tippecanoe/geometry.cpp

#include <iostream>
#include <fstream>
#include <string>
#include <stack>
#include <vector>
#include <map>
#include <algorithm>
#include <cstdio>
#include <unistd.h>
#include <cmath>
#include <limits.h>
#include <sqlite3.h>
#include <mapbox/geometry/point.hpp>
#include <mapbox/geometry/multi_polygon.hpp>
#include <mapbox/geometry/wagyu/wagyu.hpp>
#include <mapbox/geometry/wagyu/quick_clip.hpp>
#include <mapbox/geometry/snap_rounding.hpp>
#include "geometry.hpp"
#include "projection.hpp"
#include "serial.hpp"
#include "main.hpp"

static int pnpoly(drawvec &vert, size_t start, size_t nvert, long long testx, long long testy);
static int clip(double *x0, double *y0, double *x1, double *y1, double xmin, double ymin, double xmax, double ymax);

drawvec decode_geometry(FILE *meta, long long *geompos, int z, unsigned tx, unsigned ty, long long *bbox, unsigned initial_x, unsigned initial_y) {
	drawvec out;

	bbox[0] = LLONG_MAX;
	bbox[1] = LLONG_MAX;
	bbox[2] = LLONG_MIN;
	bbox[3] = LLONG_MIN;

	long long wx = initial_x, wy = initial_y;

	while (1) {
		draw d;

		if (!deserialize_byte_io(meta, &d.op, geompos)) {
			fprintf(stderr, "Internal error: Unexpected end of file in geometry\n");
			exit(EXIT_FAILURE);
		}
		if (d.op == VT_END) {
			break;
		}

		if (d.op == VT_MOVETO || d.op == VT_LINETO) {
			long long dx, dy;

			deserialize_long_long_io(meta, &dx, geompos);
			deserialize_long_long_io(meta, &dy, geompos);

			wx += dx * (1 << geometry_scale);
			wy += dy * (1 << geometry_scale);

			long long wwx = wx;
			long long wwy = wy;

			if (z != 0) {
				wwx -= tx << (32 - z);
				wwy -= ty << (32 - z);
			}

			if (wwx < bbox[0]) {
				bbox[0] = wwx;
			}
			if (wwy < bbox[1]) {
				bbox[1] = wwy;
			}
			if (wwx > bbox[2]) {
				bbox[2] = wwx;
			}
			if (wwy > bbox[3]) {
				bbox[3] = wwy;
			}

			d.x = wwx;
			d.y = wwy;
		}

		out.push_back(d);
	}

	return out;
}

void to_tile_scale(drawvec &geom, int z, int detail) {
	for (size_t i = 0; i < geom.size(); i++) {
		geom[i].x >>= (32 - detail - z);
		geom[i].y >>= (32 - detail - z);
	}
}

drawvec remove_noop(drawvec geom, int type, int shift) {
	// first pass: remove empty linetos

	long long x = 0, y = 0;
	drawvec out;

	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].op == VT_LINETO && (geom[i].x >> shift) == x && (geom[i].y >> shift) == y) {
			continue;
		}

		if (geom[i].op == VT_CLOSEPATH) {
			out.push_back(geom[i]);
		} else { /* moveto or lineto */
			out.push_back(geom[i]);
			x = geom[i].x >> shift;
			y = geom[i].y >> shift;
		}
	}

	// second pass: remove unused movetos

	if (type != VT_POINT) {
		geom = out;
		out.resize(0);

		for (size_t i = 0; i < geom.size(); i++) {
			if (geom[i].op == VT_MOVETO) {
				if (i + 1 >= geom.size()) {
					continue;
				}

				if (geom[i + 1].op == VT_MOVETO) {
					continue;
				}

				if (geom[i + 1].op == VT_CLOSEPATH) {
					fprintf(stderr, "Shouldn't happen\n");
					i++;  // also remove unused closepath
					continue;
				}
			}

			out.push_back(geom[i]);
		}
	}

	// second pass: remove empty movetos

	if (type == VT_LINE) {
		geom = out;
		out.resize(0);

		for (size_t i = 0; i < geom.size(); i++) {
			if (geom[i].op == VT_MOVETO) {
				if (i > 0 && geom[i - 1].op == VT_LINETO && (geom[i - 1].x >> shift) == (geom[i].x >> shift) && (geom[i - 1].y >> shift) == (geom[i].y >> shift)) {
					continue;
				}
			}

			out.push_back(geom[i]);
		}
	}

	return out;
}

double get_area(drawvec &geom, size_t i, size_t j) {
	double area = 0;
	for (size_t k = i; k < j; k++) {
		area += (long double) geom[k].x * (long double) geom[i + ((k - i + 1) % (j - i))].y;
		area -= (long double) geom[k].y * (long double) geom[i + ((k - i + 1) % (j - i))].x;
	}
	area /= 2;
	return area;
}

double get_mp_area(drawvec &geom) {
	double ret = 0;

