poly2d/: add triangulation (untested)

poly2d/Makefile

@@ -1,8 +1,8 @@
 #
 # Makefile - Makefile of libpoly2d
 #
-# Written 2012 by Werner Almesberger
-# Copyright 2012 by Werner Almesberger
+# Written 2012, 2013 by Werner Almesberger
+# Copyright 2012, 2013 by Werner Almesberger
 #
 # This program is free software; you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
@@ -18,7 +18,8 @@ LIB = libpoly2d.a
 OBJS = v2d_intersect.o v2d_line_distance.o \
        p2d_area.o p2d_area_holes.o \
        p2d_attrib.o p2d_contains_point.o p2d_contains_poly.o \
-       p2d_copy.o p2d_free.o p2d_gnuplot.o p2d_make.o p2d_offset.o p2d_hsort.o
+       p2d_copy.o p2d_free.o p2d_gnuplot.o p2d_make.o p2d_offset.o \
+       p2d_hsort.o f2d_tri_holes.o f2d_tri.o
 
 CFLAGS_WARN = -Wall -Wshadow -Wmissing-prototypes \
 	      -Wmissing-declarations -Wno-format-zero-length

poly2d/f2d_tri.c

@@ -0,0 +1,42 @@
+/*
+ * f2d_tri.c - Triangulate a set of nested polygons
+ *
+ * Written 2013 by Werner Almesberger
+ * Copyright 2013 Werner Almesberger
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ */
+
+
+#include "poly2d.h"
+#include "p2d_hsort.h"
+
+
+static void recurse_area(struct p2d_hier *t, struct f2d ***last)
+{
+	const struct p2d *p, *h;
+
+	for (p = &t->p; p; p = p->next) {
+		h = &p2d_to_hier(p)->holes->p;
+		f2d_tri_holes_append(p, h, last);
+		while (h) {
+			recurse_area(p2d_to_hier(h)->holes, last);
+			h = h->next;
+		}
+	}
+}
+
+
+struct f2d *f2d_tri(const struct p2d *p)
+{
+	struct p2d_hier *t;
+	struct f2d *res = NULL, **last = &res;
+
+	t = p2d_hsort(p);
+	recurse_area(t, &last);
+	p2d_hier_free(t);
+	return res;
+}

