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
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
|
/***************************************************************************
* Developer: Francisco Martínez del Río (2011) *
* fmartin@ujaen.es *
* Version: 1.4.1 *
* *
* This is a public domain program *
***************************************************************************/
#include "polygon.h"
#include "utilities.h"
#include <limits>
#include <set>
#include <cstdlib>
#include <algorithm>
void Contour::boundingbox (Point& min, Point& max)
{
min.x = min.y = numeric_limits<double>::max ();
max.x = max.y = -numeric_limits<double>::max ();
Contour::iterator i = begin();
while (i != end()) {
if (i->x < min.x)
min.x = i->x;
if (i->x > max.x)
max.x = i->x;
if (i->y < min.y)
min.y = i->y;
if (i->y > max.y)
max.y = i->y;
++i;
}
}
bool Contour::counterclockwise ()
{
if (_precomputedCC)
return _CC;
_precomputedCC = true;
double area = 0.0;
for (unsigned int c = 0; c < nvertices () - 1; c++)
area += vertex (c).x * vertex (c+1).y - vertex (c+1).x * vertex (c).y;
area += vertex (nvertices ()-1).x * vertex (0).y - vertex (0).x * vertex (nvertices ()-1).y;
return _CC = area >= 0.0;
}
void Contour::move (double x, double y)
{
for (unsigned int i = 0; i < points.size (); i++) {
points[i].x += x;
points[i].y += y;
}
}
unsigned Polygon::nvertices () const
{
unsigned int nv = 0;
for (unsigned int i = 0; i < ncontours (); i++)
nv += contours[i].nvertices ();
return nv;
}
void Polygon::boundingbox (Point& min, Point& max)
{
min.x = min.y = numeric_limits<double>::max ();
max.x = max.y = -numeric_limits<double>::max ();
Point mintmp;
Point maxtmp;
for (unsigned int i = 0; i < ncontours (); i++) {
contours[i].boundingbox (mintmp, maxtmp);
if (mintmp.x < min.x)
min.x = mintmp.x;
if (maxtmp.x > max.x)
max.x = maxtmp.x;
if (mintmp.y < min.y)
min.y = mintmp.y;
if (maxtmp.y > max.y)
max.y = maxtmp.y;
}
}
void Polygon::move (double x, double y)
{
for (unsigned int i = 0; i < contours.size (); i++)
contours[i].move (x, y);
}
/*
* The following code is necessary for implementing the computeHoles member function
*
*/
namespace { // start of anonymous namespace
struct SweepEvent;
struct SegmentComp : public binary_function<SweepEvent*, SweepEvent*, bool> {
bool operator() (SweepEvent* e1, SweepEvent* e2) const;
};
struct SweepEvent {
Point p; // point associated with the event
bool left; // is the point the left endpoint of the segment (p, other->p)?
int pl; // Polygon to which the associated segment belongs to
SweepEvent* other; // Event associated to the other endpoint of the segment
/** Does the segment (p, other->p) represent an inside-outside transition in the polygon for a vertical ray from (p.x, -infinite) that crosses the segment? */
bool inOut;
set<SweepEvent*, SegmentComp>::iterator poss; // Only used in "left" events. Position of the event (segment) in S
/** Class constructor */
SweepEvent (const Point& pp, bool b, int apl) : p (pp), left (b), pl (apl) {}
/** Return the segment associated to the SweepEvent */
Segment segment () { return Segment (p, other->p); }
/** Is the segment (p, other->p) below point x */
bool below (const Point& x) const { return (left) ? signedArea (p, other->p, x) > 0 : signedArea (other->p, p, x) > 0; }
/** Is the segment (p, other->p) above point x */
bool above (const Point& x) const { return !below (x); }
};
struct SweepEventComp : public binary_function<SweepEvent*, SweepEvent*, bool> {
bool operator() (SweepEvent* e1, SweepEvent* e2) const {
if (e1->p.x < e2->p.x) // Different x coordinate
return true;
if (e2->p.x < e1->p.x) // Different x coordinate
return false;
if (e1->p != e2->p) // Different points, but same x coordinate. The event with lower y coordinate is processed first
return e1->p.y < e2->p.y;
if (e1->left != e2->left) // Same point, but one is a left endpoint and the other a right endpoint. The right endpoint is processed first
return !e1->left;
// Same point, both events are left endpoints or both are right endpoints. The event associate to the bottom segment is processed first
return e1->below (e2->other->p);
}
};
} // end of anonymous namespace
bool SegmentComp::operator() (SweepEvent* e1, SweepEvent* e2) const {
if (e1 == e2)
return false;
if (signedArea (e1->p, e1->other->p, e2->p) != 0 || signedArea (e1->p, e1->other->p, e2->other->p) != 0) {
// Segments are not collinear
// If they share their left endpoint use the right endpoint to sort
if (e1->p == e2->p)
return e1->below (e2->other->p);
// Different points
SweepEventComp comp;
if (comp (e1, e2)) // has the segment associated to e1 been sorted in evp before the segment associated to e2?
