is not Delaunay\n");
return 0;
}
return 1;
}
int main (int argc, char * argv[])
{
GPtrArray * vertices;
GtsFifo * edges;
guint i, line;
GtsTriangle * t;
GtsVertex * v1, * v2, * v3;
GtsSurface * surface;
gboolean keep_hull = TRUE;
gboolean verbose = FALSE;
gboolean add_constraints = TRUE;
gboolean remove_holes = FALSE;
gboolean check_delaunay = FALSE;
gboolean conform = FALSE;
gboolean refine = FALSE;
gboolean split_constraints = FALSE;
gboolean randomize = FALSE;
gboolean remove_duplicates = FALSE;
gint steiner_max = -1;
gdouble quality = 0., area = G_MAXDOUBLE;
int c = 0, status = 0;
const char * fname = NULL;
GTimer * timer;
/* parse options using getopt */
while (c != EOF) {
#ifdef HAVE_GETOPT_LONG
static struct option long_options[] = {
{"duplicates", no_argument, NULL, 'd'},
{"help", no_argument, NULL, 'h'},
{"verbose", no_argument, NULL, 'v'},
{"randomize", no_argument, NULL, 'r'},
{"hull", no_argument, NULL, 'b'},
{"noconst", no_argument, NULL, 'e'},
{"holes", no_argument, NULL, 'H'},
{"split", no_argument, NULL, 'S'},
{"check", no_argument, NULL, 'c'},
{"files", required_argument, NULL, 'f'},
{"conform", no_argument, NULL, 'o'},
{"steiner", required_argument, NULL, 's'},
{"quality", required_argument, NULL, 'q'},
{"area", required_argument, NULL, 'a'}
};
int option_index = 0;
switch ((c = getopt_long (argc, argv, "hvbecf:os:q:a:HSrd",
long_options, &option_index))) {
#else /* not HAVE_GETOPT_LONG */
switch ((c = getopt (argc, argv, "hvbecf:os:q:a:HSrd"))) {
#endif /* not HAVE_GETOPT_LONG */
case 'd': /* duplicates */
remove_duplicates = TRUE;
break;
case 'b': /* do not keep convex hull */
keep_hull = FALSE;
break;
case 'e': /* do not add constrained edges */
add_constraints = FALSE;
break;
case 'H': /* remove holes */
remove_holes = TRUE;
break;
case 'S': /* split constraints */
split_constraints = TRUE;
break;
case 'r': /* randomize */
randomize = TRUE;
break;
case 'c': /* check Delaunay property */
check_delaunay = TRUE;
break;
case 'f': /* generates files */
fname = optarg;
break;
case 'v': /* verbose */
verbose = TRUE;
break;
case 'o': /* conform */
conform = TRUE;
break;
case 's': /* steiner */
steiner_max = atoi (optarg);
break;
case 'q': /* quality */
conform = TRUE;
refine = TRUE;
quality = atof (optarg);
break;
case 'a': /* area */
conform = TRUE;
refine = TRUE;
area = atof (optarg);
break;
case 'h': /* help */
fprintf (stderr,
"Usage: delaunay [OPTION] < file.gts\n"
"Construct the constrained Delaunay triangulation of the input\n"
"\n"
" -b --hull do not keep convex hull\n"
" -e --noconst do not add constrained edges\n"
" -S --split split constraints (experimental)\n"
" -H --holes remove holes from the triangulation\n"
" -d --duplicates remove duplicate vertices\n"
" -r --randomize shuffle input vertex list\n"
" -c --check check Delaunay property\n"
" -f FNAME --files=FNAME generate evolution files\n"
" -o --conform generate conforming triangulation\n"
" -s N --steiner=N maximum number of Steiner points for\n"
" conforming triangulation (default is no limit)\n"
" -q Q --quality=Q Set the minimum acceptable face quality\n"
" -a A --area=A Set the maximum acceptable face area\n"
" -v --verbose print statistics about the triangulation\n"
" -h --help display this help and exit\n"
"\n"
"Reports bugs to %s\n",
GTS_MAINTAINER);
return 0; /* success */
break;
case '?': /* wrong options */
fprintf (stderr, "Try `delaunay --help' for more information.\n");
return 1; /* failure */
}
}
/* read file => two lists: vertices and constraints */
edges = gts_fifo_new ();
vertices = g_ptr_array_new ();
if (add_constraints) /* the edge class is a GtsConstraintClass */