poly2d/f2d_tri_holes.cpp

@@ -0,0 +1,245 @@
+/*
+ * f2d_tri_holes.cpp - Triangulate a polygon with holes
+ *
+ * Written 2013 by Werner Almesberger
+ * Copyright 2013 by Werner Almesberger
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ */
+
+/*
+ * References:
+ * http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_2/
+ *   Chapter_main.html#Subsection_37.8.2
+ * http://www.cgal.org/Manual/latest/examples/Triangulation_2/
+ *   polygon_triangulation.cpp
+ */
+
+extern "C" {
+	#include <assert.h>
+
+	#include "util.h"
+	#include "poly2d.h"
+}
+
+#if 0
+/*
+ * @@@ Prevent spurious aborts with
+ *
+ * terminate called after throwing an instance of 'CGAL::Precondition_exception'
+ * what():  CGAL ERROR: precondition violation!
+ * Expr: is_simple_2(first, last, traits)
+ * File: /usr/include/CGAL/Polygon_2/Polygon_2_algorithms_impl.h
+ * Line: 420
+ *
+ * Note that we also need to check the polygons for simplicity in recurse_area,
+ * or this may still lead to assertion failures.
+ */
+
+#define CGAL_POLYGON_NO_PRECONDITIONS
+#endif
+
+#include "cgal_helper.h"
+
+//#include <vector>
+//#include <boost/shared_ptr.hpp>
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Triangulation_face_base_with_info_2.h>
+#include <CGAL/Polygon_2.h>
+
+
+struct FaceInfo2 {
+	FaceInfo2(){}
+	int nesting_level;
+
+	bool in_domain(void)
+	{ 
+		return nesting_level % 2 == 1;
+	}
+};
+
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+typedef CGAL::Triangulation_vertex_base_2<K> Vb;
+typedef CGAL::Triangulation_face_base_with_info_2<FaceInfo2, K> Fbb;
+typedef CGAL::Constrained_triangulation_face_base_2<K, Fbb> Fb;
+typedef CGAL::Triangulation_data_structure_2<Vb, Fb> TDS;
+typedef CGAL::Exact_predicates_tag Itag;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, Itag> CDT;
+typedef CDT::Point Point;
+typedef CGAL::Polygon_2<K> Polygon_2;
+
+
+#if 0
+typedef CGAL::Polygon_with_holes_2<K> Polygon_with_holes;
+
+typedef boost::shared_ptr<Polygon_with_holes> PolygonPtr;
+
+typedef std::vector<PolygonPtr> PolygonPtrVector;
+
+	struct p2d *res = NULL, **last = &res, *np;
+
+
+static void append_poly(Polygon_2 poly, struct p2d ***last)
+{
+	**last = P2_to_p2d(poly);
+	*last = &(**last)->next;
+}
+#endif
+
+
+/* ----- Mark domains ------------------------------------------------------ */
+
+
+static void mark_domains(CDT &ct, CDT::Face_handle start, int index, 
+    std::list<CDT::Edge> &border)
+{
+	std::list<CDT::Face_handle> queue;
+
+	if (start->info().nesting_level != -1)
+		return;
+
+	queue.push_back(start);
+	while (!queue.empty()) {
+		CDT::Face_handle fh = queue.front();
+
+		queue.pop_front();
+		if (fh->info().nesting_level == -1){
+			fh->info().nesting_level = index;
+			for (int i = 0; i < 3; i++) {
+				CDT::Edge e(fh, i);
+				CDT::Face_handle n = fh->neighbor(i);
+				if (n->info().nesting_level == -1) {
+					if (ct.is_constrained(e))
+						border.push_back(e);
+					else
+						queue.push_back(n);
+				}
+			}
+		}
+	}
+}
+
+
+static void mark_domains(CDT &cdt)
+{
+	int index = 0;
+
+	for (CDT::All_faces_iterator it = cdt.all_faces_begin();
+	    it != cdt.all_faces_end(); ++it)
+		it->info().nesting_level = -1;
+
+	std::list<CDT::Edge> border;
+	mark_domains(cdt, cdt.infinite_face(), index++, border);
+	while(!border.empty()) {
+		CDT::Edge e = border.front();
+
+		border.pop_front();
+		CDT::Face_handle n = e.first->neighbor(e.second);
+		if (n->info().nesting_level == -1)
+			mark_domains(cdt, n, e.first->info().nesting_level+1,
+			    border);
+	}
+}
+
+
+/* ----- Inser polygon ----------------------------------------------------- */
+
+
+void insert_polygon(CDT &cdt, const Polygon_2 &polygon)
+{
+	if (polygon.is_empty())
+		return;
+	CDT::Vertex_handle v_prev =
+	    cdt.insert(*CGAL::cpp0x::prev(polygon.vertices_end()));
+	for (Polygon_2::Vertex_iterator vit = polygon.vertices_begin();
+	    vit != polygon.vertices_end(); ++vit) {
+		CDT::Vertex_handle vh = cdt.insert(*vit);
+
+		cdt.insert_constraint(vh, v_prev);
+		v_prev = vh;
+	}  
+}
+
+
+static const struct v2d *find_point(const struct p2d *p, double x, double y)
+{
+	const struct v2d *v;
+
+	for (v = p->v; v; v = v->next)
+		if (v->x == x && v->y == y)
+			break;
+	return v;
+}
+
+
+static struct f2d *make_face(CDT::Finite_faces_iterator fit,
+    const struct p2d *p, const struct p2d *holes)
+{
+	struct f2d *f;
+	const struct p2d *h;
+	int i;
+
+	f = alloc_type(struct f2d);
+	for (i = 0; i != 3; i++) {
+		Point point = fit->vertex(i)->point();
+		const struct v2d *m;
+
+		m = find_point(p, point.x(), point.y());
+		if (m) {
+			f->v[i] = m;
+			f->p[i] = p;
+			continue;
+		}
+		for (h = holes; h; h = h->next) {
+			m = find_point(h, point.x(), point.y());
+			if (!m)
+				continue;
+			f->v[i] = m;
+			f->p[i] = h;
+			break;
+		}
+		assert(m);
+	}
+	f->next = NULL;
+	return f;
+}
+
+
+void tri_holes_append(const struct p2d *p, const struct p2d *holes,
+    struct f2d ***last)
+{
+	CDT cdt;
+	const struct p2d *h;
+	struct f2d *f;
+
+	insert_polygon(cdt, p2d_to_P2(p, 0));
+	for (h = holes; h; h = h->next) {
+		assert(p2d_is_closed(h));
+		insert_polygon(cdt, p2d_to_P2(h, 0));
+	}
+	mark_domains(cdt);
+
+	for (CDT::Finite_faces_iterator fit = cdt.finite_faces_begin();
+	    fit != cdt.finite_faces_end(); ++fit)
+		if (fit->info().in_domain()) {
+			f = make_face(fit, p, holes);
+			**last = f;
+			*last = &f->next;
+		}
+}
+
+
+extern "C" struct f2d *f2d_tri_holes(const struct p2d *p,
+    const struct p2d *holes)
+{
+	struct f2d *res = NULL, **last = &res;
+
+	tri_holes_append(p, holes, &last);
+	return res;
+}

poly2d/poly2d.h

@@ -1,8 +1,8 @@
 /*
  * poly2d.h - The public face of the 2D Polygon library
  *
- * Written 2012 by Werner Almesberger
- * Copyright 2012 Werner Almesberger
+ * Written 2012, 2013 by Werner Almesberger
+ * Copyright 2012, 2013 Werner Almesberger
  *
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -29,6 +29,12 @@ struct p2d {
 	struct p2d *next;
 };
 
+struct f2d {
+	const struct v2d *v[3];	/* vertices forming the face */
+	const struct p2d *p[3];	/* polygons vertices belong to */
+	struct f2d *next;
+};
+
 
 /*
  * forall_v2d* need -std=gnu99
@@ -161,6 +167,11 @@ struct p2d *p2d_area_holes(const struct p2d *p, const struct p2d *holes,
     double first, double next);
 struct p2d *p2d_area(const struct p2d *p, double first, double next);
 
+void f2d_tri_holes_append(const struct p2d *p, const struct p2d *holes,
+    struct f2d ***last);
+struct f2d *f2d_tri_holes(const struct p2d *p, const struct p2d *holes);
+struct f2d *f2d_tri(const struct p2d *p);
+
 struct p2d *p2d_read_gnuplot(FILE *file);
 int p2d_write_gnuplot(FILE *file, const struct p2d *p);
 int p2d_write_gnuplot_all(FILE *file, const struct p2d *p);