	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;
				}
			}

			ret += get_area(geom, i, j);
			i = j - 1;
		}
	}

	return ret;
}

static void decode_clipped(mapbox::geometry::multi_polygon<long long> &t, drawvec &out) {
	out.clear();

	for (size_t i = 0; i < t.size(); i++) {
		for (size_t j = 0; j < t[i].size(); j++) {
			drawvec ring;

			for (size_t k = 0; k < t[i][j].size(); k++) {
				ring.push_back(draw((k == 0) ? VT_MOVETO : VT_LINETO, t[i][j][k].x, t[i][j][k].y));
			}

			if (ring.size() > 0 && ring[ring.size() - 1] != ring[0]) {
				fprintf(stderr, "Had to close ring\n");
				ring.push_back(draw(VT_LINETO, ring[0].x, ring[0].y));
			}

			double area = get_area(ring, 0, ring.size());

			if ((j == 0 && area < 0) || (j != 0 && area > 0)) {
				fprintf(stderr, "Ring area has wrong sign: %f for %zu\n", area, j);
				exit(EXIT_FAILURE);
			}

			for (size_t k = 0; k < ring.size(); k++) {
				out.push_back(ring[k]);
			}
		}
	}
}

drawvec clean_or_clip_poly(drawvec &geom, int z, int detail, int buffer, bool clip) {
	mapbox::geometry::wagyu::wagyu<long long> wagyu;

	geom = remove_noop(geom, VT_POLYGON, 0);
	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;
				}
			}

			if (j >= i + 4) {
				mapbox::geometry::linear_ring<long long> lr;

				for (size_t k = i; k < j; k++) {
					lr.push_back(mapbox::geometry::point<long long>(geom[k].x, geom[k].y));
				}

				if (lr.size() >= 3) {
					wagyu.add_ring(lr);
				}
			}

			i = j - 1;
		}
	}

	if (clip) {
		long long area = 0xFFFFFFFF;
		if (z != 0) {
			area = 1LL << (32 - z);
		}
		long long clip_buffer = buffer * area / 256;

		mapbox::geometry::linear_ring<long long> lr;

		lr.push_back(mapbox::geometry::point<long long>(-clip_buffer, -clip_buffer));
		lr.push_back(mapbox::geometry::point<long long>(-clip_buffer, area + clip_buffer));
		lr.push_back(mapbox::geometry::point<long long>(area + clip_buffer, area + clip_buffer));
		lr.push_back(mapbox::geometry::point<long long>(area + clip_buffer, -clip_buffer));
		lr.push_back(mapbox::geometry::point<long long>(-clip_buffer, -clip_buffer));

		wagyu.add_ring(lr, mapbox::geometry::wagyu::polygon_type_clip);
	}

	mapbox::geometry::multi_polygon<long long> result;
	try {
		wagyu.execute(mapbox::geometry::wagyu::clip_type_union, result, mapbox::geometry::wagyu::fill_type_positive, mapbox::geometry::wagyu::fill_type_positive);
	} catch (std::runtime_error e) {
		FILE *f = fopen("/tmp/wagyu.log", "w");
		fprintf(f, "%s\n", e.what());
		fprintf(stderr, "%s\n", e.what());
		fprintf(f, "[");