line = read_list (vertices, edges,
GTS_EDGE_CLASS (gts_constraint_class ()),
stdin);
else /* the edge class is a "normal" edge: GtsEdgeClass */
line = read_list (vertices, edges,
gts_edge_class (),
stdin);
if (line > 0) {
fprintf (stderr, "delaunay: error in input file at line %u\n", line);
return 1;
}
timer = g_timer_new ();
g_timer_start (timer);
if (randomize)
shuffle_array (vertices);
/* create triangle enclosing all the vertices */
{
GSList * list = NULL;
for (i = 0; i < vertices->len; i++)
list = g_slist_prepend (list, g_ptr_array_index (vertices, i));
t = gts_triangle_enclosing (gts_triangle_class (), list, 100.);
g_slist_free (list);
}
gts_triangle_vertices (t, &v1, &v2, &v3);
/* create surface with one face: the enclosing triangle */
surface = gts_surface_new (gts_surface_class (),
gts_face_class (),
gts_edge_class (),
gts_vertex_class ());
gts_surface_add_face (surface, gts_face_new (gts_face_class (),
t->e1, t->e2, t->e3));
/* add vertices */
for (i = 0; i < vertices->len; i++) {
GtsVertex * v1 = g_ptr_array_index (vertices, i);
GtsVertex * v = gts_delaunay_add_vertex (surface, v1, NULL);
g_assert (v != v1);
if (v != NULL) {
if (!remove_duplicates) {
fprintf (stderr, "delaunay: duplicate vertex (%g,%g) in input file\n",
GTS_POINT (v)->x, GTS_POINT (v)->y);
return 1; /* Failure */
}
else
gts_vertex_replace (v1, v);
}
if (fname) {
static guint nf = 1;
char s[80];
FILE * fp;
g_snprintf (s, 80, "%s.%u", fname, nf++);
fp = fopen (s, "wt");
gts_surface_write_oogl (surface, fp);
fclose (fp);
if (check_delaunay && gts_delaunay_check (surface)) {
fprintf (stderr, "delaunay: triangulation is not Delaunay\n");
return 1;
}
}
}
g_ptr_array_free (vertices, TRUE);
/* add remaining constraints */
if (add_constraints)
gts_fifo_foreach (edges, (GtsFunc) add_constraint, surface);
/* destroy enclosing triangle */
gts_allow_floating_vertices = TRUE;
gts_object_destroy (GTS_OBJECT (v1));
gts_object_destroy (GTS_OBJECT (v2));
gts_object_destroy (GTS_OBJECT (v3));
gts_allow_floating_vertices = FALSE;
if (!keep_hull)
gts_delaunay_remove_hull (surface);
if (remove_holes)
delaunay_remove_holes (surface);
if (split_constraints) {
gpointer data[2];
data[0] = surface;
data[1] = edges;
gts_fifo_foreach (edges, (GtsFunc) split_constraint, data);
}
if (conform) {
guint encroached_number =
gts_delaunay_conform (surface,
steiner_max,
(GtsEncroachFunc) gts_vertex_encroaches_edge,
NULL);
if (encroached_number == 0 && refine) {
guint unrefined_number;
gpointer data[2];
data[0] = &quality;
data[1] = &area;
unrefined_number =
gts_delaunay_refine (surface,
steiner_max,
(GtsEncroachFunc) gts_vertex_encroaches_edge,
NULL,
(GtsKeyFunc) triangle_cost,
data);
if (verbose && unrefined_number > 0)
fprintf (stderr,
"delaunay: ran out of Steiner points (max: %d) during refinement\n"
"%d unrefined faces left\n",
steiner_max, unrefined_number);
}
else if (verbose && encroached_number > 0)
fprintf (stderr,
"delaunay: ran out of Steiner points (max: %d) during conforming\n"
"Delaunay triangulation: %d encroached constraints left\n",
steiner_max, encroached_number);
}
g_timer_stop (timer);
if (verbose) {
gts_surface_print_stats (surface, stderr);
fprintf (stderr, "# Triangulation time: %g s speed: %.0f vertex/s\n",
g_timer_elapsed (timer, NULL),
gts_surface_vertex_number (surface)/g_timer_elapsed (timer, NULL));
}
if (check_delaunay && gts_delaunay_check (surface)) {
fprintf (stderr, "delaunay: triangulation is not Delaunay\n");
status = 1; /* failure */
}
/* write triangulation */
gts_surface_write (surface, stdout);
return status;
}
/* tri:
* Main entry point to using GTS for triangulation.
