Files
tippecanoe/clip.cpp
T

1606 lines
48 KiB
C++

#include <stack>
#include <stdlib.h>
#include <mapbox/geometry/point.hpp>
#include <mapbox/geometry/multi_polygon.hpp>
#include <mapbox/geometry/wagyu/wagyu.hpp>
#include <limits.h>
#include "geometry.hpp"
#include "errors.hpp"
#include "compression.hpp"
#include "mvt.hpp"
#include "evaluator.hpp"
#include "serial.hpp"
#include "attribute.hpp"
static std::vector<std::pair<double, double>> clip_poly1(std::vector<std::pair<double, double>> &geom,
long long minx, long long miny, long long maxx, long long maxy,
long long ax, long long ay, long long bx, long long by, drawvec &edge_nodes,
bool prevent_simplify_shared_nodes);
drawvec simple_clip_poly(drawvec &geom, long long minx, long long miny, long long maxx, long long maxy,
long long ax, long long ay, long long bx, long long by, drawvec &edge_nodes, bool prevent_simplify_shared_nodes) {
drawvec out;
if (prevent_simplify_shared_nodes) {
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;
}
}
std::vector<std::pair<double, double>> tmp;
for (size_t k = i; k < j; k++) {
double x = geom[k].x;
double y = geom[k].y;
tmp.emplace_back(x, y);
}
tmp = clip_poly1(tmp, minx, miny, maxx, maxy, ax, ay, bx, by, edge_nodes, prevent_simplify_shared_nodes);
if (tmp.size() > 0) {
if (tmp[0].first != tmp[tmp.size() - 1].first || tmp[0].second != tmp[tmp.size() - 1].second) {
fprintf(stderr, "Internal error: Polygon ring not closed\n");
exit(EXIT_FAILURE);
}
}
for (size_t k = 0; k < tmp.size(); k++) {
if (k == 0) {
out.push_back(draw(VT_MOVETO, std::round(tmp[k].first), std::round(tmp[k].second)));
} else {
out.push_back(draw(VT_LINETO, std::round(tmp[k].first), std::round(tmp[k].second)));
}
}
i = j - 1;
} else {
fprintf(stderr, "Unexpected operation in polygon %d\n", (int) geom[i].op);
exit(EXIT_IMPOSSIBLE);
}
}
return out;
}
drawvec simple_clip_poly(drawvec &geom, long long minx, long long miny, long long maxx, long long maxy, bool prevent_simplify_shared_nodes) {
drawvec dv;
return simple_clip_poly(geom, minx, miny, maxx, maxy, minx, miny, maxx, maxy, dv, prevent_simplify_shared_nodes);
}
drawvec simple_clip_poly(drawvec &geom, int z, int buffer, drawvec &edge_nodes, bool prevent_simplify_shared_nodes) {
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,
0, 0, area, area, edge_nodes, prevent_simplify_shared_nodes);
}
drawvec clip_point(drawvec &geom, int z, long long buffer) {
long long min = 0;
long long area = 1LL << (32 - z);
min -= buffer * area / 256;
area += buffer * area / 256;
return clip_point(geom, min, min, area, area);
}
drawvec clip_point(drawvec &geom, long long minx, long long miny, long long maxx, long long maxy) {
drawvec out;
for (size_t i = 0; i < geom.size(); i++) {
if (geom[i].x >= minx && geom[i].y >= miny && geom[i].x <= maxx && geom[i].y <= maxy) {
out.push_back(geom[i]);
}
}
return out;
}
drawvec clip_lines(drawvec &geom, int z, long long buffer) {
long long min = 0;
long long area = 1LL << (32 - z);
min -= buffer * area / 256;
area += buffer * area / 256;
return clip_lines(geom, min, min, area, area);
}
drawvec clip_lines(drawvec &geom, long long minx, long long miny, long long maxx, long long maxy) {
drawvec out;
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) {
long long x1 = geom[i - 1].x;
long long y1 = geom[i - 1].y;
long long x2 = geom[i - 0].x;
long long y2 = geom[i - 0].y;
int c = clip(&x1, &y1, &x2, &y2, minx, miny, maxx, maxy);
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;
}
#define INSIDE 0
#define LEFT 1
#define RIGHT 2
#define BOTTOM 4
#define TOP 8
static int computeOutCode(long long x, long long y, long long xmin, long long ymin, long long xmax, long long 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;
}
int clip(long long *x0, long long *y0, long long *x1, long long *y1, long long xmin, long long ymin, long long xmax, long long 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
long long x = *x0, y = *y0;
// At least one endpoint is outside the clip rectangle; pick it.