		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;
					}
				}

				if (j >= i + 4) {
					mapbox::geometry::linear_ring<long long> lr;

					if (i != 0) {
						fprintf(f, ",");
					}
					fprintf(f, "[");

					for (size_t k = i; k < j; k++) {
						lr.push_back(mapbox::geometry::point<long long>(geom[k].x, geom[k].y));
						if (k != i) {
							fprintf(f, ",");
						}
						fprintf(f, "[%lld,%lld]", geom[k].x, geom[k].y);
					}

					fprintf(f, "]");

					if (lr.size() >= 3) {
					}
				}

				i = j - 1;
			}
		}

		fprintf(f, "]");
		fprintf(f, "\n\n\n\n\n");

		fclose(f);
		fprintf(stderr, "Internal error: Polygon cleaning failed. Log in /tmp/wagyu.log\n");
		exit(EXIT_FAILURE);
	}

	drawvec ret;
	decode_clipped(result, ret);
	return ret;
}

/* pnpoly:
Copyright (c) 1970-2003, Wm. Randolph Franklin

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimers.
Redistributions in binary form must reproduce the above copyright notice in the documentation and/or other materials provided with the distribution.
The name of W. Randolph Franklin may not be used to endorse or promote products derived from this Software without specific prior written permission.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

static int pnpoly(drawvec &vert, size_t start, size_t nvert, long long testx, long long testy) {
	size_t i, j;
	bool c = false;
	for (i = 0, j = nvert - 1; i < nvert; j = i++) {
		if (((vert[i + start].y > testy) != (vert[j + start].y > testy)) &&
		    (testx < (vert[j + start].x - vert[i + start].x) * (testy - vert[i + start].y) / (double) (vert[j + start].y - vert[i + start].y) + vert[i + start].x))
			c = !c;
	}
	return c;
}

void check_polygon(drawvec &geom, drawvec &before) {
	geom = remove_noop(geom, VT_POLYGON, 0);

	mapbox::geometry::multi_polygon<long long> mp;
	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;
				}
			}

			if (j >= i + 4) {
				mapbox::geometry::linear_ring<long long> lr;

				for (size_t k = i; k < j; k++) {
					lr.push_back(mapbox::geometry::point<long long>(geom[k].x, geom[k].y));
				}

				if (lr.size() >= 3) {
					mapbox::geometry::polygon<long long> p;
					p.push_back(lr);
					mp.push_back(p);
				}
			}

			i = j - 1;
		}
	}

	mapbox::geometry::multi_polygon<long long> mp2 = mapbox::geometry::snap_round(mp, true, true);
	if (mp != mp2) {
		fprintf(stderr, "Internal error: self-intersecting polygon\n");
	}

	size_t outer_start = -1;
	size_t outer_len = 0;

	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;
				}
			}

			double area = get_area(geom, i, j);

#if 0
			fprintf(stderr, "looking at %lld to %lld, area %f\n", (long long) i, (long long) j, area);
#endif

			if (area > 0) {
				outer_start = i;
				outer_len = j - i;
			} else {
				for (size_t k = i; k < j; k++) {
					if (!pnpoly(geom, outer_start, outer_len, geom[k].x, geom[k].y)) {
						bool on_edge = false;

						for (size_t l = outer_start; l < outer_start + outer_len; l++) {
							if (geom[k].x == geom[l].x || geom[k].y == geom[l].y) {
								on_edge = true;
								break;
							}
						}

						if (!on_edge) {
							printf("%lld,%lld at %lld not in outer ring (%lld to %lld)\n", geom[k].x, geom[k].y, (long long) k, (long long) outer_start, (long long) (outer_start + outer_len));

#if 0
							for (size_t l = outer_start; l < outer_start + outer_len; l++) {
								fprintf(stderr, " %lld,%lld", geom[l].x, geom[l].y);
							}
#endif
						}
					}
				}
			}
		}
	}
}

drawvec close_poly(drawvec &geom) {
	drawvec out;

	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;
				}
			}

			if (j - 1 > i) {
				if (geom[j - 1].x != geom[i].x || geom[j - 1].y != geom[i].y) {
					fprintf(stderr, "Internal error: polygon not closed\n");
				}
			}

			for (size_t n = i; n < j - 1; n++) {
				out.push_back(geom[n]);
			}
			out.push_back(draw(VT_CLOSEPATH, 0, 0));

			i = j - 1;
		}
	}

	return out;
}

drawvec simple_clip_poly(drawvec &geom, long long minx, long long miny, long long maxx, long long maxy) {
	drawvec out;

	mapbox::geometry::point<long long> min(minx, miny);
	mapbox::geometry::point<long long> max(maxx, maxy);
	mapbox::geometry::box<long long> bbox(min, max);

