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581 lines
16 KiB
C++
581 lines
16 KiB
C++
#pragma once
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#include <algorithm>
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#include <cmath>
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#include <exception>
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#include <iostream>
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#include <limits>
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#include <memory>
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#include <utility>
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#include <vector>
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namespace delaunator {
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//@see https://stackoverflow.com/questions/33333363/built-in-mod-vs-custom-mod-function-improve-the-performance-of-modulus-op/33333636#33333636
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inline size_t fast_mod(const size_t i, const size_t c) {
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return i >= c ? i % c : i;
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}
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// Kahan and Babuska summation, Neumaier variant; accumulates less FP error
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inline double sum(const std::vector<double>& x) {
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double sum = x[0];
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double err = 0.0;
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for (size_t i = 1; i < x.size(); i++) {
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const double k = x[i];
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const double m = sum + k;
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err += std::fabs(sum) >= std::fabs(k) ? sum - m + k : k - m + sum;
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sum = m;
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}
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return sum + err;
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}
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inline double dist(
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const double ax,
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const double ay,
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const double bx,
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const double by) {
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const double dx = ax - bx;
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const double dy = ay - by;
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return dx * dx + dy * dy;
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}
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inline double circumradius(
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const double ax,
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const double ay,
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const double bx,
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const double by,
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const double cx,
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const double cy) {
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const double dx = bx - ax;
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const double dy = by - ay;
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const double ex = cx - ax;
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const double ey = cy - ay;
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const double bl = dx * dx + dy * dy;
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const double cl = ex * ex + ey * ey;
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const double d = dx * ey - dy * ex;
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const double x = (ey * bl - dy * cl) * 0.5 / d;
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const double y = (dx * cl - ex * bl) * 0.5 / d;
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if ((bl > 0.0 || bl < 0.0) && (cl > 0.0 || cl < 0.0) && (d > 0.0 || d < 0.0)) {
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return x * x + y * y;
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} else {
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return std::numeric_limits<double>::max();
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}
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}
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inline bool orient(
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const double px,
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const double py,
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const double qx,
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const double qy,
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const double rx,
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const double ry) {
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return (qy - py) * (rx - qx) - (qx - px) * (ry - qy) < 0.0;
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}
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inline std::pair<double, double> circumcenter(
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const double ax,
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const double ay,
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const double bx,
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const double by,
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const double cx,
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const double cy) {
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const double dx = bx - ax;
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const double dy = by - ay;
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const double ex = cx - ax;
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const double ey = cy - ay;
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const double bl = dx * dx + dy * dy;
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const double cl = ex * ex + ey * ey;
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const double d = dx * ey - dy * ex;
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const double x = ax + (ey * bl - dy * cl) * 0.5 / d;
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const double y = ay + (dx * cl - ex * bl) * 0.5 / d;
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return std::make_pair(x, y);
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}
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struct compare {
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std::vector<double> const& coords;
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double cx;
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double cy;
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bool operator()(std::size_t i, std::size_t j) {
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const double d1 = dist(coords[2 * i], coords[2 * i + 1], cx, cy);
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const double d2 = dist(coords[2 * j], coords[2 * j + 1], cx, cy);
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const double diff1 = d1 - d2;
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const double diff2 = coords[2 * i] - coords[2 * j];
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const double diff3 = coords[2 * i + 1] - coords[2 * j + 1];
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if (diff1 > 0.0 || diff1 < 0.0) {
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return diff1 < 0;
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} else if (diff2 > 0.0 || diff2 < 0.0) {
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return diff2 < 0;
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} else {
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return diff3 < 0;
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}
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}
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};
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inline bool in_circle(
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const double ax,
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const double ay,
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const double bx,
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const double by,
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const double cx,
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const double cy,
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const double px,
