/* -*- mode: c++; c-basic-offset: 4 -*- */

#ifndef MPL_PATH_H

#define MPL_PATH_H

#include <limits>

#include <math.h>

#include <vector>

#include <cmath>

#include <algorithm>

#include <string>

#include "agg_conv_contour.h"

#include "agg_conv_curve.h"

#include "agg_conv_stroke.h"

#include "agg_conv_transform.h"

#include "agg_trans_affine.h"

#include "path_converters.h"

#include "_backend_agg_basic_types.h"

const size_t NUM_VERTICES[] = { 1, 1, 1, 2, 3 };

struct XY

{

double x;

double y;

XY(double x_, double y_) : x(x_), y(y_)

{

}

bool operator==(const XY& o)

{

return (x == o.x && y == o.y);

}

bool operator!=(const XY& o)

{

return (x != o.x || y != o.y);

}

};

typedef std::vector<XY> Polygon;

void _finalize_polygon(std::vector<Polygon> &result, int closed_only)

{

if (result.size() == 0) {

return;

}

Polygon &polygon = result.back();

/* Clean up the last polygon in the result. */

if (polygon.size() == 0) {

result.pop_back();

} else if (closed_only) {

if (polygon.size() < 3) {

result.pop_back();

} else if (polygon.front() != polygon.back()) {

polygon.push_back(polygon.front());

}

}

}

//

// The following function was found in the Agg 2.3 examples (interactive_polygon.cpp).

// It has been generalized to work on (possibly curved) polylines, rather than

// just polygons. The original comments have been kept intact.

// -- Michael Droettboom 2007-10-02

//

//======= Crossings Multiply algorithm of InsideTest ========================

//

// By Eric Haines, 3D/Eye Inc, [email protected]

//

// This version is usually somewhat faster than the original published in

// Graphics Gems IV; by turning the division for testing the X axis crossing

// into a tricky multiplication test this part of the test became faster,

// which had the additional effect of making the test for "both to left or

// both to right" a bit slower for triangles than simply computing the

// intersection each time. The main increase is in triangle testing speed,

// which was about 15% faster; all other polygon complexities were pretty much

// the same as before. On machines where division is very expensive (not the

// case on the HP 9000 series on which I tested) this test should be much

// faster overall than the old code. Your mileage may (in fact, will) vary,

// depending on the machine and the test data, but in general I believe this

// code is both shorter and faster. This test was inspired by unpublished

// Graphics Gems submitted by Joseph Samosky and Mark Haigh-Hutchinson.

// Related work by Samosky is in:

//

// Samosky, Joseph, "SectionView: A system for interactively specifying and

// visualizing sections through three-dimensional medical image data",

// M.S. Thesis, Department of Electrical Engineering and Computer Science,

// Massachusetts Institute of Technology, 1993.

//

// Shoot a test ray along +X axis. The strategy is to compare vertex Y values

// to the testing point's Y and quickly discard edges which are entirely to one

// side of the test ray. Note that CONVEX and WINDING code can be added as

// for the CrossingsTest() code; it is left out here for clarity.

//

// Input 2D polygon _pgon_ with _numverts_ number of vertices and test point

// _point_, returns 1 if inside, 0 if outside.

template <class PathIterator, class PointArray, class ResultArray>

void point_in_path_impl(PointArray &points, PathIterator &path, ResultArray &inside_flag)

{

uint8_t yflag1;

double vtx0, vty0, vtx1, vty1;

double tx, ty;

double sx, sy;

double x, y;

size_t i;

bool all_done;

size_t n = safe_first_shape(points);

std::vector<uint8_t> yflag0(n);

std::vector<uint8_t> subpath_flag(n);

path.rewind(0);

for (i = 0; i < n; ++i) {

inside_flag[i] = 0;

}

unsigned code = 0;

do {

if (code != agg::path_cmd_move_to) {

code = path.vertex(&x, &y);

if (code == agg::path_cmd_stop ||

(code & agg::path_cmd_end_poly) == agg::path_cmd_end_poly) {

continue;