	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;
				}
			}

			mapbox::geometry::linear_ring<long long> ring;
			for (size_t k = i; k < j; k++) {
				ring.push_back(mapbox::geometry::point<long long>(geom[k].x, geom[k].y));
			}

			mapbox::geometry::linear_ring<long long> lr = mapbox::geometry::wagyu::quick_clip::quick_lr_clip(ring, bbox);

			if (lr.size() > 0) {
				for (size_t k = 0; k < lr.size(); k++) {
					if (k == 0) {
						out.push_back(draw(VT_MOVETO, lr[k].x, lr[k].y));
					} else {
						out.push_back(draw(VT_LINETO, lr[k].x, lr[k].y));
					}
				}

				if (lr.size() > 0 && lr[0] != lr[lr.size() - 1]) {
					out.push_back(draw(VT_LINETO, lr[0].x, lr[0].y));
				}
			}

			i = j - 1;
		} else {
			fprintf(stderr, "Unexpected operation in polygon %d\n", (int) geom[i].op);
			exit(EXIT_FAILURE);
		}
	}

	return out;
}

drawvec simple_clip_poly(drawvec &geom, int z, int buffer) {
	long long area = 1LL << (32 - z);
	long long clip_buffer = buffer * area / 256;

	return simple_clip_poly(geom, -clip_buffer, -clip_buffer, area + clip_buffer, area + clip_buffer);
}

drawvec reduce_tiny_poly(drawvec &geom, int z, int detail, bool *reduced, double *accum_area) {
	drawvec out;
	long long pixel = (1 << (32 - detail - z)) * 2;

	*reduced = true;
	bool included_last_outer = false;

	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;
				}
			}

			double area = get_area(geom, i, j);

			// XXX There is an ambiguity here: If the area of a ring is 0 and it is followed by holes,
			// we don't know whether the area-0 ring was a hole too or whether it was the outer ring
			// that these subsequent holes are somehow being subtracted from. I hope that if a polygon
			// was simplified down to nothing, its holes also became nothing.

			if (area != 0) {
				// These are pixel coordinates, so area > 0 for the outer ring.
				// If the outer ring of a polygon was reduced to a pixel, its
				// inner rings must just have their area de-accumulated rather
				// than being drawn since we don't really know where they are.

				if (std::fabs(area) <= pixel * pixel || (area < 0 && !included_last_outer)) {
					// printf("area is only %f vs %lld so using square\n", area, pixel * pixel);

					*accum_area += area;
					if (area > 0 && *accum_area > pixel * pixel) {
						// XXX use centroid;

						out.push_back(draw(VT_MOVETO, geom[i].x - pixel / 2, geom[i].y - pixel / 2));
						out.push_back(draw(VT_LINETO, geom[i].x + pixel / 2, geom[i].y - pixel / 2));
						out.push_back(draw(VT_LINETO, geom[i].x + pixel / 2, geom[i].y + pixel / 2));
						out.push_back(draw(VT_LINETO, geom[i].x - pixel / 2, geom[i].y + pixel / 2));
						out.push_back(draw(VT_LINETO, geom[i].x - pixel / 2, geom[i].y - pixel / 2));

						*accum_area -= pixel * pixel;
					}

					if (area > 0) {
						included_last_outer = false;
					}
				} else {
					// printf("area is %f so keeping instead of %lld\n", area, pixel * pixel);

					for (size_t k = i; k <= j && k < geom.size(); k++) {
						out.push_back(geom[k]);
					}

					*reduced = false;

					if (area > 0) {
						included_last_outer = true;
					}
				}
			}

			i = j - 1;
		} else {
			fprintf(stderr, "how did we get here with %d in %d?\n", geom[i].op, (int) geom.size());

			for (size_t n = 0; n < geom.size(); n++) {
				fprintf(stderr, "%d/%lld/%lld ", geom[n].op, geom[n].x, geom[n].y);
			}
			fprintf(stderr, "\n");

			out.push_back(geom[i]);
		}
	}

	return out;
}

drawvec clip_point(drawvec &geom, int z, long long buffer) {
	drawvec out;

	long long min = 0;
	long long area = 1LL << (32 - z);

	min -= buffer * area / 256;
	area += buffer * area / 256;

	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].x >= min && geom[i].y >= min && geom[i].x <= area && geom[i].y <= area) {
			out.push_back(geom[i]);
		}
	}

	return out;
}

int quick_check(long long *bbox, int z, long long buffer) {
	long long min = 0;
	long long area = 1LL << (32 - z);

	min -= buffer * area / 256;
	area += buffer * area / 256;