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const double py) {
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const double dx = ax - px;
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const double dy = ay - py;
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const double ex = bx - px;
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const double ey = by - py;
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const double fx = cx - px;
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const double fy = cy - py;
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const double ap = dx * dx + dy * dy;
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const double bp = ex * ex + ey * ey;
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const double cp = fx * fx + fy * fy;
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return (dx * (ey * cp - bp * fy) -
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dy * (ex * cp - bp * fx) +
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ap * (ex * fy - ey * fx)) < 0.0;
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}
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constexpr double EPSILON = std::numeric_limits<double>::epsilon();
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constexpr std::size_t INVALID_INDEX = std::numeric_limits<std::size_t>::max();
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inline bool check_pts_equal(double x1, double y1, double x2, double y2) {
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return std::fabs(x1 - x2) <= EPSILON &&
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std::fabs(y1 - y2) <= EPSILON;
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}
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// monotonically increases with real angle, but doesn't need expensive trigonometry
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inline double pseudo_angle(const double dx, const double dy) {
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const double p = dx / (std::abs(dx) + std::abs(dy));
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return (dy > 0.0 ? 3.0 - p : 1.0 + p) / 4.0; // [0..1)
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}
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struct DelaunatorPoint {
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std::size_t i;
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double x;
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double y;
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std::size_t t;
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std::size_t prev;
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std::size_t next;
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bool removed;
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};
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class Delaunator {
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public:
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std::vector<double> const& coords;
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std::vector<std::size_t> triangles;
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std::vector<std::size_t> halfedges;
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std::vector<std::size_t> hull_prev;
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std::vector<std::size_t> hull_next;
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std::vector<std::size_t> hull_tri;
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std::size_t hull_start;
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Delaunator(std::vector<double> const& in_coords);
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double get_hull_area();
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private:
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std::vector<std::size_t> m_hash;
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double m_center_x;
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double m_center_y;
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std::size_t m_hash_size;
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std::vector<std::size_t> m_edge_stack;
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std::size_t legalize(std::size_t a);
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std::size_t hash_key(double x, double y) const;
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std::size_t add_triangle(
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std::size_t i0,
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std::size_t i1,
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std::size_t i2,
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std::size_t a,
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std::size_t b,
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std::size_t c);
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void link(std::size_t a, std::size_t b);
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};
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Delaunator::Delaunator(std::vector<double> const& in_coords)
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: coords(in_coords),
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triangles(),
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halfedges(),
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hull_prev(),
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hull_next(),
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hull_tri(),
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hull_start(),
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m_hash(),
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m_center_x(),
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m_center_y(),
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m_hash_size(),
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m_edge_stack() {
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std::size_t n = coords.size() >> 1;
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double max_x = std::numeric_limits<double>::min();
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double max_y = std::numeric_limits<double>::min();
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double min_x = std::numeric_limits<double>::max();
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double min_y = std::numeric_limits<double>::max();
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std::vector<std::size_t> ids;
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ids.reserve(n);
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for (std::size_t i = 0; i < n; i++) {
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const double x = coords[2 * i];
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const double y = coords[2 * i + 1];
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if (x < min_x) min_x = x;
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if (y < min_y) min_y = y;
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if (x > max_x) max_x = x;
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if (y > max_y) max_y = y;
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ids.push_back(i);
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}
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const double cx = (min_x + max_x) / 2;
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const double cy = (min_y + max_y) / 2;
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double min_dist = std::numeric_limits<double>::max();
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std::size_t i0 = INVALID_INDEX;
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std::size_t i1 = INVALID_INDEX;
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std::size_t i2 = INVALID_INDEX;
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// pick a seed point close to the centroid
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for (std::size_t i = 0; i < n; i++) {
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const double d = dist(cx, cy, coords[2 * i], coords[2 * i + 1]);
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if (d < min_dist) {
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i0 = i;
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min_dist = d;
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}
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}
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const double i0x = coords[2 * i0];
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const double i0y = coords[2 * i0 + 1];
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min_dist = std::numeric_limits<double>::max();
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// find the point closest to the seed