}

}

sx = vtx0 = vtx1 = x;

sy = vty0 = vty1 = y;

for (i = 0; i < n; ++i) {

ty = points(i, 1);

if (std::isfinite(ty)) {

// get test bit for above/below X axis

yflag0[i] = (vty0 >= ty);

subpath_flag[i] = 0;

}

}

do {

code = path.vertex(&x, &y);

// The following cases denote the beginning on a new subpath

if (code == agg::path_cmd_stop ||

(code & agg::path_cmd_end_poly) == agg::path_cmd_end_poly) {

x = sx;

y = sy;

} else if (code == agg::path_cmd_move_to) {

break;

}

for (i = 0; i < n; ++i) {

tx = points(i, 0);

ty = points(i, 1);

if (!(std::isfinite(tx) && std::isfinite(ty))) {

continue;

}

yflag1 = (vty1 >= ty);

// Check if endpoints straddle (are on opposite sides) of

// X axis (i.e. the Y's differ); if so, +X ray could

// intersect this edge. The old test also checked whether

// the endpoints are both to the right or to the left of

// the test point. However, given the faster intersection

// point computation used below, this test was found to be

// a break-even proposition for most polygons and a loser

// for triangles (where 50% or more of the edges which

// survive this test will cross quadrants and so have to

// have the X intersection computed anyway). I credit

// Joseph Samosky with inspiring me to try dropping the

// "both left or both right" part of my code.

if (yflag0[i] != yflag1) {

// Check intersection of pgon segment with +X ray.

// Note if >= point's X; if so, the ray hits it. The

// division operation is avoided for the ">=" test by

// checking the sign of the first vertex wrto the test

// point; idea inspired by Joseph Samosky's and Mark

// Haigh-Hutchinson's different polygon inclusion

// tests.

if (((vty1 - ty) * (vtx0 - vtx1) >= (vtx1 - tx) * (vty0 - vty1)) == yflag1) {

subpath_flag[i] ^= 1;

}

}

// Move to the next pair of vertices, retaining info as

// possible.

yflag0[i] = yflag1;

}

vtx0 = vtx1;

vty0 = vty1;

vtx1 = x;

vty1 = y;

} while (code != agg::path_cmd_stop &&

(code & agg::path_cmd_end_poly) != agg::path_cmd_end_poly);

all_done = true;

for (i = 0; i < n; ++i) {

tx = points(i, 0);

ty = points(i, 1);

if (!(std::isfinite(tx) && std::isfinite(ty))) {

continue;

}

yflag1 = (vty1 >= ty);

if (yflag0[i] != yflag1) {

if (((vty1 - ty) * (vtx0 - vtx1) >= (vtx1 - tx) * (vty0 - vty1)) == yflag1) {

subpath_flag[i] = subpath_flag[i] ^ true;

}

}

inside_flag[i] |= subpath_flag[i];

if (inside_flag[i] == 0) {

all_done = false;

}

}

if (all_done) {

break;

}

} while (code != agg::path_cmd_stop);

}

template <class PathIterator, class PointArray, class ResultArray>

inline void points_in_path(PointArray &points,

const double r,

PathIterator &path,

agg::trans_affine &trans,

ResultArray &result)

{

typedef agg::conv_transform<PathIterator> transformed_path_t;

typedef PathNanRemover<transformed_path_t> no_nans_t;

typedef agg::conv_curve<no_nans_t> curve_t;

typedef agg::conv_contour<curve_t> contour_t;

for (auto i = 0; i < safe_first_shape(points); ++i) {

result[i] = false;

}

if (path.total_vertices() < 3) {

return;

}

transformed_path_t trans_path(path, trans);

no_nans_t no_nans_path(trans_path, true, path.has_codes());

curve_t curved_path(no_nans_path);

if (r != 0.0) {

contour_t contoured_path(curved_path);

contoured_path.width(r);

point_in_path_impl(points, contoured_path, result);

} else {

point_in_path_impl(points, curved_path, result);

}

}

template <class PathIterator>

inline bool point_in_path(

double x, double y, const double r, PathIterator &path, agg::trans_affine &trans)

{

py::ssize_t shape[] = {1, 2};

py::array_t<double> points_arr(shape);

*points_arr.mutable_data(0, 0) = x;