return e1->below (e2->p);
// The segment associated to e2 has been sorted in evp before the segment associated to e1
return e2->above (e1->p);
}
// Segments are collinear. Just a consistent criterion is used
if (e1->p == e2->p)
return e1 < e2;
SweepEventComp comp;
return comp (e1, e2);
}
//#define _DEBUG_
void Polygon::computeHoles ()
{
if (ncontours () < 2) {
if (ncontours () == 1 && contour (0).clockwise ())
contour (0).changeOrientation ();
return;
}
vector<SweepEvent> ev;
vector<SweepEvent*> evp;
ev.reserve (nvertices ()*2);
evp.reserve (nvertices ()*2);
for (unsigned i = 0; i < ncontours (); i++) {
// cout << contour (i);
contour (i).setCounterClockwise ();
// cout << contour (i);
for (unsigned j = 0; j < contour (i).nedges (); j++) {
Segment s = contour(i).segment (j);
if (s.begin ().x == s.end ().x) // vertical segments are not processed
continue;
ev.push_back (SweepEvent (s.begin (), true, i));
ev.push_back (SweepEvent (s.end (), true, i));
SweepEvent* se1 = &ev[ev.size ()-2];
SweepEvent* se2 = &ev[ev.size ()-1];
se1->other = se2;
se2->other = se1;
if (se1->p.x < se2->p.x) {
se2->left = false;
se1->inOut = false;
} else {
se1->left = false;
se2->inOut = true;
}
evp.push_back (se1);
evp.push_back (se2);
}
}
sort (evp.begin (), evp.end (), SweepEventComp ());
set<SweepEvent*, SegmentComp> S; // Status line
vector<bool> processed (ncontours (), false);
vector<int> holeOf (ncontours (), -1);
int nprocessed = 0;
for (unsigned i = 0; i < evp.size () && nprocessed < ncontours (); i++) {
SweepEvent* e = evp[i];
#ifdef _DEBUG_
cout << "Process event: " << *e << endl;
#endif
if (e->left) { // the segment must be inserted into S
e->poss = S.insert(e).first;
if (!processed[e->pl]) {
processed[e->pl] = true;
nprocessed++;
set<SweepEvent*, SegmentComp>::iterator prev = e->poss;
if (prev == S.begin()) {
contour (e->pl).setCounterClockwise ();
} else {
prev--;
if (!(*prev)->inOut) {
holeOf[e->pl] = (*prev)->pl;
contour (e->pl).setExternal (false);
contour ((*prev)->pl).addHole (e->pl);
if (contour((*prev)->pl).counterclockwise ())
contour (e->pl).setClockwise ();
else
contour (e->pl).setCounterClockwise ();
} else if (holeOf[(*prev)->pl] != -1) {
holeOf[e->pl] = holeOf[(*prev)->pl];
contour (e->pl).setExternal (false);
contour (holeOf[e->pl]).addHole (e->pl);
if (contour(holeOf[e->pl]).counterclockwise ())
contour (e->pl).setClockwise ();
else
contour (e->pl).setCounterClockwise ();
} else {
contour (e->pl).setCounterClockwise ();
}
}
}
} else { // the segment must be removed from S
S.erase (e->other->poss);
}
#ifdef _DEBUG_
cout << "Tras ajuste: " << endl;
for (set<SweepEvent*, SegmentComp>::const_iterator it2 = S.begin(); it2 != S.end(); it2++)
cout << **it2 << endl;
cout << endl;
string st;
getline (cin, st);
#endif
}
}
|
