1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
|
#ifndef GEOM_CONVEX_COVER_H
#define GEOM_CONVEX_COVER_H
/**
* \file
* \brief \todo brief description
*
* Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au>
* Copyright 2006 Michael G. Sloan <mgsloan@gmail.com>
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*
*/
/** A convex cover is a sequence of convex polygons that completely cover the path. For now a
* convex hull class is included here (the convex-hull header is wrong)
*/
#include <2geom/point.h>
#include <vector>
namespace Geom{
/** ConvexHull
* A convexhull is a convex region - every point between two points in the convex hull is also in
* 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.
* An empty hull has no points, we allow a single point or two points degenerate cases.
* We could provide the centroid as a member for efficient direction determination. We can update the
* centroid with all operations with the same time complexity as the operation.
*/
class ConvexHull{
public: // XXX: should be private :)
// extracts the convex hull of boundary. internal use only
void find_pivot();
void angle_sort();
void graham_scan();
void graham();
public:
std::vector<Point> boundary;
//Point centroid;
void merge(Point p);
bool contains_point(Point p);
bool strict_contains_point(Point p);
inline Point operator[](int i) const {
int l = boundary.size();
if(l == 0) return Point();
return boundary[i >= 0 ? i % l : (i % l) + l];
}
/*inline Point &operator[](unsigned i) {
int l = boundary.size();
if(l == 0) return Point();
return boundary[i >= 0 ? i % l : i % l + l];
}*/
public:
ConvexHull() {}
ConvexHull(std::vector<Point> const & points) {
boundary = points;
graham();
}
template <typename T>
ConvexHull(T b, T e) :boundary(b,e) {}
~ConvexHull()
{
}
public:
/** Is the convex hull clockwise? We use the definition of clockwise from point.h
**/
bool is_clockwise() const;
bool no_colinear_points() const;
bool top_point_first() const;
bool meets_invariants() const;
// contains no points
bool empty() const { return boundary.empty();}
// contains exactly one point
bool singular() const { return boundary.size() == 1;}
// all points are on a line
bool linear() const { return boundary.size() == 2;}
bool is_degenerate() const;
// area of the convex hull
double centroid_and_area(Geom::Point& centroid) const;
double area() const {
Point tmp;
return centroid_and_area(tmp);
}
// furthest point in a direction (lg time)
Point const * furthest(Point direction) const;
bool is_left(Point p, int n);
bool is_strict_left(Point p, int n);
int find_left(Point p);
int find_strict_left(Point p);
double narrowest_diameter(Point &a, Point &b, Point &c);
};
// do two convex hulls intersect?
bool intersectp(ConvexHull a, ConvexHull b);
std::vector<Point> bridge_points(ConvexHull a, ConvexHull b);
// find the convex hull intersection
ConvexHull intersection(ConvexHull a, ConvexHull b);
ConvexHull sweepline_intersection(ConvexHull const &a, ConvexHull const &b);
// find the convex hull of a set of convex hulls
ConvexHull merge(ConvexHull a, ConvexHull b);
// naive approach
ConvexHull graham_merge(ConvexHull a, ConvexHull b);
unsigned find_bottom_right(ConvexHull const &a);
/*** Arbitrary transform operator.
* Take a convex hull and apply an arbitrary convexity preserving transform.
* we should be concerned about singular tranforms here.
*/
template <class T> ConvexHull operator*(ConvexHull const &p, T const &m) {
ConvexHull pr;
pr.boundary.reserve(p.boundary.size());
for(unsigned i = 0; i < p.boundary.size(); i++) {
pr.boundary.push_back(p.boundary[i]*m);
}
return pr;
}
ConvexHull clip(ConvexHull const & ch, Point n, double d);
//TODO: reinstate
/*class ConvexCover{
public:
Path const* path;
std::vector<ConvexHull> cc;
ConvexCover(Path const &sp);
};*/
};
#endif //2GEOM_CONVEX_COVER_H
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
|