*points_arr.mutable_data(0, 1) = y;

auto points = points_arr.mutable_unchecked<2>();

int result[1];

result[0] = 0;

points_in_path(points, r, path, trans, result);

return result[0] != 0;

}

template <class PathIterator>

inline bool point_on_path(

double x, double y, const double r, PathIterator &path, agg::trans_affine &trans)

{

typedef agg::conv_transform<PathIterator> transformed_path_t;

typedef PathNanRemover<transformed_path_t> no_nans_t;

typedef agg::conv_curve<no_nans_t> curve_t;

typedef agg::conv_stroke<curve_t> stroke_t;

py::ssize_t shape[] = {1, 2};

py::array_t<double> points_arr(shape);

*points_arr.mutable_data(0, 0) = x;

*points_arr.mutable_data(0, 1) = y;

auto points = points_arr.mutable_unchecked<2>();

int result[1];

result[0] = 0;

transformed_path_t trans_path(path, trans);

no_nans_t nan_removed_path(trans_path, true, path.has_codes());

curve_t curved_path(nan_removed_path);

stroke_t stroked_path(curved_path);

stroked_path.width(r * 2.0);

point_in_path_impl(points, stroked_path, result);

return result[0] != 0;

}

struct extent_limits

{

double x0;

double y0;

double x1;

double y1;

double xm;

double ym;

};

void reset_limits(extent_limits &e)

{

e.x0 = std::numeric_limits<double>::infinity();

e.y0 = std::numeric_limits<double>::infinity();

e.x1 = -std::numeric_limits<double>::infinity();

e.y1 = -std::numeric_limits<double>::infinity();

/* xm and ym are the minimum positive values in the data, used

by log scaling */

e.xm = std::numeric_limits<double>::infinity();

e.ym = std::numeric_limits<double>::infinity();

}

inline void update_limits(double x, double y, extent_limits &e)

{

if (x < e.x0)

e.x0 = x;

if (y < e.y0)

e.y0 = y;

if (x > e.x1)

e.x1 = x;

if (y > e.y1)

e.y1 = y;

/* xm and ym are the minimum positive values in the data, used

by log scaling */

if (x > 0.0 && x < e.xm)

e.xm = x;

if (y > 0.0 && y < e.ym)

e.ym = y;

}

template <class PathIterator>

void update_path_extents(PathIterator &path, agg::trans_affine &trans, extent_limits &extents)

{

typedef agg::conv_transform<PathIterator> transformed_path_t;

typedef PathNanRemover<transformed_path_t> nan_removed_t;

double x, y;

unsigned code;

transformed_path_t tpath(path, trans);

nan_removed_t nan_removed(tpath, true, path.has_codes());

nan_removed.rewind(0);

while ((code = nan_removed.vertex(&x, &y)) != agg::path_cmd_stop) {

if ((code & agg::path_cmd_end_poly) == agg::path_cmd_end_poly) {

continue;

}

update_limits(x, y, extents);

}

}

template <class PathGenerator, class TransformArray, class OffsetArray>

void get_path_collection_extents(agg::trans_affine &master_transform,

PathGenerator &paths,

TransformArray &transforms,

OffsetArray &offsets,

agg::trans_affine &offset_trans,

extent_limits &extent)

{

if (offsets.size() != 0 && offsets.shape(1) != 2) {

throw std::runtime_error("Offsets array must have shape (N, 2)");

}

auto Npaths = paths.size();

auto Noffsets = safe_first_shape(offsets);

auto N = std::max(Npaths, Noffsets);

auto Ntransforms = std::min(safe_first_shape(transforms), N);

agg::trans_affine trans;

reset_limits(extent);

for (auto i = 0; i < N; ++i) {

typename PathGenerator::path_iterator path(paths(i % Npaths));

if (Ntransforms) {

py::ssize_t ti = i % Ntransforms;

trans = agg::trans_affine(transforms(ti, 0, 0),

transforms(ti, 1, 0),

transforms(ti, 0, 1),

transforms(ti, 1, 1),

transforms(ti, 0, 2),

transforms(ti, 1, 2));

} else {

trans = master_transform;

}

if (Noffsets) {

double xo = offsets(i % Noffsets, 0);

double yo = offsets(i % Noffsets, 1);

offset_trans.transform(&xo, &yo);

trans *= agg::trans_affine_translation(xo, yo);