	// bbox entirely outside the tile
	if (bbox[0] > area || bbox[1] > area) {
		return 0;
	}
	if (bbox[2] < min || bbox[3] < min) {
		return 0;
	}

	// bbox entirely within the tile
	if (bbox[0] > min && bbox[1] > min && bbox[2] < area && bbox[3] < area) {
		return 1;
	}

	// some overlap of edge
	return 2;
}

bool point_within_tile(long long x, long long y, int z, long long buffer) {
	// No adjustment for buffer, because the point must be
	// strictly within the tile to appear exactly once

	long long area = 1LL << (32 - z);

	return x >= 0 && y >= 0 && x < area && y < area;
}

drawvec clip_lines(drawvec &geom, int z, long long buffer) {
	drawvec out;

	long long min = 0;
	long long area = 1LL << (32 - z);
	min -= buffer * area / 256;
	area += buffer * area / 256;

	for (size_t i = 0; i < geom.size(); i++) {
		if (i > 0 && (geom[i - 1].op == VT_MOVETO || geom[i - 1].op == VT_LINETO) && geom[i].op == VT_LINETO) {
			double x1 = geom[i - 1].x;
			double y1 = geom[i - 1].y;

			double x2 = geom[i - 0].x;
			double y2 = geom[i - 0].y;

			int c = clip(&x1, &y1, &x2, &y2, min, min, area, area);

			if (c > 1) {  // clipped
				out.push_back(draw(VT_MOVETO, x1, y1));
				out.push_back(draw(VT_LINETO, x2, y2));
				out.push_back(draw(VT_MOVETO, geom[i].x, geom[i].y));
			} else if (c == 1) {  // unchanged
				out.push_back(geom[i]);
			} else {  // clipped away entirely
				out.push_back(draw(VT_MOVETO, geom[i].x, geom[i].y));
			}
		} else {
			out.push_back(geom[i]);
		}
	}

	return out;
}

static double square_distance_from_line(long long point_x, long long point_y, long long segA_x, long long segA_y, long long segB_x, long long segB_y) {
	double p2x = segB_x - segA_x;
	double p2y = segB_y - segA_y;
	double something = p2x * p2x + p2y * p2y;
	double u = 0 == something ? 0 : ((point_x - segA_x) * p2x + (point_y - segA_y) * p2y) / something;

	if (u > 1) {
		u = 1;
	} else if (u < 0) {
		u = 0;
	}

	double x = segA_x + u * p2x;
	double y = segA_y + u * p2y;

	double dx = x - point_x;
	double dy = y - point_y;

	return dx * dx + dy * dy;
}

// https://github.com/Project-OSRM/osrm-backend/blob/733d1384a40f/Algorithms/DouglasePeucker.cpp
static void douglas_peucker(drawvec &geom, int start, int n, double e, size_t kept, size_t retain) {
	e = e * e;
	std::stack<int> recursion_stack;

	{
		int left_border = 0;
		int right_border = 1;
		// Sweep linerarily over array and identify those ranges that need to be checked
		do {
			if (geom[start + right_border].necessary) {
				recursion_stack.push(left_border);
				recursion_stack.push(right_border);
				left_border = right_border;
			}
			++right_border;
		} while (right_border < n);
	}

	while (!recursion_stack.empty()) {
		// pop next element
		int second = recursion_stack.top();
		recursion_stack.pop();
		int first = recursion_stack.top();
		recursion_stack.pop();

		double max_distance = -1;
		int farthest_element_index = second;

		// find index idx of element with max_distance
		int i;
		for (i = first + 1; i < second; i++) {
			double temp_dist = square_distance_from_line(geom[start + i].x, geom[start + i].y, geom[start + first].x, geom[start + first].y, geom[start + second].x, geom[start + second].y);

			double distance = std::fabs(temp_dist);

			if ((distance > e || kept < retain) && distance > max_distance) {
				farthest_element_index = i;
				max_distance = distance;
			}
		}

		if (max_distance >= 0) {
			// mark idx as necessary
			geom[start + farthest_element_index].necessary = 1;
			kept++;

			if (1 < farthest_element_index - first) {
				recursion_stack.push(first);
				recursion_stack.push(farthest_element_index);
			}
			if (1 < second - farthest_element_index) {
				recursion_stack.push(farthest_element_index);
				recursion_stack.push(second);
			}
		}
	}
}