int outcodeOut = outcode0 ? outcode0 : outcode1;
// XXX truncating division
// 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;
}
}
static void decode_clipped(mapbox::geometry::multi_polygon<long long> &t, drawvec &out, double scale) {
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, std::round(t[i][j][k].x / scale), std::round(t[i][j][k].y / scale)));
}
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_IMPOSSIBLE);
}
for (size_t k = 0; k < ring.size(); k++) {
out.push_back(ring[k]);
}
}
}
}
drawvec clean_or_clip_poly(drawvec &geom, int z, int buffer, bool clip, bool try_scaling) {
geom = remove_noop(geom, VT_POLYGON, 0);
mapbox::geometry::multi_polygon<long long> result;
double scale = 16.0;
if (!try_scaling) {
scale = 1.0;
}
bool again = true;
while (again) {
mapbox::geometry::wagyu::wagyu<long long> wagyu;
again = 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;
}
}
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 * scale, geom[k].y * scale));
}
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>(scale * -clip_buffer, scale * -clip_buffer));
lr.push_back(mapbox::geometry::point<long long>(scale * -clip_buffer, scale * (area + clip_buffer)));
lr.push_back(mapbox::geometry::point<long long>(scale * (area + clip_buffer), scale * (area + clip_buffer)));
lr.push_back(mapbox::geometry::point<long long>(scale * (area + clip_buffer), scale * -clip_buffer));
lr.push_back(mapbox::geometry::point<long long>(scale * -clip_buffer, scale * -clip_buffer));
wagyu.add_ring(lr, mapbox::geometry::wagyu::polygon_type_clip);
}
try {
result.clear();
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]", (long long) geom[k].x, (long long) 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_IMPOSSIBLE);
}
if (scale != 1) {
for (auto const &outer : result) {
for (auto const &ring : outer) {
for (auto const &p : ring) {
if (p.x / scale != std::round(p.x / scale) ||
p.y / scale != std::round(p.y / scale)) {
scale = 1;
again = true;
break;
}
}
}
}
}
}
drawvec ret;
decode_clipped(result, ret, scale);
return ret;
}
void to_tile_scale(drawvec &geom, int z, int detail) {
if (32 - detail - z < 0) {
for (size_t i = 0; i < geom.size(); i++) {
geom[i].x = std::round((double) geom[i].x * (1LL << (-(32 - detail - z))));
geom[i].y = std::round((double) geom[i].y * (1LL << (-(32 - detail - z))));
}
} else {
for (size_t i = 0; i < geom.size(); i++) {
geom[i].x = std::round((double) geom[i].x / (1LL << (32 - detail - z)));
geom[i].y = std::round((double) geom[i].y / (1LL << (32 - detail - z)));
}
}
}
drawvec from_tile_scale(drawvec const &geom, int z, int detail) {
drawvec out;
for (size_t i = 0; i < geom.size(); i++) {
draw d = geom[i];
d.x *= (1LL << (32 - detail - z));
d.y *= (1LL << (32 - detail - z));
out.push_back(d);
}
return out;
}
drawvec remove_noop(drawvec geom, int type, int shift) {
// first pass: remove empty linetos
long long ox = 0, oy = 0;
drawvec out;
for (size_t i = 0; i < geom.size(); i++) {
long long nx = std::round((double) geom[i].x / (1LL << shift));
long long ny = std::round((double) geom[i].y / (1LL << shift));
if (geom[i].op == VT_LINETO && nx == ox && ny == oy) {
continue;
}
if (geom[i].op == VT_CLOSEPATH) {
out.push_back(geom[i]);
} else { /* moveto or lineto */
out.push_back(geom[i]);
ox = nx;
oy = ny;
}
}
// 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()) {
// followed by end-of-geometry: not needed
continue;
}
if (geom[i + 1].op == VT_MOVETO) {
// followed by another moveto: not needed
continue;
}
if (geom[i + 1].op == VT_CLOSEPATH) {
// followed by closepath: not possible
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 (i > 1 && geom[i].op == VT_MOVETO) {
if (geom[i - 1].op == VT_LINETO &&
std::round((double) geom[i - 1].x / (1LL << shift)) == std::round((double) geom[i].x / (1LL << shift)) &&
std::round((double) geom[i - 1].y / (1LL << shift)) == std::round((double) geom[i].y / (1LL << shift))) {
continue;
}
}
out.push_back(geom[i]);
}
}
return out;
}
double get_area_scaled(const drawvec &geom, size_t i, size_t j) {
const double max_exact_double = (double) ((1LL << 53) - 1);
// keep scaling the geometry down until we can calculate its area without overflow
for (long long scale = 2; scale < (1LL << 30); scale *= 2) {
long long bx = geom[i].x;
long long by = geom[i].y;
bool again = false;
// https://en.wikipedia.org/wiki/Shoelace_formula
double area = 0;
for (size_t k = i; k < j; k++) {
area += (double) ((geom[k].x - bx) / scale) * (double) ((geom[i + ((k - i + 1) % (j - i))].y - by) / scale);
if (std::fabs(area) >= max_exact_double) {
again = true;
break;
}
area -= (double) ((geom[k].y - by) / scale) * (double) ((geom[i + ((k - i + 1) % (j - i))].x - bx) / scale);
if (std::fabs(area) >= max_exact_double) {
again = true;
break;
}
}
if (again) {
continue;
} else {
area /= 2;
return area * scale * scale;
}
}
fprintf(stderr, "get_area_scaled: can't happen\n");
exit(EXIT_IMPOSSIBLE);
}
double get_area(const drawvec &geom, size_t i, size_t j) {
const double max_exact_double = (double) ((1LL << 53) - 1);
// Coordinates in `geom` are 40-bit integers, so there is no good way
// to multiply them without possible precision loss. Since they probably
// do not use the full precision, shift them nearer to the origin so
// their product is more likely to be exactly representable as a double.