}

update_path_extents(path, trans, extent);

}

}

template <class PathGenerator, class TransformArray, class OffsetArray>

void point_in_path_collection(double x,

double y,

double radius,

agg::trans_affine &master_transform,

PathGenerator &paths,

TransformArray &transforms,

OffsetArray &offsets,

agg::trans_affine &offset_trans,

bool filled,

std::vector<int> &result)

{

auto Npaths = paths.size();

if (Npaths == 0) {

return;

}

auto Noffsets = safe_first_shape(offsets);

auto N = std::max(Npaths, Noffsets);

auto Ntransforms = std::min(safe_first_shape(transforms), N);

agg::trans_affine trans;

for (auto i = 0; i < N; ++i) {

typename PathGenerator::path_iterator path = paths(i % Npaths);

if (Ntransforms) {

auto ti = i % Ntransforms;

trans = agg::trans_affine(transforms(ti, 0, 0),

transforms(ti, 1, 0),

transforms(ti, 0, 1),

transforms(ti, 1, 1),

transforms(ti, 0, 2),

transforms(ti, 1, 2));

trans *= master_transform;

} else {

trans = master_transform;

}

if (Noffsets) {

double xo = offsets(i % Noffsets, 0);

double yo = offsets(i % Noffsets, 1);

offset_trans.transform(&xo, &yo);

trans *= agg::trans_affine_translation(xo, yo);

}

if (filled) {

if (point_in_path(x, y, radius, path, trans)) {

result.push_back(i);

}

} else {

if (point_on_path(x, y, radius, path, trans)) {

result.push_back(i);

}

}

}

}

template <class PathIterator1, class PathIterator2>

bool path_in_path(PathIterator1 &a,

agg::trans_affine &atrans,

PathIterator2 &b,

agg::trans_affine &btrans)

{

typedef agg::conv_transform<PathIterator2> transformed_path_t;

typedef PathNanRemover<transformed_path_t> no_nans_t;

typedef agg::conv_curve<no_nans_t> curve_t;

if (a.total_vertices() < 3) {

return false;

}

transformed_path_t b_path_trans(b, btrans);

no_nans_t b_no_nans(b_path_trans, true, b.has_codes());

curve_t b_curved(b_no_nans);

double x, y;

b_curved.rewind(0);

while (b_curved.vertex(&x, &y) != agg::path_cmd_stop) {

if (!point_in_path(x, y, 0.0, a, atrans)) {

return false;

}

}

return true;

}

/** The clip_path_to_rect code here is a clean-room implementation of

the Sutherland-Hodgman clipping algorithm described here:

https://en.wikipedia.org/wiki/Sutherland-Hodgman_clipping_algorithm

*/

namespace clip_to_rect_filters

{

/* There are four different passes needed to create/remove

vertices (one for each side of the rectangle). The differences

between those passes are encapsulated in these functor classes.

*/

struct bisectx

{

double m_x;

bisectx(double x) : m_x(x)

{

}

inline void bisect(double sx, double sy, double px, double py, double *bx, double *by) const

{

*bx = m_x;

double dx = px - sx;

double dy = py - sy;

*by = sy + dy * ((m_x - sx) / dx);

}

};

struct xlt : public bisectx

{

xlt(double x) : bisectx(x)

{

}

inline bool is_inside(double x, double y) const

{

return x <= m_x;

}

};

struct xgt : public bisectx

{

xgt(double x) : bisectx(x)

{

}

inline bool is_inside(double x, double y) const

{

return x >= m_x;

}

};

struct bisecty

{

double m_y;

bisecty(double y) : m_y(y)

{

}

inline void bisect(double sx, double sy, double px, double py, double *bx, double *by) const

{

*by = m_y;

double dx = px - sx;

double dy = py - sy;

*bx = sx + dx * ((m_y - sy) / dy);

}

};

struct ylt : public bisecty

{

ylt(double y) : bisecty(y)

{

}

inline bool is_inside(double x, double y) const

{

return y <= m_y;

}

};

struct ygt : public bisecty

{

ygt(double y) : bisecty(y)

