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
|
#include <mbgl/util/geometry_within.hpp>
#include <algorithm>
namespace mbgl {
namespace {
bool rayIntersect(const Point<double>& p, const Point<double>& p1, const Point<double>& p2) {
return ((p1.y > p.y) != (p2.y > p.y)) && (p.x < (p2.x - p1.x) * (p.y - p1.y) / (p2.y - p1.y) + p1.x);
}
bool onBoundary(const Point<double>& p, const Point<double>& p1, const Point<double>& p2) {
const auto x1 = p.x - p1.x;
const auto y1 = p.y - p1.y;
const auto x2 = p.x - p2.x;
const auto y2 = p.y - p2.y;
return (x1 * y2 - x2 * y1 == 0) && (x1 * x2 <= 0) && (y1 * y2 <= 0);
}
// a, b are end points for line segment1, c and d are end points for line segment2
bool lineIntersectLine(const Point<double>& a, const Point<double>& b, const Point<double>& c, const Point<double>& d) {
const auto perp = [](const Point<double>& v1, const Point<double>& v2) { return (v1.x * v2.y - v1.y * v2.x); };
// check if two segments are parallel or not
// precondition is end point a, b is inside polygon, if line a->b is
// parallel to polygon edge c->d, then a->b won't intersect with c->d
auto vectorP = Point<double>(b.x - a.x, b.y - a.y);
auto vectorQ = Point<double>(d.x - c.x, d.y - c.y);
if (perp(vectorQ, vectorP) == 0) return false;
// check if p1 and p2 are in different sides of line segment q1->q2
const auto twoSided =
[](const Point<double>& p1, const Point<double>& p2, const Point<double>& q1, const Point<double>& q2) {
double x1, y1, x2, y2, x3, y3;
// q1->p1 (x1, y1), q1->p2 (x2, y2), q1->q2 (x3, y3)
x1 = p1.x - q1.x;
y1 = p1.y - q1.y;
x2 = p2.x - q1.x;
y2 = p2.y - q1.y;
x3 = q2.x - q1.x;
y3 = q2.y - q1.y;
if ((x1 * y3 - x3 * y1) * (x2 * y3 - x3 * y2) < 0) return true;
return false;
};
// If lines are intersecting with each other, the relative location should be:
// a and b lie in different sides of segment c->d
// c and d lie in different sides of segment a->b
if (twoSided(a, b, c, d) && twoSided(c, d, a, b)) return true;
return false;
}
bool lineIntersectPolygon(const Point<double>& p1, const Point<double>& p2, const Polygon<double>& polygon) {
for (auto ring : polygon) {
auto length = ring.size();
// loop through every edge of the ring
for (std::size_t i = 0; i < length - 1; ++i) {
if (lineIntersectLine(p1, p2, ring[i], ring[i + 1])) {
return true;
}
}
}
return false;
}
void updateBBox(WithinBBox& bbox, const Point<double>& p) {
bbox[0] = std::min(p.x, bbox[0]);
bbox[1] = std::min(p.y, bbox[1]);
bbox[2] = std::max(p.x, bbox[2]);
bbox[3] = std::max(p.y, bbox[3]);
}
bool isBBoxValid(const WithinBBox& bbox) {
return bbox != DefaultBBox;
}
} // namespace
bool boxWithinBox(const WithinBBox& bbox1, const WithinBBox& bbox2) {
if (!isBBoxValid(bbox1) || !isBBoxValid(bbox2)) return false;
if (bbox1[0] <= bbox2[0]) return false;
if (bbox1[2] >= bbox2[2]) return false;
if (bbox1[1] <= bbox2[1]) return false;
if (bbox1[3] >= bbox2[3]) return false;
return true;
}
WithinBBox calculateBBox(const Geometry<double>& geometries) {
WithinBBox result = DefaultBBox;
return geometries.match(
[&result](const Point<double>& point) {
updateBBox(result, point);
return result;
},
[&result](const MultiPoint<double>& points) {
for (const auto point : points) {
updateBBox(result, point);
}
return result;
},
[&result](const LineString<double>& line) {
for (const auto point : line) {
updateBBox(result, point);
}
return result;
},
[&result](const MultiLineString<double>& lines) {
for (const auto& line : lines) {
for (const auto point : line) {
updateBBox(result, point);
}
}
return result;
},
[&result](const Polygon<double>& polygon) {
for (const auto& ring : polygon) {
for (const auto point : ring) {
updateBBox(result, point);
}
}
return result;
},
[&result](const MultiPolygon<double>& polygons) {
for (const auto& polygon : polygons) {
for (const auto& ring : polygon) {
for (const auto point : ring) {
updateBBox(result, point);
}
}
}
return result;
},
[](const auto&) { return DefaultBBox; });
}
// ray casting algorithm for detecting if point is in polygon
bool pointWithinPolygon(const Point<double>& point, const Polygon<double>& polygon) {
bool within = false;
for (const auto& ring : polygon) {
const auto length = ring.size();
// loop through every edge of the ring
for (std::size_t i = 0; i < length - 1; ++i) {
if (onBoundary(point, ring[i], ring[i + 1])) return false;
if (rayIntersect(point, ring[i], ring[i + 1])) {
within = !within;
}
}
}
return within;
}
bool pointWithinPolygons(const Point<double>& point, const MultiPolygon<double>& polygons) {
for (const auto& polygon : polygons) {
if (pointWithinPolygon(point, polygon)) return true;
}
return false;
}
bool lineStringWithinPolygon(const LineString<double>& line, const Polygon<double>& polygon) {
const auto length = line.size();
// First, check if geometry points of line segments are all inside polygon
for (std::size_t i = 0; i < length; ++i) {
if (!pointWithinPolygon(line[i], polygon)) {
return false;
}
}
// Second, check if there is line segment intersecting polygon edge
for (std::size_t i = 0; i < length - 1; ++i) {
if (lineIntersectPolygon(line[i], line[i + 1], polygon)) {
return false;
}
}
return true;
}
bool lineStringWithinPolygons(const LineString<double>& line, const MultiPolygon<double>& polygons) {
for (const auto& polygon : polygons) {
if (lineStringWithinPolygon(line, polygon)) return true;
}
return false;
}
} // namespace mbgl
|