//
// (In practice they are actually 34-bit integers: 32 bits for the
// Mercator world plane, plus another two bits so features can stick
// off either the left or right side. But that is still too many bits
// for the product to fit either in a 64-bit long long or in a
// double where the largest exact integer is 2^53.)
//
// If the intermediate calculation still exceeds 2^53, start trying to
// recalculate the area by scaling down the geometry. This will not
// produce as precise an area, but it will still be close, and the
// sign will be correct, which is more important, since the sign
// determines the winding order of the rings. We can then use that
// sign with this generally more precise area calculation.
long long bx = geom[i].x;
long long by = geom[i].y;
// https://en.wikipedia.org/wiki/Shoelace_formula
double area = 0;
bool overflow = false;
for (size_t k = i; k < j; k++) {
area += (double) (geom[k].x - bx) * (double) (geom[i + ((k - i + 1) % (j - i))].y - by);
if (std::fabs(area) >= max_exact_double) {
overflow = true;
}
area -= (double) (geom[k].y - by) * (double) (geom[i + ((k - i + 1) % (j - i))].x - bx);
if (std::fabs(area) >= max_exact_double) {
overflow = true;
}
}
area /= 2;
if (overflow) {
double scaled_area = get_area_scaled(geom, i, j);
if ((area < 0 && scaled_area > 0) || (area > 0 && scaled_area < 0)) {
area = -area;
}
}
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;
}
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;
}
static bool inside(std::pair<double, double> d, int edge, long long minx, long long miny, long long maxx, long long maxy) {
switch (edge) {
case 0: // top
return d.second > miny;
case 1: // right
return d.first < maxx;
case 2: // bottom
return d.second < maxy;
case 3: // left
return d.first > minx;
}
fprintf(stderr, "internal error inside\n");
exit(EXIT_FAILURE);
}
static std::pair<double, double> intersect(std::pair<double, double> a, std::pair<double, double> b, int edge, long long minx, long long miny, long long maxx, long long maxy) {
switch (edge) {
case 0: // top
return std::pair<double, double>((a.first + (double) (b.first - a.first) * (miny - a.second) / (b.second - a.second)), miny);
case 1: // right
return std::pair<double, double>(maxx, (a.second + (double) (b.second - a.second) * (maxx - a.first) / (b.first - a.first)));
case 2: // bottom
return std::pair<double, double>((a.first + (double) (b.first - a.first) * (maxy - a.second) / (b.second - a.second)), maxy);
case 3: // left
return std::pair<double, double>(minx, (a.second + (double) (b.second - a.second) * (minx - a.first) / (b.first - a.first)));
}
fprintf(stderr, "internal error intersecting\n");
exit(EXIT_FAILURE);
}
// http://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm
static std::vector<std::pair<double, double>> clip_poly1(std::vector<std::pair<double, double>> &geom,
long long minx, long long miny, long long maxx, long long maxy,
long long ax, long long ay, long long bx, long long by, drawvec &edge_nodes,
bool prevent_simplify_shared_nodes) {
std::vector<std::pair<double, double>> out = geom;
for (int edge = 0; edge < 4; edge++) {
if (out.size() > 0) {
std::vector<std::pair<double, double>> in = out;
out.resize(0);
std::pair<double, double> S = in[in.size() - 1];
for (size_t e = 0; e < in.size(); e++) {
std::pair<double, double> E = in[e];
if (!inside(S, edge, minx, miny, maxx, maxy)) {
// was outside the buffer
if (!inside(E, edge, minx, miny, maxx, maxy)) {
// still outside the buffer
} else if (!inside(E, edge, ax, ay, bx, by)) {
// outside the tile but inside the buffer
out.push_back(intersect(S, E, edge, minx, miny, maxx, maxy)); // on buffer edge
out.push_back(E);
} else {
out.push_back(intersect(S, E, edge, minx, miny, maxx, maxy)); // on buffer edge
if (prevent_simplify_shared_nodes) {
out.push_back(intersect(S, E, edge, ax, ay, bx, by)); // on tile boundary
edge_nodes.push_back(draw(VT_MOVETO, std::round(out.back().first), std::round(out.back().second)));
}
out.push_back(E);
}
} else if (!inside(S, edge, ax, ay, bx, by)) {
// was inside the buffer but outside the tile edge
if (!inside(E, edge, minx, miny, maxx, maxy)) {
// now outside the buffer
out.push_back(intersect(S, E, edge, minx, miny, maxx, maxy)); // on buffer edge
} else if (!inside(E, edge, ax, ay, bx, by)) {
// still outside the tile edge but inside the buffer
out.push_back(E);
} else {
// now inside the tile
if (prevent_simplify_shared_nodes) {
out.push_back(intersect(S, E, edge, ax, ay, bx, by)); // on tile boundary
edge_nodes.push_back(draw(VT_MOVETO, std::round(out.back().first), std::round(out.back().second)));
}
out.push_back(E);
}
} else {
// was inside the tile
if (!inside(E, edge, minx, miny, maxx, maxy)) {
// now outside the buffer
if (prevent_simplify_shared_nodes) {
out.push_back(intersect(S, E, edge, ax, ay, bx, by)); // on tile boundary
edge_nodes.push_back(draw(VT_MOVETO, std::round(out.back().first), std::round(out.back().second)));
}
out.push_back(intersect(S, E, edge, minx, miny, maxx, maxy)); // on buffer edge
} else if (!inside(E, edge, ax, ay, bx, by)) {
// now inside the buffer but outside the tile edge
if (prevent_simplify_shared_nodes) {
out.push_back(intersect(S, E, edge, ax, ay, bx, by)); // on tile boundary
edge_nodes.push_back(draw(VT_MOVETO, std::round(out.back().first), std::round(out.back().second)));
}
out.push_back(E);
} else {
// still inside the tile
out.push_back(E);
}
}
S = E;
}
}
}
if (out.size() > 0) {
// If the polygon begins and ends outside the edge,
// the starting and ending points will be left as the
// places where it intersects the edge. Need to add
// another point to close the loop.