// If any line segment crosses a tile boundary, add a node there
// that cannot be simplified away, to prevent the edge of any
// feature from jumping abruptly at the tile boundary.
drawvec impose_tile_boundaries(drawvec &geom, long long extent) {
	drawvec out;

	for (size_t i = 0; i < geom.size(); i++) {
		if (i > 0 && geom[i].op == VT_LINETO && (geom[i - 1].op == VT_MOVETO || geom[i - 1].op == VT_LINETO)) {
			double x1 = geom[i - 1].x;
			double y1 = geom[i - 1].y;

			double x2 = geom[i - 0].x;
			double y2 = geom[i - 0].y;

			int c = clip(&x1, &y1, &x2, &y2, 0, 0, extent, extent);

			if (c > 1) {  // clipped
				if (x1 != geom[i - 1].x || y1 != geom[i - 1].y) {
					out.push_back(draw(VT_LINETO, x1, y1));
					out[out.size() - 1].necessary = 1;
				}
				if (x2 != geom[i - 0].x || y2 != geom[i - 0].y) {
					out.push_back(draw(VT_LINETO, x2, y2));
					out[out.size() - 1].necessary = 1;
				}
			}
		}

		out.push_back(geom[i]);
	}

	return out;
}

drawvec simplify_lines(drawvec &geom, int z, int detail, bool mark_tile_bounds, double simplification, size_t retain) {
	int res = 1 << (32 - detail - z);
	long long area = 1LL << (32 - z);

	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].op == VT_MOVETO) {
			geom[i].necessary = 1;
		} else if (geom[i].op == VT_LINETO) {
			geom[i].necessary = 0;
		} else {
			geom[i].necessary = 1;
		}
	}

	if (mark_tile_bounds) {
		geom = impose_tile_boundaries(geom, area);
	}

	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;
				}
			}

			geom[i].necessary = 1;
			geom[j - 1].necessary = 1;

			if (j - i > 1) {
				douglas_peucker(geom, i, j - i, res * simplification, 2, retain);
			}
			i = j - 1;
		}
	}

	drawvec out;
	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].necessary) {
			out.push_back(geom[i]);
		}
	}

	return out;
}

drawvec reorder_lines(drawvec &geom) {
	// Only reorder simple linestrings with a single moveto

	if (geom.size() == 0) {
		return geom;
	}

	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].op == VT_MOVETO) {
			if (i != 0) {
				return geom;
			}
		} else if (geom[i].op == VT_LINETO) {
			if (i == 0) {
				return geom;
			}
		} else {
			return geom;
		}
	}

	// Reorder anything that goes up and to the left
	// instead of down and to the right
	// so that it will coalesce better

	unsigned long long l1 = encode(geom[0].x, geom[0].y);
	unsigned long long l2 = encode(geom[geom.size() - 1].x, geom[geom.size() - 1].y);

	if (l1 > l2) {
		drawvec out;
		for (size_t i = 0; i < geom.size(); i++) {
			out.push_back(geom[geom.size() - 1 - i]);
		}
		out[0].op = VT_MOVETO;
		out[out.size() - 1].op = VT_LINETO;
		return out;
	}

	return geom;
}

drawvec fix_polygon(drawvec &geom) {
	int outer = 1;
	drawvec out;

	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].op == VT_CLOSEPATH) {
			outer = 1;
		} else if (geom[i].op == VT_MOVETO) {
			// Find the end of the ring

			size_t j;
			for (j = i + 1; j < geom.size(); j++) {
				if (geom[j].op != VT_LINETO) {
					break;
				}
			}

			// Make a temporary copy of the ring.
			// Close it if it isn't closed.

			drawvec ring;
			for (size_t a = i; a < j; a++) {
				ring.push_back(geom[a]);
			}
			if (j - i != 0 && (ring[0].x != ring[j - i - 1].x || ring[0].y != ring[j - i - 1].y)) {
				ring.push_back(ring[0]);
			}

			// Reverse ring if winding order doesn't match
			// inner/outer expectation

			double area = get_area(ring, 0, ring.size());
			if ((area > 0) != outer) {
				drawvec tmp;
				for (int a = ring.size() - 1; a >= 0; a--) {
					tmp.push_back(ring[a]);
				}
				ring = tmp;
			}