{

}

inline bool is_inside(double x, double y) const

{

return y >= m_y;

}

};

}

template <class Filter>

inline void clip_to_rect_one_step(const Polygon &polygon, Polygon &result, const Filter &filter)

{

bool sinside, pinside;

result.clear();

if (polygon.size() == 0) {

return;

}

auto [sx, sy] = polygon.back();

for (auto [px, py] : polygon) {

sinside = filter.is_inside(sx, sy);

pinside = filter.is_inside(px, py);

if (sinside ^ pinside) {

double bx, by;

filter.bisect(sx, sy, px, py, &bx, &by);

result.emplace_back(bx, by);

}

if (pinside) {

result.emplace_back(px, py);

}

sx = px;

sy = py;

}

}

template <class PathIterator>

void

clip_path_to_rect(PathIterator &path, agg::rect_d &rect, bool inside, std::vector<Polygon> &results)

{

double xmin, ymin, xmax, ymax;

if (rect.x1 < rect.x2) {

xmin = rect.x1;

xmax = rect.x2;

} else {

xmin = rect.x2;

xmax = rect.x1;

}

if (rect.y1 < rect.y2) {

ymin = rect.y1;

ymax = rect.y2;

} else {

ymin = rect.y2;

ymax = rect.y1;

}

if (!inside) {

std::swap(xmin, xmax);

std::swap(ymin, ymax);

}

typedef agg::conv_curve<PathIterator> curve_t;

curve_t curve(path);

Polygon polygon1, polygon2;

double x = 0, y = 0;

unsigned code = 0;

curve.rewind(0);

do {

// Grab the next subpath and store it in polygon1

polygon1.clear();

do {

if (code == agg::path_cmd_move_to) {

polygon1.emplace_back(x, y);

}

code = curve.vertex(&x, &y);

if (code == agg::path_cmd_stop) {

break;

}

if (code != agg::path_cmd_move_to) {

polygon1.emplace_back(x, y);

}

} while ((code & agg::path_cmd_end_poly) != agg::path_cmd_end_poly);

// The result of each step is fed into the next (note the

// swapping of polygon1 and polygon2 at each step).

clip_to_rect_one_step(polygon1, polygon2, clip_to_rect_filters::xlt(xmax));

clip_to_rect_one_step(polygon2, polygon1, clip_to_rect_filters::xgt(xmin));

clip_to_rect_one_step(polygon1, polygon2, clip_to_rect_filters::ylt(ymax));

clip_to_rect_one_step(polygon2, polygon1, clip_to_rect_filters::ygt(ymin));

// Empty polygons aren't very useful, so skip them

if (polygon1.size()) {

_finalize_polygon(results, 1);

results.push_back(polygon1);

}

} while (code != agg::path_cmd_stop);

_finalize_polygon(results, 1);

}

template <class VerticesArray, class ResultArray>

void affine_transform_2d(VerticesArray &vertices, agg::trans_affine &trans, ResultArray &result)

{

if (vertices.size() != 0 && vertices.shape(1) != 2) {

throw std::runtime_error("Invalid vertices array.");

}

size_t n = vertices.shape(0);

double x;

double y;

double t0;

double t1;

double t;

for (size_t i = 0; i < n; ++i) {

x = vertices(i, 0);

y = vertices(i, 1);

t0 = trans.sx * x;

t1 = trans.shx * y;

t = t0 + t1 + trans.tx;

result(i, 0) = t;

t0 = trans.shy * x;

t1 = trans.sy * y;

t = t0 + t1 + trans.ty;

result(i, 1) = t;

}

}

template <class VerticesArray, class ResultArray>

void affine_transform_1d(VerticesArray &vertices, agg::trans_affine &trans, ResultArray &result)

{

if (vertices.shape(0) != 2) {

throw std::runtime_error("Invalid vertices array.");

}

double x;

double y;

double t0;

double t1;

double t;

x = vertices(0);

y = vertices(1);

t0 = trans.sx * x;

t1 = trans.shx * y;

t = t0 + t1 + trans.tx;

result(0) = t;

t0 = trans.shy * x;

t1 = trans.sy * y;

t = t0 + t1 + trans.ty;

result(1) = t;