if (out[0].first != out[out.size() - 1].first || out[0].second != out[out.size() - 1].second) {
out.push_back(out[0]);
}
if (out.size() < 3) {
// fprintf(stderr, "Polygon degenerated to a line segment\n");
out.clear();
return out;
}
}
return out;
}
double 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) {
long long p2x = segB_x - segA_x;
long long p2y = segB_y - segA_y;
// These calculations must be made in integers instead of floating point
// to make them consistent between x86 and arm floating point implementations.
//
// Coordinates may be up to 34 bits, so their product is up to 68 bits,
// making their sum up to 69 bits. Downshift before multiplying to keep them in range.
double something = ((p2x / 4) * (p2x / 8) + (p2y / 4) * (p2y / 8)) * 32.0;
// likewise
double u = (0 == something) ? 0 : ((point_x - segA_x) / 4 * (p2x / 8) + (point_y - segA_y) / 4 * (p2y / 8)) * 32.0 / (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;
double out = std::round(sqrt(dx * dx + dy * dy) * 16.0) / 16.0;
return out;
}
// https://github.com/Project-OSRM/osrm-backend/blob/733d1384a40f/Algorithms/DouglasePeucker.cpp
void douglas_peucker(drawvec &geom, int start, int n, double e, size_t kept, size_t retain, bool prevent_simplify_shared_nodes) {
std::stack<int> recursion_stack;
if (!geom[start + 0].necessary || !geom[start + n - 1].necessary) {
fprintf(stderr, "endpoints not marked necessary\n");
exit(EXIT_IMPOSSIBLE);
}
int prev = 0;
for (int here = 1; here < n; here++) {
if (geom[start + here].necessary) {
recursion_stack.push(prev);
recursion_stack.push(here);
prev = here;
if (prevent_simplify_shared_nodes) {
if (retain > 0) {
retain--;
}
}
}
}
// These segments are put on the stack from start to end,
// independent of winding, so note that anything that uses
// "retain" to force it to keep at least N points will
// keep a different set of points when wound one way than
// when wound the other way.
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;
// find index idx of element with max_distance
int i;
if (geom[start + first] < geom[start + second]) {
farthest_element_index = first;
for (i = first + 1; i < second; i++) {
double temp_dist = 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 || (distance == max_distance && geom[start + i] < geom[start + farthest_element_index]))) {
farthest_element_index = i;
max_distance = distance;
}
}
} else {
farthest_element_index = second;
for (i = second - 1; i > first; i--) {
double temp_dist = distance_from_line(geom[start + i].x, geom[start + i].y, geom[start + second].x, geom[start + second].y, geom[start + first].x, geom[start + first].y);
double distance = std::fabs(temp_dist);
if ((distance > e || kept < retain) && (distance > max_distance || (distance == max_distance && geom[start + i] < geom[start + farthest_element_index]))) {
farthest_element_index = i;
max_distance = distance;
}
}
}
if (max_distance >= 0) {
// mark idx as necessary
geom[start + farthest_element_index].necessary = 1;
kept++;
if (geom[start + first] < geom[start + second]) {
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);
}
} else {
if (1 < second - farthest_element_index) {
recursion_stack.push(farthest_element_index);
recursion_stack.push(second);
}
if (1 < farthest_element_index - first) {
recursion_stack.push(first);
recursion_stack.push(farthest_element_index);
}
}
}
}
}
// cut-down version of simplify_lines(), not dealing with shared node preservation
static drawvec simplify_lines_basic(drawvec &geom, int z, int detail, double simplification, size_t retain) {
int res = 1 << (32 - detail - 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;
// if this is actually the endpoint, not an intermediate point,
// it will be marked as necessary below
} else {
geom[i].necessary = 1;
}
}
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, false);
}
i = j - 1;
}
}
size_t out = 0;
for (size_t i = 0; i < geom.size(); i++) {
if (geom[i].necessary) {
geom[out++] = geom[i];
}
}
geom.resize(out);
return geom;
}
drawvec reduce_tiny_poly(drawvec const &geom, int z, int detail, bool *still_needs_simplification, bool *reduced_away, double *accum_area, double tiny_polygon_size) {
drawvec out;
const double pixel = (1LL << (32 - detail - z)) * (double) tiny_polygon_size;
bool included_last_outer = false;
*still_needs_simplification = false;
*reduced_away = 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.