			// Copy ring into output, fixing the moveto/lineto ops if necessary because of
			// reversal or closing

			for (size_t a = 0; a < ring.size(); a++) {
				if (a == 0) {
					out.push_back(draw(VT_MOVETO, ring[a].x, ring[a].y));
				} else {
					out.push_back(draw(VT_LINETO, ring[a].x, ring[a].y));
				}
			}

			// Next ring or polygon begins on the non-lineto that ended this one
			// and is not an outer ring unless there is a terminator first

			i = j - 1;
			outer = 0;
		} else {
			fprintf(stderr, "Internal error: polygon ring begins with %d, not moveto\n", geom[i].op);
			exit(EXIT_FAILURE);
		}
	}

	return out;
}

std::vector<drawvec> chop_polygon(std::vector<drawvec> &geoms) {
	while (1) {
		bool again = false;
		std::vector<drawvec> out;

		for (size_t i = 0; i < geoms.size(); i++) {
			if (geoms[i].size() > 700) {
				static bool warned = false;
				if (!warned) {
					fprintf(stderr, "Warning: splitting up polygon with more than 700 sides\n");
					warned = true;
				}

				long long midx = 0, midy = 0, count = 0;
				long long maxx = LLONG_MIN, maxy = LLONG_MIN, minx = LLONG_MAX, miny = LLONG_MAX;

				for (size_t j = 0; j < geoms[i].size(); j++) {
					if (geoms[i][j].op == VT_MOVETO || geoms[i][j].op == VT_LINETO) {
						midx += geoms[i][j].x;
						midy += geoms[i][j].y;
						count++;

						if (geoms[i][j].x > maxx) {
							maxx = geoms[i][j].x;
						}
						if (geoms[i][j].y > maxy) {
							maxy = geoms[i][j].y;
						}
						if (geoms[i][j].x < minx) {
							minx = geoms[i][j].x;
						}
						if (geoms[i][j].y < miny) {
							miny = geoms[i][j].y;
						}
					}
				}

				midx /= count;
				midy /= count;

				drawvec c1, c2;

				if (maxy - miny > maxx - minx) {
					// printf("clipping y to %lld %lld %lld %lld\n", minx, miny, maxx, midy);
					c1 = simple_clip_poly(geoms[i], minx, miny, maxx, midy);
					// printf("          and %lld %lld %lld %lld\n", minx, midy, maxx, maxy);
					c2 = simple_clip_poly(geoms[i], minx, midy, maxx, maxy);
				} else {
					// printf("clipping x to %lld %lld %lld %lld\n", minx, miny, midx, maxy);
					c1 = simple_clip_poly(geoms[i], minx, miny, midx, maxy);
					// printf("          and %lld %lld %lld %lld\n", midx, midy, maxx, maxy);
					c2 = simple_clip_poly(geoms[i], midx, miny, maxx, maxy);
				}

				if (c1.size() >= geoms[i].size()) {
					fprintf(stderr, "Subdividing complex polygon failed\n");
				} else {
					out.push_back(c1);
				}
				if (c2.size() >= geoms[i].size()) {
					fprintf(stderr, "Subdividing complex polygon failed\n");
				} else {
					out.push_back(c2);
				}

				again = true;
			} else {
				out.push_back(geoms[i]);
			}
		}

		if (!again) {
			return out;
		}

		geoms = out;
	}
}

#define INSIDE 0
#define LEFT 1
#define RIGHT 2
#define BOTTOM 4
#define TOP 8

static int computeOutCode(double x, double y, double xmin, double ymin, double xmax, double ymax) {
	int code = INSIDE;

	if (x < xmin) {
		code |= LEFT;
	} else if (x > xmax) {
		code |= RIGHT;
	}

	if (y < ymin) {
		code |= BOTTOM;
	} else if (y > ymax) {
		code |= TOP;
	}

	return code;
}

static int clip(double *x0, double *y0, double *x1, double *y1, double xmin, double ymin, double xmax, double ymax) {
	int outcode0 = computeOutCode(*x0, *y0, xmin, ymin, xmax, ymax);
	int outcode1 = computeOutCode(*x1, *y1, xmin, ymin, xmax, ymax);
	int accept = 0;
	int changed = 0;

	while (1) {
		if (!(outcode0 | outcode1)) {  // Bitwise OR is 0. Trivially accept and get out of loop
			accept = 1;
			break;
		} else if (outcode0 & outcode1) {  // Bitwise AND is not 0. Trivially reject and get out of loop
			break;
		} else {
			// failed both tests, so calculate the line segment to clip
			// from an outside point to an intersection with clip edge
			double x = *x0, y = *y0;

