1 | #pragma once |
2 | |
3 | #include <mapbox/geometry/polygon.hpp> |
4 | #include <mapbox/geometry/envelope.hpp> |
5 | #include <mapbox/geometry/point.hpp> |
6 | #include <mapbox/geometry/point_arithmetic.hpp> |
7 | |
8 | #include <algorithm> |
9 | #include <cmath> |
10 | #include <iostream> |
11 | #include <queue> |
12 | |
13 | namespace mapbox { |
14 | |
15 | namespace detail { |
16 | |
17 | // get squared distance from a point to a segment |
18 | template <class T> |
19 | T getSegDistSq(const geometry::point<T>& p, |
20 | const geometry::point<T>& a, |
21 | const geometry::point<T>& b) { |
22 | auto x = a.x; |
23 | auto y = a.y; |
24 | auto dx = b.x - x; |
25 | auto dy = b.y - y; |
26 | |
27 | if (dx != 0 || dy != 0) { |
28 | |
29 | auto t = ((p.x - x) * dx + (p.y - y) * dy) / (dx * dx + dy * dy); |
30 | |
31 | if (t > 1) { |
32 | x = b.x; |
33 | y = b.y; |
34 | |
35 | } else if (t > 0) { |
36 | x += dx * t; |
37 | y += dy * t; |
38 | } |
39 | } |
40 | |
41 | dx = p.x - x; |
42 | dy = p.y - y; |
43 | |
44 | return dx * dx + dy * dy; |
45 | } |
46 | |
47 | // signed distance from point to polygon outline (negative if point is outside) |
48 | template <class T> |
49 | auto pointToPolygonDist(const geometry::point<T>& point, const geometry::polygon<T>& polygon) { |
50 | bool inside = false; |
51 | auto minDistSq = std::numeric_limits<double>::infinity(); |
52 | |
53 | for (const auto& ring : polygon) { |
54 | for (std::size_t i = 0, len = ring.size(), j = len - 1; i < len; j = i++) { |
55 | const auto& a = ring[i]; |
56 | const auto& b = ring[j]; |
57 | |
58 | if ((a.y > point.y) != (b.y > point.y) && |
59 | (point.x < (b.x - a.x) * (point.y - a.y) / (b.y - a.y) + a.x)) inside = !inside; |
60 | |
61 | minDistSq = std::min(minDistSq, getSegDistSq(point, a, b)); |
62 | } |
63 | } |
64 | |
65 | return (inside ? 1 : -1) * std::sqrt(x: minDistSq); |
66 | } |
67 | |
68 | template <class T> |
69 | struct Cell { |
70 | Cell(const geometry::point<T>& c_, T h_, const geometry::polygon<T>& polygon) |
71 | : c(c_), |
72 | h(h_), |
73 | d(pointToPolygonDist(c, polygon)), |
74 | max(d + h * std::sqrt(x: 2)) |
75 | {} |
76 | |
77 | geometry::point<T> c; // cell center |
78 | T h; // half the cell size |
79 | T d; // distance from cell center to polygon |
80 | T max; // max distance to polygon within a cell |
81 | }; |
82 | |
83 | // get polygon centroid |
84 | template <class T> |
85 | Cell<T> getCentroidCell(const geometry::polygon<T>& polygon) { |
86 | T area = 0; |
87 | geometry::point<T> c { 0, 0 }; |
88 | const auto& ring = polygon.at(0); |
89 | |
90 | for (std::size_t i = 0, len = ring.size(), j = len - 1; i < len; j = i++) { |
91 | const geometry::point<T>& a = ring[i]; |
92 | const geometry::point<T>& b = ring[j]; |
93 | auto f = a.x * b.y - b.x * a.y; |
94 | c.x += (a.x + b.x) * f; |
95 | c.y += (a.y + b.y) * f; |
96 | area += f * 3; |
97 | } |
98 | |
99 | return Cell<T>(area == 0 ? ring.at(0) : c / area, 0, polygon); |
100 | } |
101 | |
102 | } // namespace detail |
103 | |
104 | template <class T> |
105 | geometry::point<T> polylabel(const geometry::polygon<T>& polygon, T precision = 1, bool debug = false) { |
106 | using namespace detail; |
107 | |
108 | // find the bounding box of the outer ring |
109 | const geometry::box<T> envelope = geometry::envelope(polygon.at(0)); |
110 | |
111 | const geometry::point<T> size { |
112 | envelope.max.x - envelope.min.x, |
113 | envelope.max.y - envelope.min.y |
114 | }; |
115 | |
116 | const T cellSize = std::min(size.x, size.y); |
117 | T h = cellSize / 2; |
118 | |
119 | // a priority queue of cells in order of their "potential" (max distance to polygon) |
120 | auto compareMax = [] (const Cell<T>& a, const Cell<T>& b) { |
121 | return a.max < b.max; |
122 | }; |
123 | using Queue = std::priority_queue<Cell<T>, std::vector<Cell<T>>, decltype(compareMax)>; |
124 | Queue cellQueue(compareMax); |
125 | |
126 | if (cellSize == 0) { |
127 | return envelope.min; |
128 | } |
129 | |
130 | // cover polygon with initial cells |
131 | for (T x = envelope.min.x; x < envelope.max.x; x += cellSize) { |
132 | for (T y = envelope.min.y; y < envelope.max.y; y += cellSize) { |
133 | cellQueue.push(Cell<T>({x + h, y + h}, h, polygon)); |
134 | } |
135 | } |
136 | |
137 | // take centroid as the first best guess |
138 | auto bestCell = getCentroidCell(polygon); |
139 | |
140 | // special case for rectangular polygons |
141 | Cell<T> bboxCell(envelope.min + size / 2.0, 0, polygon); |
142 | if (bboxCell.d > bestCell.d) { |
143 | bestCell = bboxCell; |
144 | } |
145 | |
146 | auto numProbes = cellQueue.size(); |
147 | while (!cellQueue.empty()) { |
148 | // pick the most promising cell from the queue |
149 | auto cell = cellQueue.top(); |
150 | cellQueue.pop(); |
151 | |
152 | // update the best cell if we found a better one |
153 | if (cell.d > bestCell.d) { |
154 | bestCell = cell; |
155 | if (debug) std::cout << "found best " << ::round(x: 1e4 * cell.d) / 1e4 << " after " << numProbes << " probes" << std::endl; |
156 | } |
157 | |
158 | // do not drill down further if there's no chance of a better solution |
159 | if (cell.max - bestCell.d <= precision) continue; |
160 | |
161 | // split the cell into four cells |
162 | h = cell.h / 2; |
163 | cellQueue.push(Cell<T>({cell.c.x - h, cell.c.y - h}, h, polygon)); |
164 | cellQueue.push(Cell<T>({cell.c.x + h, cell.c.y - h}, h, polygon)); |
165 | cellQueue.push(Cell<T>({cell.c.x - h, cell.c.y + h}, h, polygon)); |
166 | cellQueue.push(Cell<T>({cell.c.x + h, cell.c.y + h}, h, polygon)); |
167 | numProbes += 4; |
168 | } |
169 | |
170 | if (debug) { |
171 | std::cout << "num probes: " << numProbes << std::endl; |
172 | std::cout << "best distance: " << bestCell.d << std::endl; |
173 | } |
174 | |
175 | return bestCell.c; |
176 | } |
177 | |
178 | } // namespace mapbox |
179 | |