// i.e., this outer ring is small enough that we are including it
// in a tiny polygon rather than letting it represent itself,
// OR it is an inner ring and we haven't output an outer ring for it to be
// cut out of, so we are just subtracting its area from the tiny polygon
// rather than trying to deal with it geometrically
if ((area > 0 && area <= pixel * pixel) || (area < 0 && !included_last_outer)) {
*accum_area += area;
*reduced_away = true;
if (area > 0 && *accum_area > pixel * pixel) {
// XXX use centroid;
out.emplace_back(VT_MOVETO, geom[i].x - pixel / 2, geom[i].y - pixel / 2);
out.emplace_back(VT_LINETO, geom[i].x - pixel / 2 + pixel, geom[i].y - pixel / 2);
out.emplace_back(VT_LINETO, geom[i].x - pixel / 2 + pixel, geom[i].y - pixel / 2 + pixel);
out.emplace_back(VT_LINETO, geom[i].x - pixel / 2, geom[i].y - pixel / 2 + pixel);
out.emplace_back(VT_LINETO, geom[i].x - pixel / 2, geom[i].y - pixel / 2);
*accum_area -= pixel * pixel;
}
if (area > 0) {
included_last_outer = false;
}
}
// i.e., this ring is large enough that it gets to represent itself
// or it is a tiny hole out of a real polygon, which we are still treating
// as a real geometry because otherwise we can accumulate enough tiny holes
// that we will drop the next several outer rings getting back up to 0.
else {
for (size_t k = i; k < j && k < geom.size(); k++) {
out.push_back(geom[k]);
}
// which means that the overall polygon has a real geometry,
// which means that it gets to be simplified.
*still_needs_simplification = true;
if (area > 0) {
included_last_outer = true;
}
}
} else {
// area is 0: doesn't count as either having been reduced away,
// since it was probably just degenerate from having been clipped,
// or as needing simplification, since it produces no output.
}
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, (long long) geom[n].x, (long long) geom[n].y);
}
fprintf(stderr, "\n");
out.push_back(geom[i]);
}
}
return out;
}
std::string overzoom(std::vector<input_tile> const &tiles, int nz, int nx, int ny,
int detail, int buffer, std::set<std::string> const &keep, bool do_compress,
std::vector<std::pair<unsigned, unsigned>> *next_overzoomed_tiles,
bool demultiply, json_object *filter, bool preserve_input_order,
std::unordered_map<std::string, attribute_op> const &attribute_accum,
std::vector<std::string> const &unidecode_data, double simplification,
double tiny_polygon_size, std::vector<mvt_layer> const &bins) {
std::vector<source_tile> decoded;
for (auto const &t : tiles) {
mvt_tile tile;
try {
bool was_compressed;
if (!tile.decode(t.tile, was_compressed)) {
fprintf(stderr, "Couldn't parse tile %d/%u/%u\n", t.z, t.x, t.y);
exit(EXIT_MVT);
}
} catch (std::exception const &e) {
fprintf(stderr, "PBF decoding error in tile %d/%u/%u\n", t.z, t.x, t.y);
exit(EXIT_PROTOBUF);
}
source_tile out;
out.tile = tile;
out.z = t.z;
out.x = t.x;
out.y = t.y;
decoded.push_back(out);
}
return overzoom(decoded, nz, nx, ny, detail, buffer, keep, do_compress, next_overzoomed_tiles, demultiply, filter, preserve_input_order, attribute_accum, unidecode_data, simplification, tiny_polygon_size, bins);
}
struct tile_feature {
drawvec geom;
int t;
bool has_id;
unsigned long long id;
std::vector<unsigned> tags;
mvt_layer const *layer;
size_t seq = 0;
};
static void feature_out(std::vector<tile_feature> const &features, mvt_layer &outlayer, std::set<std::string> const &keep, std::unordered_map<std::string, attribute_op> const &attribute_accum, std::shared_ptr<std::string> const &tile_stringpool) {
// Add geometry to output feature
mvt_feature outfeature;
outfeature.type = features[0].t;
for (auto const &g : features[0].geom) {
outfeature.geometry.emplace_back(g.op, g.x, g.y);
}
// ID and attributes, if it didn't get clipped away
if (outfeature.geometry.size() > 0) {
if (features[0].has_id) {
outfeature.has_id = true;
outfeature.id = features[0].id;
}
outfeature.seq = features[0].seq;
if (attribute_accum.size() > 0) {
// convert the attributes of the output feature
// from mvt_value to serial_val so they can have
// attributes from the other features of the
// multiplier cluster accumulated onto them
std::unordered_map<std::string, accum_state> attribute_accum_state;
std::vector<std::string> full_keys;
std::vector<serial_val> full_values;
for (size_t i = 0; i + 1 < features[0].tags.size(); i += 2) {