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for (std::size_t i = 0; i < n; i++) {
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if (i == i0) continue;
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const double d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1]);
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if (d < min_dist && d > 0.0) {
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i1 = i;
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min_dist = d;
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}
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}
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double i1x = coords[2 * i1];
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double i1y = coords[2 * i1 + 1];
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double min_radius = std::numeric_limits<double>::max();
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// find the third point which forms the smallest circumcircle with the first two
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for (std::size_t i = 0; i < n; i++) {
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if (i == i0 || i == i1) continue;
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const double r = circumradius(
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i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1]);
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if (r < min_radius) {
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i2 = i;
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min_radius = r;
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}
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}
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if (!(min_radius < std::numeric_limits<double>::max())) {
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throw std::runtime_error("not triangulation");
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}
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double i2x = coords[2 * i2];
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double i2y = coords[2 * i2 + 1];
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if (orient(i0x, i0y, i1x, i1y, i2x, i2y)) {
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std::swap(i1, i2);
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std::swap(i1x, i2x);
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std::swap(i1y, i2y);
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}
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std::tie(m_center_x, m_center_y) = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y);
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// sort the points by distance from the seed triangle circumcenter
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std::sort(ids.begin(), ids.end(), compare{ coords, m_center_x, m_center_y });
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// initialize a hash table for storing edges of the advancing convex hull
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m_hash_size = static_cast<std::size_t>(std::llround(std::ceil(std::sqrt(n))));
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m_hash.resize(m_hash_size);
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std::fill(m_hash.begin(), m_hash.end(), INVALID_INDEX);
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// initialize arrays for tracking the edges of the advancing convex hull
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hull_prev.resize(n);
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hull_next.resize(n);
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hull_tri.resize(n);
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hull_start = i0;
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hull_next[i0] = hull_prev[i2] = i1;
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hull_next[i1] = hull_prev[i0] = i2;
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hull_next[i2] = hull_prev[i1] = i0;
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hull_tri[i0] = 0;
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hull_tri[i1] = 1;
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hull_tri[i2] = 2;
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m_hash[hash_key(i0x, i0y)] = i0;
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m_hash[hash_key(i1x, i1y)] = i1;
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m_hash[hash_key(i2x, i2y)] = i2;
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std::size_t max_triangles = n < 3 ? 1 : 2 * n - 5;
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triangles.reserve(max_triangles * 3);
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halfedges.reserve(max_triangles * 3);
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add_triangle(i0, i1, i2, INVALID_INDEX, INVALID_INDEX, INVALID_INDEX);
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double xp = std::numeric_limits<double>::quiet_NaN();
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double yp = std::numeric_limits<double>::quiet_NaN();
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for (std::size_t k = 0; k < n; k++) {
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const std::size_t i = ids[k];
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const double x = coords[2 * i];
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const double y = coords[2 * i + 1];
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// skip near-duplicate points
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if (k > 0 && check_pts_equal(x, y, xp, yp)) continue;
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xp = x;
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yp = y;
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// skip seed triangle points
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if (
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check_pts_equal(x, y, i0x, i0y) ||
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check_pts_equal(x, y, i1x, i1y) ||
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check_pts_equal(x, y, i2x, i2y)) continue;
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// find a visible edge on the convex hull using edge hash
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std::size_t start = 0;
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size_t key = hash_key(x, y);
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for (size_t j = 0; j < m_hash_size; j++) {
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start = m_hash[fast_mod(key + j, m_hash_size)];
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if (start != INVALID_INDEX && start != hull_next[start]) break;
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}
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start = hull_prev[start];
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size_t e = start;
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size_t q;
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while (q = hull_next[e], !orient(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1])) { //TODO: does it works in a same way as in JS
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e = q;
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if (e == start) {
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e = INVALID_INDEX;
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break;
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}
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}
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if (e == INVALID_INDEX) continue; // likely a near-duplicate point; skip it
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// add the first triangle from the point
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std::size_t t = add_triangle(
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e,
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i,
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hull_next[e],
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INVALID_INDEX,
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INVALID_INDEX,
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hull_tri[e]);
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hull_tri[i] = legalize(t + 2);
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hull_tri[e] = t;
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// walk forward through the hull, adding more triangles and flipping recursively
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std::size_t next = hull_next[e];
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while (
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q = hull_next[next],
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orient(x, y, coords[2 * next], coords[2 * next + 1], coords[2 * q], coords[2 * q + 1])) {
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t = add_triangle(next, i, q, hull_tri[i], INVALID_INDEX, hull_tri[next]);
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hull_tri[i] = legalize(t + 2);
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hull_next[next] = next; // mark as removed
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next = q;
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}
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// walk backward from the other side, adding more triangles and flipping
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if (e == start) {
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while (
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q = hull_prev[e],
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orient(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1])) {
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t = add_triangle(q, i, e, INVALID_INDEX, hull_tri[e], hull_tri[q]);
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legalize(t + 2);
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hull_tri[q] = t;
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hull_next[e] = e; // mark as removed
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e = q;
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}
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}
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// update the hull indices
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hull_prev[i] = e;
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hull_start = e;
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hull_prev[next] = i;
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hull_next[e] = i;
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hull_next[i] = next;
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m_hash[hash_key(x, y)] = i;
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m_hash[hash_key(coords[2 * e], coords[2 * e + 1])] = e;
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}
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}
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double Delaunator::get_hull_area() {
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std::vector<double> hull_area;
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size_t e = hull_start;
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do {
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hull_area.push_back((coords[2 * e] - coords[2 * hull_prev[e]]) * (coords[2 * e + 1] + coords[2 * hull_prev[e] + 1]));
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e = hull_next[e];
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} while (e != hull_start);
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return sum(hull_area);
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}
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std::size_t Delaunator::legalize(std::size_t a) {
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std::size_t i = 0;
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std::size_t ar = 0;
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m_edge_stack.clear();
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// recursion eliminated with a fixed-size stack
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while (true) {
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const size_t b = halfedges[a];
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/* if the pair of triangles doesn't satisfy the Delaunay condition
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* (p1 is inside the circumcircle of [p0, pl, pr]), flip them,
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* then do the same check/flip recursively for the new pair of triangles
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*
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* pl pl
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* /||\ / \
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* al/ || \bl al/ \a
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* / || \ / \
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* / a||b \ flip /___ar___\
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* p0\ || /p1 => p0\---bl---/p1
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* \ || / \ /
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* ar\ || /br b\ /br
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* \||/ \ /
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* pr pr
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*/
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const size_t a0 = 3 * (a / 3);
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ar = a0 + (a + 2) % 3;
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if (b == INVALID_INDEX) {
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if (i > 0) {
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i--;
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a = m_edge_stack[i];
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continue;
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} else {
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//i = INVALID_INDEX;
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break;
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}
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}
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const size_t b0 = 3 * (b / 3);
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const size_t al = a0 + (a + 1) % 3;
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const size_t bl = b0 + (b + 2) % 3;
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const std::size_t p0 = triangles[ar];
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const std::size_t pr = triangles[a];
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const std::size_t pl = triangles[al];
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const std::size_t p1 = triangles[bl];
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const bool illegal = in_circle(
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coords[2 * p0],
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coords[2 * p0 + 1],
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coords[2 * pr],
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coords[2 * pr + 1],
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coords[2 * pl],
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coords[2 * pl + 1],
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coords[2 * p1],
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coords[2 * p1 + 1]);
|
|
|
|
if (illegal) {
|
|
triangles[a] = p1;
|
|
triangles[b] = p0;
|
|
|
|
auto hbl = halfedges[bl];
|
|
|
|
// edge swapped on the other side of the hull (rare); fix the halfedge reference
|
|
if (hbl == INVALID_INDEX) {
|
|
std::size_t e = hull_start;
|
|
do {
|
|
if (hull_tri[e] == bl) {
|
|
hull_tri[e] = a;
|
|
break;
|
|
}
|
|
e = hull_next[e];
|
|
} while (e != hull_start);
|
|
}
|
|
link(a, hbl);
|
|
link(b, halfedges[ar]);
|
|
link(ar, bl);
|
|
std::size_t br = b0 + (b + 1) % 3;
|
|
|
|
if (i < m_edge_stack.size()) {
|
|
m_edge_stack[i] = br;
|
|
} else {
|
|
m_edge_stack.push_back(br);
|
|
}
|
|
i++;
|
|
|
|
} else {
|
|
if (i > 0) {
|
|
i--;
|
|
a = m_edge_stack[i];
|
|
continue;
|
|
} else {
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
return ar;
|
|
}
|
|
|
|
inline std::size_t Delaunator::hash_key(const double x, const double y) const {
|
|
const double dx = x - m_center_x;
|
|
const double dy = y - m_center_y;
|
|
return fast_mod(
|
|
static_cast<std::size_t>(std::llround(std::floor(pseudo_angle(dx, dy) * static_cast<double>(m_hash_size)))),
|
|
m_hash_size);
|
|
}
|
|
|
|
std::size_t Delaunator::add_triangle(
|
|
std::size_t i0,
|
|
std::size_t i1,
|
|
std::size_t i2,
|
|
std::size_t a,
|
|
std::size_t b,
|
|
std::size_t c) {
|
|
std::size_t t = triangles.size();
|
|
triangles.push_back(i0);
|
|
triangles.push_back(i1);
|
|
triangles.push_back(i2);
|
|
link(t, a);
|
|
link(t + 1, b);
|
|
link(t + 2, c);
|
|
return t;
|
|
}
|
|
|
|
void Delaunator::link(const std::size_t a, const std::size_t b) {
|
|
std::size_t s = halfedges.size();
|
|
if (a == s) {
|
|
halfedges.push_back(b);
|
|
} else if (a < s) {
|
|
halfedges[a] = b;
|
|
} else {
|
|
throw std::runtime_error("Cannot link edge");
|
|
}
|
|
if (b != INVALID_INDEX) {
|
|
std::size_t s2 = halfedges.size();
|
|
if (b == s2) {
|
|
halfedges.push_back(a);
|
|
} else if (b < s2) {
|
|
halfedges[b] = a;
|
|
} else {
|
|
throw std::runtime_error("Cannot link edge");
|
|
}
|
|
}
|
|
}
|
|
|
|
} //namespace delaunator
|