* Input is npt points with x and y coordinates stored either separately
* in x[] and y[] (sepArr != 0) or consecutively in x[] (sepArr == 0).
* Optionally, the input can include nsegs line segments, whose endpoint
* indices are supplied in segs[2*i] and segs[2*i+1] yielding a constrained
* triangulation.
*
* The return value is the corresponding gts surface, which can be queries for
* the triangles and line segments composing the triangulation.
*/
static GtsSurface*
tri(double *x, double *y, int npt, int *segs, int nsegs, int sepArr)
{
int i;
GtsSurface *surface;
GVertex **vertices = N_GNEW(npt, GVertex *);
GtsEdge **edges = N_GNEW(nsegs, GtsEdge*);
GSList *list = NULL;
GtsVertex *v1, *v2, *v3;
GtsTriangle *t;
GtsVertexClass *vcl = (GtsVertexClass *) g_vertex_class();
GtsEdgeClass *ecl = GTS_EDGE_CLASS (gts_constraint_class ());
if (sepArr) {
for (i = 0; i < npt; i++) {
GVertex *p = (GVertex *) gts_vertex_new(vcl, x[i], y[i], 0);
p->idx = i;
vertices[i] = p;
}
}
else {
for (i = 0; i < npt; i++) {
GVertex *p = (GVertex *) gts_vertex_new(vcl, x[2*i], x[2*i+1], 0);
p->idx = i;
vertices[i] = p;
}
}
/* N.B. Edges need to be created here, presumably before the
* the vertices are added to the face. In particular, they cannot
* be added created and added vi gts_delaunay_add_constraint() below.
*/
for (i = 0; i < nsegs; i++) {
edges[i] = gts_edge_new(ecl,
(GtsVertex *) (vertices[ segs[ 2 * i]]),
(GtsVertex *) (vertices[ segs[ 2 * i + 1]]));
}
for (i = 0; i < npt; i++)
list = g_slist_prepend(list, vertices[i]);
t = gts_triangle_enclosing(gts_triangle_class(), list, 100.);
g_slist_free(list);
gts_triangle_vertices(t, &v1, &v2, &v3);
surface = gts_surface_new(gts_surface_class(),
(GtsFaceClass *) g_face_class(),
gts_edge_class(),
gts_vertex_class());
gts_surface_add_face(surface, gts_face_new(gts_face_class(),
t->e1, t->e2, t->e3));
for (i = 0; i < npt; i++) {
GtsVertex *v1 = (GtsVertex *) vertices[i];
GtsVertex *v = gts_delaunay_add_vertex(surface, v1, NULL);
/* if v != NULL, it is a previously added pt with the same
* coordinates as v1, in which case we replace v1 with v
*/
if (v) {
/* agerr (AGWARN, "Duplicate point %d %d\n", i, ((GVertex*)v)->idx); */
gts_vertex_replace (v1, v);
}
}
for (i = 0; i < nsegs; i++) {
gts_delaunay_add_constraint(surface,GTS_CONSTRAINT(edges[i]));
}
/* destroy enclosing triangle */
gts_allow_floating_vertices = TRUE;
gts_allow_floating_edges = TRUE;
/*
gts_object_destroy(GTS_OBJECT(v1));
gts_object_destroy(GTS_OBJECT(v2));
gts_object_destroy(GTS_OBJECT(v3));
*/
destroy(v1);
destroy(v2);
destroy(v3);
gts_allow_floating_edges = FALSE;
gts_allow_floating_vertices = FALSE;
if (nsegs)
delaunay_remove_holes(surface);
free (edges);
free(vertices);
return surface;
}