auto f = attribute_accum.find(features[0].layer->keys[features[0].tags[i]]);
if (f != attribute_accum.end()) {
// this attribute has an accumulator, so convert it
full_keys.push_back(features[0].layer->keys[features[0].tags[i]]);
full_values.push_back(mvt_value_to_serial_val(features[0].layer->values[features[0].tags[i + 1]]));
} else {
// otherwise just tag it directly onto the output feature
if (keep.size() == 0 || keep.find(features[0].layer->keys[features[0].tags[i]]) != keep.end()) {
outlayer.tag(outfeature, features[0].layer->keys[features[0].tags[i]], features[0].layer->values[features[0].tags[i + 1]]);
}
}
}
// accumulate whatever attributes are specified to be accumulated
// onto the feature that will survive into the output, from the
// features that will not
for (size_t i = 1; i < features.size(); i++) {
for (size_t j = 0; j + 1 < features[i].tags.size(); j += 2) {
std::string key = features[i].layer->keys[features[i].tags[j]];
auto f = attribute_accum.find(key);
if (f != attribute_accum.end()) {
serial_val val = mvt_value_to_serial_val(features[i].layer->values[features[i].tags[j + 1]]);
preserve_attribute(f->second, key, val, full_keys, full_values, attribute_accum_state);
}
}
}
// convert the final attributes back to mvt_value
// and tag them onto the output feature
for (size_t i = 0; i < full_keys.size(); i++) {
if (keep.size() == 0 || keep.find(full_keys[i]) != keep.end()) {
outlayer.tag(outfeature, full_keys[i], stringified_to_mvt_value(full_values[i].type, full_values[i].s.c_str(), tile_stringpool));
}
}
} else {
for (size_t i = 0; i + 1 < features[0].tags.size(); i += 2) {
if (keep.size() == 0 || keep.find(features[0].layer->keys[features[0].tags[i]]) != keep.end()) {
outlayer.tag(outfeature, features[0].layer->keys[features[0].tags[i]], features[0].layer->values[features[0].tags[i + 1]]);
}
}
}
outlayer.features.push_back(std::move(outfeature));
}
}
static struct preservecmp {
bool operator()(const mvt_feature &a, const mvt_feature &b) {
return a.seq < b.seq;
}
} preservecmp;
struct index_event {
unsigned long long where;
enum {
ENTER = 0, // new bin in is now active
CHECK, // point needs to be checked against active bins
EXIT // bin has ceased to be active
} kind;
size_t layer;
size_t feature;
bool operator<(const index_event &ie) const {
if (where < ie.where) {
return true;
} else if (where == ie.where) {
if (kind < ie.kind) {
return true;
} else if (kind == ie.kind) {
if (layer < ie.layer) {
return true;
} else if (layer == ie.layer) {
if (feature < ie.feature) {
return true;
}
}
}
}
return false;
}
};
mvt_tile assign_to_bins(mvt_tile const &features, std::vector<mvt_layer> const &bins, int z, int x, int y) {
std::vector<index_event> events;
// Index bins
for (size_t i = 0; i < bins.size(); i++) {
for (size_t j = 0; j < bins[i].features.size(); j++) {
}
}
// Index points
for (size_t i = 0; i < features.layers.size(); i++) {
for (size_t j = 0; j < features.layers[i].features.size(); j++) {
index_event ie;
}
}
return features;
}
std::string overzoom(std::vector<source_tile> const &tiles, int nz, int nx, int ny,
int detail, int buffer, std::set<std::string> const &keep, bool do_compress,
std::vector<std::pair<unsigned, unsigned>> *next_overzoomed_tiles,
bool demultiply, json_object *filter, bool preserve_input_order,
std::unordered_map<std::string, attribute_op> const &attribute_accum,
std::vector<std::string> const &unidecode_data, double simplification,
double tiny_polygon_size, std::vector<mvt_layer> const &bins) {
mvt_tile outtile;
std::shared_ptr<std::string> tile_stringpool = std::make_shared<std::string>();
for (auto const &tile : tiles) {
for (auto const &layer : tile.tile.layers) {
mvt_layer *outlayer = NULL;
int det = detail;
if (det <= 0) {
det = std::round(log(layer.extent) / log(2));
}
for (size_t i = 0; i < outtile.layers.size(); i++) {
if (outtile.layers[i].name == layer.name) {
outlayer = &outtile.layers[i];
}
}
if (outlayer == NULL) {
mvt_layer newlayer = mvt_layer();
newlayer.name = layer.name;
newlayer.version = layer.version;
newlayer.extent = 1LL << det;
outtile.layers.push_back(newlayer);
outlayer = &outtile.layers.back();
}
std::vector<tile_feature> pending_tile_features;
double accum_area = 0;
static const std::string retain_points_multiplier_first = "tippecanoe:retain_points_multiplier_first";