}

template <class BBoxArray>

int count_bboxes_overlapping_bbox(agg::rect_d &a, BBoxArray &bboxes)

{

agg::rect_d b;

int count = 0;

if (a.x2 < a.x1) {

std::swap(a.x1, a.x2);

}

if (a.y2 < a.y1) {

std::swap(a.y1, a.y2);

}

size_t num_bboxes = safe_first_shape(bboxes);

for (size_t i = 0; i < num_bboxes; ++i) {

b = agg::rect_d(bboxes(i, 0, 0), bboxes(i, 0, 1), bboxes(i, 1, 0), bboxes(i, 1, 1));

if (b.x2 < b.x1) {

std::swap(b.x1, b.x2);

}

if (b.y2 < b.y1) {

std::swap(b.y1, b.y2);

}

if (!((b.x2 <= a.x1) || (b.y2 <= a.y1) || (b.x1 >= a.x2) || (b.y1 >= a.y2))) {

++count;

}

}

return count;

}

inline bool isclose(double a, double b)

{

// relative and absolute tolerance values are chosen empirically

// it looks the atol value matters here because of round-off errors

const double rtol = 1e-10;

const double atol = 1e-13;

// as per python's math.isclose

return fabs(a-b) <= fmax(rtol * fmax(fabs(a), fabs(b)), atol);

}

inline bool segments_intersect(const double &x1,

const double &y1,

const double &x2,

const double &y2,

const double &x3,

const double &y3,

const double &x4,

const double &y4)

{

// determinant

double den = ((y4 - y3) * (x2 - x1)) - ((x4 - x3) * (y2 - y1));

// If den == 0 we have two possibilities:

if (isclose(den, 0.0)) {

double t_area = (x2*y3 - x3*y2) - x1*(y3 - y2) + y1*(x3 - x2);

// 1 - If the area of the triangle made by the 3 first points (2 from the first segment

// plus one from the second) is zero, they are collinear

if (isclose(t_area, 0.0)) {

if (x1 == x2 && x2 == x3) { // segments have infinite slope (vertical lines)

// and lie on the same line

return (fmin(y1, y2) <= fmin(y3, y4) && fmin(y3, y4) <= fmax(y1, y2)) ||

(fmin(y3, y4) <= fmin(y1, y2) && fmin(y1, y2) <= fmax(y3, y4));

}

else {

return (fmin(x1, x2) <= fmin(x3, x4) && fmin(x3, x4) <= fmax(x1, x2)) ||

(fmin(x3, x4) <= fmin(x1, x2) && fmin(x1, x2) <= fmax(x3, x4));

}

}

// 2 - If t_area is not zero, the segments are parallel, but not collinear

else {

return false;

}

}

const double n1 = ((x4 - x3) * (y1 - y3)) - ((y4 - y3) * (x1 - x3));

const double n2 = ((x2 - x1) * (y1 - y3)) - ((y2 - y1) * (x1 - x3));

const double u1 = n1 / den;

const double u2 = n2 / den;

return ((u1 > 0.0 || isclose(u1, 0.0)) &&

(u1 < 1.0 || isclose(u1, 1.0)) &&

(u2 > 0.0 || isclose(u2, 0.0)) &&

(u2 < 1.0 || isclose(u2, 1.0)));

}

template <class PathIterator1, class PathIterator2>

bool path_intersects_path(PathIterator1 &p1, PathIterator2 &p2)

{

typedef PathNanRemover<mpl::PathIterator> no_nans_t;

typedef agg::conv_curve<no_nans_t> curve_t;

if (p1.total_vertices() < 2 || p2.total_vertices() < 2) {

return false;

}

no_nans_t n1(p1, true, p1.has_codes());

no_nans_t n2(p2, true, p2.has_codes());

curve_t c1(n1);

curve_t c2(n2);

double x11, y11, x12, y12;

double x21, y21, x22, y22;

c1.vertex(&x11, &y11);

while (c1.vertex(&x12, &y12) != agg::path_cmd_stop) {

// if the segment in path 1 is (almost) 0 length, skip to next vertex

if ((isclose((x11 - x12) * (x11 - x12) + (y11 - y12) * (y11 - y12), 0))){

continue;

