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#pragma once
#include <mapbox/geometry/polygon.hpp>
#include <mapbox/geometry/envelope.hpp>
#include <mapbox/geometry/point.hpp>
#include <mapbox/geometry/point_arithmetic.hpp>
#include <algorithm>
#include <cmath>
#include <iostream>
#include <queue>
namespace mapbox {
namespace detail {
// get squared distance from a point to a segment
template <class T>
T getSegDistSq(const geometry::point<T>& p,
const geometry::point<T>& a,
const geometry::point<T>& b) {
auto x = a.x;
auto y = a.y;
auto dx = b.x - x;
auto dy = b.y - y;
if (dx != 0 || dy != 0) {
auto t = ((p.x - x) * dx + (p.y - y) * dy) / (dx * dx + dy * dy);
if (t > 1) {
x = b.x;
y = b.y;
} else if (t > 0) {
x += dx * t;
y += dy * t;
}
}
dx = p.x - x;
dy = p.y - y;
return dx * dx + dy * dy;
}
// signed distance from point to polygon outline (negative if point is outside)
template <class T>
auto pointToPolygonDist(const geometry::point<T>& point, const geometry::polygon<T>& polygon) {
bool inside = false;
auto minDistSq = std::numeric_limits<double>::infinity();
for (const auto& ring : polygon) {
for (std::size_t i = 0, len = ring.size(), j = len - 1; i < len; j = i++) {
const auto& a = ring[i];
const auto& b = ring[j];
if ((a.y > point.y) != (b.y > point.y) &&
(point.x < (b.x - a.x) * (point.y - a.y) / (b.y - a.y) + a.x)) inside = !inside;
minDistSq = std::min(minDistSq, getSegDistSq(point, a, b));
}
}
return (inside ? 1 : -1) * std::sqrt(minDistSq);
}
template <class T>
struct Cell {
Cell(const geometry::point<T>& c_, T h_, const geometry::polygon<T>& polygon)
: c(c_),
h(h_),
d(pointToPolygonDist(c, polygon)),
max(d + h * std::sqrt(2))
{}
geometry::point<T> c; // cell center
T h; // half the cell size
T d; // distance from cell center to polygon
T max; // max distance to polygon within a cell
};
// get polygon centroid
template <class T>
Cell<T> getCentroidCell(const geometry::polygon<T>& polygon) {
T area = 0;
geometry::point<T> c { 0, 0 };
const auto& ring = polygon.at(0);
for (std::size_t i = 0, len = ring.size(), j = len - 1; i < len; j = i++) {
const geometry::point<T>& a = ring[i];
const geometry::point<T>& b = ring[j];
auto f = a.x * b.y - b.x * a.y;
c.x += (a.x + b.x) * f;
c.y += (a.y + b.y) * f;
area += f * 3;
}
return Cell<T>(area == 0 ? ring.at(0) : c / area, 0, polygon);
}
} // namespace detail
template <class T>
geometry::point<T> polylabel(const geometry::polygon<T>& polygon, T precision = 1, bool debug = false) {
using namespace detail;
// find the bounding box of the outer ring
const geometry::box<T> envelope = geometry::envelope(polygon.at(0));
const geometry::point<T> size {
envelope.max.x - envelope.min.x,
envelope.max.y - envelope.min.y
};
const T cellSize = std::min(size.x, size.y);
T h = cellSize / 2;
// a priority queue of cells in order of their "potential" (max distance to polygon)
auto compareMax = [] (const Cell<T>& a, const Cell<T>& b) {
return a.max < b.max;
};
using Queue = std::priority_queue<Cell<T>, std::vector<Cell<T>>, decltype(compareMax)>;
Queue cellQueue(compareMax);
if (cellSize == 0) {
return envelope.min;
}
// cover polygon with initial cells
for (T x = envelope.min.x; x < envelope.max.x; x += cellSize) {
for (T y = envelope.min.y; y < envelope.max.y; y += cellSize) {
cellQueue.push(Cell<T>({x + h, y + h}, h, polygon));
}
}
// take centroid as the first best guess
auto bestCell = getCentroidCell(polygon);
// second guess: bounding box centroid
Cell<T> bboxCell(envelope.min + size / 2.0, 0, polygon);
if (bboxCell.d > bestCell.d) {
bestCell = bboxCell;
}
auto numProbes = cellQueue.size();
while (!cellQueue.empty()) {
// pick the most promising cell from the queue
auto cell = cellQueue.top();
cellQueue.pop();
// update the best cell if we found a better one
if (cell.d > bestCell.d) {
bestCell = cell;
if (debug) std::cout << "found best " << ::round(1e4 * cell.d) / 1e4 << " after " << numProbes << " probes" << std::endl;
}
// do not drill down further if there's no chance of a better solution
if (cell.max - bestCell.d <= precision) continue;
// split the cell into four cells
h = cell.h / 2;
cellQueue.push(Cell<T>({cell.c.x - h, cell.c.y - h}, h, polygon));
cellQueue.push(Cell<T>({cell.c.x + h, cell.c.y - h}, h, polygon));
cellQueue.push(Cell<T>({cell.c.x - h, cell.c.y + h}, h, polygon));
cellQueue.push(Cell<T>({cell.c.x + h, cell.c.y + h}, h, polygon));
numProbes += 4;
}
if (debug) {
std::cout << "num probes: " << numProbes << std::endl;
std::cout << "best distance: " << bestCell.d << std::endl;
}
return bestCell.c;
}
} // namespace mapbox
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