static const std::string retain_points_multiplier_sequence = "tippecanoe:retain_points_multiplier_sequence";
for (auto feature : layer.features) {
drawvec geom;
int t = feature.type;
// Convert feature geometry to world coordinates
long long tilesize = 1LL << (32 - tile.z); // source tile size in world coordinates
draw ring_closure(0, 0, 0);
bool sametile = (nz == tile.z && nx == tile.x && ny == tile.y && outlayer->extent >= layer.extent);
for (auto const &g : feature.geometry) {
if (g.op == mvt_closepath) {
geom.push_back(ring_closure);
} else {
geom.emplace_back(g.op,
g.x * tilesize / layer.extent + tile.x * tilesize,
g.y * tilesize / layer.extent + tile.y * tilesize);
if (g.op == mvt_moveto) {
ring_closure = geom.back();
ring_closure.op = mvt_lineto;
}
}
}
// Now offset from world coordinates to output tile coordinates,
// but retain world scale, because that is what tippecanoe clipping expects
long long outtilesize = 1LL << (32 - nz); // destination tile size in world coordinates
for (auto &g : geom) {
g.x -= nx * outtilesize;
g.y -= ny * outtilesize;
}
if (!sametile) {
// Clip to output tile
long long xmin = LLONG_MAX;
long long ymin = LLONG_MAX;
long long xmax = LLONG_MIN;
long long ymax = LLONG_MIN;
for (auto const &g : geom) {
xmin = std::min(xmin, g.x);
ymin = std::min(ymin, g.y);
xmax = std::max(xmax, g.x);
ymax = std::max(ymax, g.y);
}
long long b = outtilesize * buffer / 256;
if (xmax < -b || ymax < -b || xmin > outtilesize + b || ymin > outtilesize + b) {
// quick exclusion by bounding box
continue;
}
if (t == VT_LINE) {
geom = clip_lines(geom, nz, buffer);
} else if (t == VT_POLYGON) {
drawvec dv;
geom = simple_clip_poly(geom, nz, buffer, dv, false);
} else if (t == VT_POINT) {
geom = clip_point(geom, nz, buffer);
}
}
if (geom.size() == 0) {
// clipped away
continue;
}
bool flush_multiplier_cluster = false;
if (demultiply) {
for (ssize_t i = feature.tags.size() - 2; i >= 0; i -= 2) {
if (layer.keys[feature.tags[i]] == retain_points_multiplier_first) {
mvt_value v = layer.values[feature.tags[i + 1]];
if (v.type == mvt_bool && v.numeric_value.bool_value) {
flush_multiplier_cluster = true;
feature.tags.erase(feature.tags.begin() + i, feature.tags.begin() + i + 2);
}
} else if (i < (ssize_t) feature.tags.size() && layer.keys[feature.tags[i]] == retain_points_multiplier_sequence) {
mvt_value v = layer.values[feature.tags[i + 1]];
feature.seq = mvt_value_to_long_long(v);
feature.tags.erase(feature.tags.begin() + i, feature.tags.begin() + i + 2);
}
}
} else {
flush_multiplier_cluster = true;
}
if (flush_multiplier_cluster) {
if (pending_tile_features.size() > 0) {
feature_out(pending_tile_features, *outlayer, keep, attribute_accum, tile_stringpool);
pending_tile_features.clear();
}
}
std::set<std::string> exclude_attributes;
if (filter != NULL && !evaluate(feature, layer, filter, exclude_attributes, nz, unidecode_data)) {
continue;
}
bool still_need_simplification_after_reduction = false;
if (t == VT_POLYGON && tiny_polygon_size > 0) {
bool simplified_away_by_reduction = false;
geom = reduce_tiny_poly(geom, nz, detail, &still_need_simplification_after_reduction, &simplified_away_by_reduction, &accum_area, tiny_polygon_size);
} else {
still_need_simplification_after_reduction = true;
}
if (simplification > 0 && still_need_simplification_after_reduction) {
if (t == VT_POLYGON) {
geom = simplify_lines_basic(geom, nz, detail, simplification, 4);
} else if (t == VT_LINE) {
geom = simplify_lines_basic(geom, nz, detail, simplification, 0);
}
}
// Scale to output tile extent
to_tile_scale(geom, nz, det);
if (!sametile) {
// Clean geometries
geom = remove_noop(geom, t, 0);
if (t == VT_POLYGON) {
geom = clean_or_clip_poly(geom, 0, 0, false, false);
}
}
if (t == VT_POLYGON) {
geom = close_poly(geom);
}
tile_feature tf;
tf.geom = std::move(geom);
tf.t = t;
tf.has_id = feature.has_id;
tf.id = feature.id;
tf.tags = std::move(feature.tags);
tf.layer = &layer;
tf.seq = feature.seq;
pending_tile_features.push_back(tf);
}
if (pending_tile_features.size() > 0) {
feature_out(pending_tile_features, *outlayer, keep, attribute_accum, tile_stringpool);
pending_tile_features.clear();
}
if (preserve_input_order) {
std::stable_sort(outlayer->features.begin(), outlayer->features.end(), preservecmp);
}
}
}
if (next_overzoomed_tiles != NULL) {
// will any child tiles have features in them?
// find out recursively from the tile we just made.
//
// (yes, we should keep them instead of remaking them
// later, but that first requires figuring out where to
// keep them.)
if (outtile.layers.size() > 0) {
for (size_t x = 0; x < 2; x++) {
for (size_t y = 0; y < 2; y++) {
source_tile st;
st.tile = outtile;
st.z = nz;
st.x = nx;
st.y = ny;
std::vector<source_tile> sts;
sts.push_back(st);
std::string child = overzoom(sts,
nz + 1, nx * 2 + x, ny * 2 + y,
detail, buffer, keep, false, NULL,
demultiply, filter, preserve_input_order, attribute_accum, unidecode_data, simplification, tiny_polygon_size, bins);
if (child.size() > 0) {
next_overzoomed_tiles->emplace_back(nx * 2 + x, ny * 2 + y);
}
}
}
}
}
if (bins.size() > 0) {
outtile = assign_to_bins(outtile, bins, nz, nx, ny);
}
for (ssize_t i = outtile.layers.size() - 1; i >= 0; i--) {
if (outtile.layers[i].features.size() == 0) {
outtile.layers.erase(outtile.layers.begin() + i);
}
}
if (outtile.layers.size() > 0) {
std::string pbf = outtile.encode();
std::string compressed;
if (do_compress) {
compress(pbf, compressed, true);
} else {
compressed = pbf;
}
return compressed;
} else {
return "";
}
}
drawvec fix_polygon(const drawvec &geom, bool use_winding, bool reverse_winding) {
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;
}
}
// A polygon ring must contain at least three points
// (and really should contain four). If this one does
// not have any, avoid a division by zero trying to
// calculate the centroid below.
if (j - i < 1) {
i = j - 1;
outer = 0;
continue;
}
// 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]);
}
// A polygon ring at this point should contain at least four points.
// Flesh it out with some vertex copies if it doesn't.
while (ring.size() < 4) {
ring.push_back(ring[0]);
}
// Reverse ring if winding order doesn't match
// inner/outer expectation
bool reverse_ring = false;
if (use_winding) {
// GeoJSON winding is reversed from vector winding
reverse_ring = true;
} else if (reverse_winding) {
// GeoJSON winding is reversed from vector winding
reverse_ring = false;
} else {
double area = get_area(ring, 0, ring.size());
if ((area > 0) != outer) {
reverse_ring = true;
}
}
if (reverse_ring) {
drawvec tmp;
for (int a = ring.size() - 1; a >= 0; a--) {
tmp.push_back(ring[a]);
}
ring = tmp;
}
// Now we are rotating the ring to make the first/last point
// one that would be unlikely to be simplified away.
// calculate centroid
// a + 1 < size() because point 0 is duplicated at the end
long long xtotal = 0;
long long ytotal = 0;
long long count = 0;
for (size_t a = 0; a + 1 < ring.size(); a++) {
xtotal += ring[a].x;
ytotal += ring[a].y;
count++;
}
xtotal /= count;
ytotal /= count;
// figure out which point is furthest from the centroid
long long dist2 = 0;
long long furthest = 0;
for (size_t a = 0; a + 1 < ring.size(); a++) {
// division by 16 because these are z0 coordinates and we need to avoid overflow
long long xd = (ring[a].x - xtotal) / 16;
long long yd = (ring[a].y - ytotal) / 16;
long long d2 = xd * xd + yd * yd;
if (d2 > dist2 || (d2 == dist2 && ring[a] < ring[furthest])) {
dist2 = d2;
furthest = a;
}
}
// then figure out which point is furthest from *that*,
// which will hopefully be a good origin point since it should be
// at a far edge of the shape.
long long dist2b = 0;
long long furthestb = 0;
for (size_t a = 0; a + 1 < ring.size(); a++) {
// division by 16 because these are z0 coordinates and we need to avoid overflow
long long xd = (ring[a].x - ring[furthest].x) / 16;
long long yd = (ring[a].y - ring[furthest].y) / 16;
long long d2 = xd * xd + yd * yd;
if (d2 > dist2b || (d2 == dist2b && ring[a] < ring[furthestb])) {
dist2b = d2;
furthestb = a;
}
}
// rotate ring so the furthest point is the duplicated one.
// the idea is that simplification will then be more efficient,
// never wasting the start and end points, which are always retained,
// on a point that has little impact on the shape.
// 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++) {
size_t a2 = (a + furthestb) % (ring.size() - 1);
if (a == 0) {
out.push_back(draw(VT_MOVETO, ring[a2].x, ring[a2].y));
} else {
out.push_back(draw(VT_LINETO, ring[a2].x, ring[a2].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_IMPOSSIBLE);
}
}
return out;
}