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1297 lines (1090 loc) · 37.3 KB
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/* -*- 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_path_storage.h"
#include "agg_trans_affine.h"
#include "path_converters.h"
#include "_backend_agg_basic_types.h"
#include "numpy_cpp.h"
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 = points.size();
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;
size_t i;
for (i = 0; i < points.size(); ++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_curves());
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)
{
npy_intp shape[] = {1, 2};
numpy::array_view<double, 2> points(shape);
points(0, 0) = x;
points(0, 1) = y;
int result[1];
result[0] = 0;
points_in_path(points, r, path, trans, result);
return result[0] != 0;
}
template <class PathIterator, class PointArray, class ResultArray>
void points_on_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_stroke<curve_t> stroke_t;
size_t i;
for (i = 0; i < points.size(); ++i) {
result[i] = false;
}
transformed_path_t trans_path(path, trans);
no_nans_t nan_removed_path(trans_path, true, path.has_curves());
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);
}
template <class PathIterator>
inline bool point_on_path(
double x, double y, const double r, PathIterator &path, agg::trans_affine &trans)
{
npy_intp shape[] = {1, 2};
numpy::array_view<double, 2> points(shape);
points(0, 0) = x;
points(0, 1) = y;
int result[1];
result[0] = 0;
points_on_path(points, r, path, trans, 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_curves());
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.dim(1) != 2) {
throw std::runtime_error("Offsets array must be Nx2");
}
size_t Npaths = paths.size();
size_t Noffsets = offsets.size();
size_t N = std::max(Npaths, Noffsets);
size_t Ntransforms = std::min(transforms.size(), N);
size_t i;
agg::trans_affine trans;
reset_limits(extent);
for (i = 0; i < N; ++i) {
typename PathGenerator::path_iterator path(paths(i % Npaths));
if (Ntransforms) {
size_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,
e_offset_position offset_position,
std::vector<int> &result)
{
size_t Npaths = paths.size();
if (Npaths == 0) {
return;
}
size_t Noffsets = offsets.size();
size_t N = std::max(Npaths, Noffsets);
size_t Ntransforms = std::min(transforms.size(), N);
size_t i;
agg::trans_affine trans;
for (i = 0; i < N; ++i) {
typename PathGenerator::path_iterator path = paths(i % Npaths);
if (Ntransforms) {
size_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));
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);
if (offset_position == OFFSET_POSITION_DATA) {
trans = agg::trans_affine_translation(xo, yo) * trans;
} else {
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_curves());
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:
http://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)
{
double sx, sy, px, py, bx, by;
bool sinside, pinside;
result.clear();
if (polygon.size() == 0) {
return;
}
sx = polygon.back().x;
sy = polygon.back().y;
for (Polygon::const_iterator i = polygon.begin(); i != polygon.end(); ++i) {
px = i->x;
py = i->y;
sinside = filter.is_inside(sx, sy);
pinside = filter.is_inside(px, py);
if (sinside ^ pinside) {
filter.bisect(sx, sy, px, py, &bx, &by);
result.push_back(XY(bx, by));
}
if (pinside) {
result.push_back(XY(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.push_back(XY(x, y));
}
code = curve.vertex(&x, &y);
if (code == agg::path_cmd_stop) {
break;
}
if (code != agg::path_cmd_move_to) {
polygon1.push_back(XY(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.dim(1) != 2) {
throw std::runtime_error("Invalid vertices array.");
}
size_t n = vertices.size();
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.dim(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 = bboxes.size();
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, double rtol, double atol)
{
// 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)
{
// relative and absolute tolerance values are chosen empirically
// it looks the atol value matters here bacause of round-off errors
const double rtol = 1e-10;
const double atol = 1e-13;
// determinant
double den = ((y4 - y3) * (x2 - x1)) - ((x4 - x3) * (y2 - y1));
if (isclose(den, 0.0, rtol, atol)) { // collinear segments
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 {
double intercept = (y1*x2 - y2*x1)*(x4 - x3) - (y3*x4 - y4*x3)*(x1 - x2);
if (isclose(intercept, 0.0, rtol, atol)) { // segments lie on the same line
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));
}
}
return false;
}
double n1 = ((x4 - x3) * (y1 - y3)) - ((y4 - y3) * (x1 - x3));
double n2 = ((x2 - x1) * (y1 - y3)) - ((y2 - y1) * (x1 - x3));
double u1 = n1 / den;
double u2 = n2 / den;
return ((u1 > 0.0 || isclose(u1, 0.0, rtol, atol)) &&
(u1 < 1.0 || isclose(u1, 1.0, rtol, atol)) &&
(u2 > 0.0 || isclose(u2, 0.0, rtol, atol)) &&
(u2 < 1.0 || isclose(u2, 1.0, rtol, atol)));
}
template <class PathIterator1, class PathIterator2>
bool path_intersects_path(PathIterator1 &p1, PathIterator2 &p2)
{
typedef PathNanRemover<py::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_curves());
no_nans_t n2(p2, true, p2.has_curves());
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) {
c2.rewind(0);
c2.vertex(&x21, &y21);
while (c2.vertex(&x22, &y22) != agg::path_cmd_stop) {
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<py::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_curves());
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<py::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_curves());
clipped_t clipped(nan_removed, do_clip && !path.has_curves(), width, height);
simplify_t simplified(clipped, simplify, path.simplify_threshold());
curve_t curve(simplified);
result.push_back(Polygon());
Polygon *polygon = &result.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);
result.push_back(Polygon());
polygon = &result.back();
} else {
if (code == agg::path_cmd_move_to) {
_finalize_polygon(result, closed_only);
result.push_back(Polygon());