1 #ifndef GEOM_CONVEX_COVER_H
2 #define GEOM_CONVEX_COVER_H
4 /**
5 * \file
6 * \brief \todo brief description
7 *
8 * Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au>
9 * Copyright 2006 Michael G. Sloan <mgsloan@gmail.com>
10 *
11 * This library is free software; you can redistribute it and/or
12 * modify it either under the terms of the GNU Lesser General Public
13 * License version 2.1 as published by the Free Software Foundation
14 * (the "LGPL") or, at your option, under the terms of the Mozilla
15 * Public License Version 1.1 (the "MPL"). If you do not alter this
16 * notice, a recipient may use your version of this file under either
17 * the MPL or the LGPL.
18 *
19 * You should have received a copy of the LGPL along with this library
20 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
22 * You should have received a copy of the MPL along with this library
23 * in the file COPYING-MPL-1.1
24 *
25 * The contents of this file are subject to the Mozilla Public License
26 * Version 1.1 (the "License"); you may not use this file except in
27 * compliance with the License. You may obtain a copy of the License at
28 * http://www.mozilla.org/MPL/
29 *
30 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
31 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
32 * the specific language governing rights and limitations.
33 *
34 */
36 /** A convex cover is a sequence of convex polygons that completely cover the path. For now a
37 * convex hull class is included here (the convex-hull header is wrong)
38 */
40 #include <2geom/point.h>
41 #include <vector>
43 namespace Geom{
45 /** ConvexHull
46 * A convexhull is a convex region - every point between two points in the convex hull is also in
47 * the convex hull. It is defined by a set of points travelling in a clockwise direction. We require the first point to be top most, and of the topmost, leftmost.
49 * An empty hull has no points, we allow a single point or two points degenerate cases.
51 * We could provide the centroid as a member for efficient direction determination. We can update the
52 * centroid with all operations with the same time complexity as the operation.
53 */
55 class ConvexHull{
56 public: // XXX: should be private :)
57 // extracts the convex hull of boundary. internal use only
58 void find_pivot();
59 void angle_sort();
60 void graham_scan();
61 void graham();
62 public:
63 std::vector<Point> boundary;
64 //Point centroid;
66 void merge(Point p);
67 bool contains_point(Point p);
68 bool strict_contains_point(Point p);
70 inline Point operator[](int i) const {
72 int l = boundary.size();
73 if(l == 0) return Point();
74 return boundary[i >= 0 ? i % l : (i % l) + l];
75 }
77 /*inline Point &operator[](unsigned i) {
78 int l = boundary.size();
79 if(l == 0) return Point();
80 return boundary[i >= 0 ? i % l : i % l + l];
81 }*/
83 public:
84 ConvexHull() {}
85 ConvexHull(std::vector<Point> const & points) {
86 boundary = points;
87 graham();
88 }
90 template <typename T>
91 ConvexHull(T b, T e) :boundary(b,e) {}
93 ~ConvexHull()
94 {
95 }
97 public:
98 /** Is the convex hull clockwise? We use the definition of clockwise from point.h
99 **/
100 bool is_clockwise() const;
101 bool no_colinear_points() const;
102 bool top_point_first() const;
103 bool meets_invariants() const;
105 // contains no points
106 bool empty() const { return boundary.empty();}
108 // contains exactly one point
109 bool singular() const { return boundary.size() == 1;}
111 // all points are on a line
112 bool linear() const { return boundary.size() == 2;}
113 bool is_degenerate() const;
115 // area of the convex hull
116 double centroid_and_area(Geom::Point& centroid) const;
117 double area() const {
118 Point tmp;
119 return centroid_and_area(tmp);
120 }
122 // furthest point in a direction (lg time)
123 Point const * furthest(Point direction) const;
125 bool is_left(Point p, int n);
126 bool is_strict_left(Point p, int n);
127 int find_left(Point p);
128 int find_strict_left(Point p);
129 double narrowest_diameter(Point &a, Point &b, Point &c);
131 };
133 // do two convex hulls intersect?
134 bool intersectp(ConvexHull a, ConvexHull b);
136 std::vector<Point> bridge_points(ConvexHull a, ConvexHull b);
138 // find the convex hull intersection
139 ConvexHull intersection(ConvexHull a, ConvexHull b);
140 ConvexHull sweepline_intersection(ConvexHull const &a, ConvexHull const &b);
142 // find the convex hull of a set of convex hulls
143 ConvexHull merge(ConvexHull a, ConvexHull b);
145 // naive approach
146 ConvexHull graham_merge(ConvexHull a, ConvexHull b);
148 unsigned find_bottom_right(ConvexHull const &a);
150 /*** Arbitrary transform operator.
151 * Take a convex hull and apply an arbitrary convexity preserving transform.
152 * we should be concerned about singular tranforms here.
153 */
154 template <class T> ConvexHull operator*(ConvexHull const &p, T const &m) {
155 ConvexHull pr;
157 pr.boundary.reserve(p.boundary.size());
159 for(unsigned i = 0; i < p.boundary.size(); i++) {
160 pr.boundary.push_back(p.boundary[i]*m);
161 }
162 return pr;
163 }
165 ConvexHull clip(ConvexHull const & ch, Point n, double d);
167 //TODO: reinstate
168 /*class ConvexCover{
169 public:
170 Path const* path;
171 std::vector<ConvexHull> cc;
173 ConvexCover(Path const &sp);
174 };*/
176 };
178 #endif //2GEOM_CONVEX_COVER_H
180 /*
181 Local Variables:
182 mode:c++
183 c-file-style:"stroustrup"
184 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
185 indent-tabs-mode:nil
186 fill-column:99
187 End:
188 */
189 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :