#include #include #include #include #include #include "geometry.hpp" struct point { double x; double y; point(double x_, double y_) : x(x_), y(y_) { } }; typedef std::pair segment; // https://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect // // beware of // https://stackoverflow.com/questions/9043805/test-if-two-lines-intersect-javascript-function/16725715#16725715 // which does not seem to produce correct results. std::pair get_line_intersection(double p0_x, double p0_y, double p1_x, double p1_y, double p2_x, double p2_y, double p3_x, double p3_y) { double d01_x, d01_y, d23_x, d23_y; d01_x = p1_x - p0_x; d01_y = p1_y - p0_y; d23_x = p3_x - p2_x; d23_y = p3_y - p2_y; float det = (-d23_x * d01_y + d01_x * d23_y); if (det != 0) { double t, s; t = (d23_x * (p0_y - p2_y) - d23_y * (p0_x - p2_x)) / det; s = (-d01_y * (p0_x - p2_x) + d01_x * (p0_y - p2_y)) / det; if (s >= 0 && s <= 1 && t >= 0 && t <= 1) { return std::make_pair(t, s); #if 0 printf("%f,%f to %f,%f and %f,%f to %f,%f: %f and %f\n", p0_x, p0_y, p1_x, p1_y, p2_x, p2_y, p3_x, p3_y, t, s); printf("%f,%f or %f,%f\n", p0_x + t * d01_x, p0_y + t * d01_y, p2_x + s * d23_x, p2_y + s * d23_y); #endif } } return std::make_pair(-1, -1); } bool intersect(std::vector &segs, size_t s1, size_t s2) { auto intersections = get_line_intersection(std::round(segs[s1].first.x), std::round(segs[s1].first.y), std::round(segs[s1].second.x), std::round(segs[s1].second.y), std::round(segs[s2].first.x), std::round(segs[s2].first.y), std::round(segs[s2].second.x), std::round(segs[s2].second.y)); bool changed = false; if (intersections.first >= 0) { // XXX introduce a new node } else { // XXX handle collinear } return changed; } struct scan_transition { double y; size_t segment; scan_transition(double y_, size_t segment_) : y(y_), segment(segment_) { } bool operator<(scan_transition const &s) const { if (y < s.y) { return true; } else { return false; } } }; std::vector snap_round(std::vector segs) { bool again = true; while (again) { again = false; // set up for a scanline traversal of the segments // to find the pairs that intersect // while not looking at pairs that can't possibly intersect // index by rounded y coordinates, since we will be // intersecting with rounded coordinates std::vector tops; std::vector bottoms; for (size_t i = 0; i < segs.size(); i++) { if (std::round(segs[i].first.y) < std::round(segs[i].second.y)) { tops.emplace_back(std::round(segs[i].first.y), i); bottoms.emplace_back(std::round(segs[i].second.y), i); } else { tops.emplace_back(std::round(segs[i].second.y), i); bottoms.emplace_back(std::round(segs[i].first.y), i); } } std::sort(tops.begin(), tops.end()); std::sort(bottoms.begin(), bottoms.end()); // do the scan std::set active; std::set> already; size_t bottom = 0; for (size_t i = 0; i < tops.size(); i++) { // activate anything that is coming into view active.insert(tops[i].segment); if (i + 1 < tops.size() && tops[i + 1].y == tops[i].y) { continue; } // look at the active segments for (size_t s1 : active) { for (size_t s2 : active) { if (s1 < s2) { if (already.find(std::make_pair(s1, s2)) == already.end()) { if (intersect(segs, s1, s2)) { // if the segments intersected, // we need to do another scan, // because introducing a new node // may have caused new intersections again = true; } already.insert(std::make_pair(s1, s2)); } } } } // deactivate anything that is going out of view if (i + 1 < tops.size()) { while (bottom < bottoms.size() && bottoms[bottom].y < tops[i + 1].y) { auto found = active.find(bottoms[bottom].segment); active.erase(found); bottom++; } } } if (again) { // let the intersections settle down before we start trying // to make additional changes continue; } // find identical opposite-winding segments and adjust for them // // this is in the same loop because we may introduce new self-intersections // in the course of trying to keep spindles alive, and will then need to // resolve those. } return segs; } drawvec clean_polygon(drawvec const &geom, int z, int detail) { double scale = 1LL << (32 - detail - z); // decompose polygon rings into segments std::vector> segments; for (size_t i = 0; i < geom.size(); i++) { if (geom[i].op == VT_MOVETO) { size_t j; for (j = i + 1; j < geom.size(); j++) { if (geom[j].op != VT_LINETO) { break; } } for (size_t k = i; k + 1 < j; k++) { std::pair seg = std::make_pair( point(geom[k].x / scale, geom[k].y / scale), point(geom[k + 1].x / scale, geom[k + 1].y / scale)); segments.push_back(seg); } i = j - 1; } } // snap-round intersecting segments segments = snap_round(segments); // reassemble segments into rings // remove collinear points? // determine ring nesting return drawvec(); }