}

c2.rewind(0);

c2.vertex(&x21, &y21);

while (c2.vertex(&x22, &y22) != agg::path_cmd_stop) {

// if the segment in path 2 is (almost) 0 length, skip to next vertex

if ((isclose((x21 - x22) * (x21 - x22) + (y21 - y22) * (y21 - y22), 0))){

continue;

}

if (segments_intersect(x11, y11, x12, y12, x21, y21, x22, y22)) {

return true;

}

x21 = x22;

y21 = y22;

}

x11 = x12;

y11 = y12;

}

return false;

}

// returns whether the segment from (x1,y1) to (x2,y2)

// intersects the rectangle centered at (cx,cy) with size (w,h)

// see doc/segment_intersects_rectangle.svg for a more detailed explanation

inline bool segment_intersects_rectangle(double x1, double y1,

double x2, double y2,

double cx, double cy,

double w, double h)

{

return fabs(x1 + x2 - 2.0 * cx) < fabs(x1 - x2) + w &&

fabs(y1 + y2 - 2.0 * cy) < fabs(y1 - y2) + h &&

2.0 * fabs((x1 - cx) * (y1 - y2) - (y1 - cy) * (x1 - x2)) <

w * fabs(y1 - y2) + h * fabs(x1 - x2);

}

template <class PathIterator>

bool path_intersects_rectangle(PathIterator &path,

double rect_x1, double rect_y1,

double rect_x2, double rect_y2,

bool filled)

{

typedef PathNanRemover<mpl::PathIterator> no_nans_t;

typedef agg::conv_curve<no_nans_t> curve_t;

if (path.total_vertices() == 0) {

return false;

}

no_nans_t no_nans(path, true, path.has_codes());

curve_t curve(no_nans);

double cx = (rect_x1 + rect_x2) * 0.5, cy = (rect_y1 + rect_y2) * 0.5;

double w = fabs(rect_x1 - rect_x2), h = fabs(rect_y1 - rect_y2);

double x1, y1, x2, y2;

curve.vertex(&x1, &y1);

if (2.0 * fabs(x1 - cx) <= w && 2.0 * fabs(y1 - cy) <= h) {

return true;

}

while (curve.vertex(&x2, &y2) != agg::path_cmd_stop) {

if (segment_intersects_rectangle(x1, y1, x2, y2, cx, cy, w, h)) {

return true;

}

x1 = x2;

y1 = y2;

}

if (filled) {

agg::trans_affine trans;

if (point_in_path(cx, cy, 0.0, path, trans)) {

return true;

}

}

return false;

}

template <class PathIterator>

void convert_path_to_polygons(PathIterator &path,

agg::trans_affine &trans,

double width,

double height,

int closed_only,

std::vector<Polygon> &result)

{

typedef agg::conv_transform<mpl::PathIterator> transformed_path_t;

typedef PathNanRemover<transformed_path_t> nan_removal_t;

typedef PathClipper<nan_removal_t> clipped_t;

typedef PathSimplifier<clipped_t> simplify_t;

typedef agg::conv_curve<simplify_t> curve_t;

bool do_clip = width != 0.0 && height != 0.0;

bool simplify = path.should_simplify();

transformed_path_t tpath(path, trans);

nan_removal_t nan_removed(tpath, true, path.has_codes());

clipped_t clipped(nan_removed, do_clip, width, height);

simplify_t simplified(clipped, simplify, path.simplify_threshold());

curve_t curve(simplified);

Polygon *polygon = &result.emplace_back();

double x, y;

unsigned code;

while ((code = curve.vertex(&x, &y)) != agg::path_cmd_stop) {

if ((code & agg::path_cmd_end_poly) == agg::path_cmd_end_poly) {

_finalize_polygon(result, 1);

polygon = &result.emplace_back();

} else {

if (code == agg::path_cmd_move_to) {

_finalize_polygon(result, closed_only);

polygon = &result.emplace_back();

}

polygon->emplace_back(x, y);

}

}

_finalize_polygon(result, closed_only);

}

template <class VertexSource>

void

__cleanup_path(VertexSource &source, std::vector<double> &vertices, std::vector<uint8_t> &codes)

{