			// At least one endpoint is outside the clip rectangle; pick it.
			int outcodeOut = outcode0 ? outcode0 : outcode1;

			// Now find the intersection point;
			// use formulas y = y0 + slope * (x - x0), x = x0 + (1 / slope) * (y - y0)
			if (outcodeOut & TOP) {  // point is above the clip rectangle
				x = *x0 + (*x1 - *x0) * (ymax - *y0) / (*y1 - *y0);
				y = ymax;
			} else if (outcodeOut & BOTTOM) {  // point is below the clip rectangle
				x = *x0 + (*x1 - *x0) * (ymin - *y0) / (*y1 - *y0);
				y = ymin;
			} else if (outcodeOut & RIGHT) {  // point is to the right of clip rectangle
				y = *y0 + (*y1 - *y0) * (xmax - *x0) / (*x1 - *x0);
				x = xmax;
			} else if (outcodeOut & LEFT) {  // point is to the left of clip rectangle
				y = *y0 + (*y1 - *y0) * (xmin - *x0) / (*x1 - *x0);
				x = xmin;
			}

			// Now we move outside point to intersection point to clip
			// and get ready for next pass.
			if (outcodeOut == outcode0) {
				*x0 = x;
				*y0 = y;
				outcode0 = computeOutCode(*x0, *y0, xmin, ymin, xmax, ymax);
				changed = 1;
			} else {
				*x1 = x;
				*y1 = y;
				outcode1 = computeOutCode(*x1, *y1, xmin, ymin, xmax, ymax);
				changed = 1;
			}
		}
	}

	if (accept == 0) {
		return 0;
	} else {
		return changed + 1;
	}
}

drawvec stairstep(drawvec &geom, int z, int detail) {
	drawvec out;
	double scale = 1 << (32 - detail - z);

	for (size_t i = 0; i < geom.size(); i++) {
		geom[i].x = std::round(geom[i].x / scale);
		geom[i].y = std::round(geom[i].y / scale);
	}

	for (size_t i = 0; i < geom.size(); i++) {
		if (geom[i].op == VT_MOVETO) {
			out.push_back(geom[i]);
		} else {
			long long x0 = out[out.size() - 1].x;
			long long y0 = out[out.size() - 1].y;
			long long x1 = geom[i].x;
			long long y1 = geom[i].y;
			bool swap = false;

			if (y0 < y1) {
				swap = true;
				std::swap(x0, x1);
				std::swap(y0, y1);
			}

			long long xx = x0, yy = y0;
			long long dx = std::abs(x1 - x0);
			long long sx = (x0 < x1) ? 1 : -1;
			long long dy = std::abs(y1 - y0);
			long long sy = (y0 < y1) ? 1 : -1;
			long long err = ((dx > dy) ? dx : -dy) / 2;
			int last = -1;

			drawvec tmp;
			tmp.push_back(draw(VT_LINETO, xx, yy));

			while (xx != x1 || yy != y1) {
				long long e2 = err;

				if (e2 > -dx) {
					err -= dy;
					xx += sx;
					if (last == 1) {
						tmp[tmp.size() - 1] = draw(VT_LINETO, xx, yy);
					} else {
						tmp.push_back(draw(VT_LINETO, xx, yy));
					}
					last = 1;
				}
				if (e2 < dy) {
					err += dx;
					yy += sy;
					if (last == 2) {
						tmp[tmp.size() - 1] = draw(VT_LINETO, xx, yy);
					} else {
						tmp.push_back(draw(VT_LINETO, xx, yy));
					}
					last = 2;
				}
			}

			if (swap) {
				for (size_t j = tmp.size(); j > 0; j--) {
					out.push_back(tmp[j - 1]);
				}
			} else {
				for (size_t j = 0; j < tmp.size(); j++) {
					out.push_back(tmp[j]);
				}
			}

			// out.push_back(draw(VT_LINETO, xx, yy));
		}
	}

	for (size_t i = 0; i < out.size(); i++) {
		out[i].x *= 1 << (32 - detail - z);
		out[i].y *= 1 << (32 - detail - z);
	}

	return out;
}