KIKIMR-19287: add task_stats_drawing script

1 files changed, 1251 insertions, 0 deletions

diff --git a/contrib/python/matplotlib/py3/src/_path.h b/contrib/python/matplotlib/py3/src/_path.h
new file mode 100644
index 0000000000..61c4ed07d0
--- /dev/null
+++ b/contrib/python/matplotlib/py3/src/_path.h
@@ -0,0 +1,1251 @@
+/* -*- 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, erich@eye.com
+//
+// 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_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)
+{
+    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>
+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;
+
+    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;
+
+    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.dim(1) != 2) {
+        throw std::runtime_error("Offsets array must have shape (N, 2)");
+    }
+
+    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,
+                              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);
+            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)
+{
+    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)
+{
+    // 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<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_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<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_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<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_codes());
+    clipped_t clipped(nan_removed, do_clip, 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());
+                polygon = &result.back();
+            }
+            polygon->push_back(XY(x, y));
+        }
+    }
+
+    _finalize_polygon(result, closed_only);
+}
+
+template <class VertexSource>
+void
+__cleanup_path(VertexSource &source, std::vector<double> &vertices, std::vector<npy_uint8> &codes)
+{
+    unsigned code;
+    double x, y;
+    do {
+        code = source.vertex(&x, &y);
+        vertices.push_back(x);
+        vertices.push_back(y);
+        codes.push_back((npy_uint8)code);
+    } while (code != agg::path_cmd_stop);
+}
+
+template <class PathIterator>
+void cleanup_path(PathIterator &path,
+                  agg::trans_affine &trans,
+                  bool remove_nans,
+                  bool do_clip,
+                  const agg::rect_base<double> &rect,
+                  e_snap_mode snap_mode,
+                  double stroke_width,
+                  bool do_simplify,
+                  bool return_curves,
+                  SketchParams sketch_params,
+                  std::vector<double> &vertices,
+                  std::vector<unsigned char> &codes)
+{
+    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 PathSnapper<clipped_t> snapped_t;
+    typedef PathSimplifier<snapped_t> simplify_t;
+    typedef agg::conv_curve<simplify_t> curve_t;
+    typedef Sketch<curve_t> sketch_t;
+
+    transformed_path_t tpath(path, trans);
+    nan_removal_t nan_removed(tpath, remove_nans, path.has_codes());
+    clipped_t clipped(nan_removed, do_clip, rect);
+    snapped_t snapped(clipped, snap_mode, path.total_vertices(), stroke_width);
+    simplify_t simplified(snapped, do_simplify, path.simplify_threshold());
+
+    vertices.reserve(path.total_vertices() * 2);
+    codes.reserve(path.total_vertices());
+
+    if (return_curves && sketch_params.scale == 0.0) {
+        __cleanup_path(simplified, vertices, codes);
+    } else {
+        curve_t curve(simplified);
+        sketch_t sketch(curve, sketch_params.scale, sketch_params.length, sketch_params.randomness);
+        __cleanup_path(sketch, vertices, codes);
+    }
+}
+
+void quad2cubic(double x0, double y0,
+                double x1, double y1,
+                double x2, double y2,
+                double *outx, double *outy)
+{
+
+    outx[0] = x0 + 2./3. * (x1 - x0);
+    outy[0] = y0 + 2./3. * (y1 - y0);
+    outx[1] = outx[0] + 1./3. * (x2 - x0);
+    outy[1] = outy[0] + 1./3. * (y2 - y0);
+    outx[2] = x2;
+    outy[2] = y2;
+}
+
+
+void __add_number(double val, char format_code, int precision,
+                  std::string& buffer)
+{
+    if (precision == -1) {
+        // Special-case for compat with old ttconv code, which *truncated*
+        // values with a cast to int instead of rounding them as printf
+        // would do.  The only point where non-integer values arise is from
+        // quad2cubic conversion (as we already perform a first truncation
+        // on Python's side), which can introduce additional floating point
+        // error (by adding 2/3 delta-x and then 1/3 delta-x), so compensate by
+        // first rounding to the closest 1/3 and then truncating.
+        char str[255];
+        PyOS_snprintf(str, 255, "%d", (int)(round(val * 3)) / 3);
+        buffer += str;
+    } else {
+        char *str = PyOS_double_to_string(
+          val, format_code, precision, Py_DTSF_ADD_DOT_0, NULL);
+        // Delete trailing zeros and decimal point
+        char *c = str + strlen(str) - 1;  // Start at last character.
+        // Rewind through all the zeros and, if present, the trailing decimal
+        // point.  Py_DTSF_ADD_DOT_0 ensures we won't go past the start of str.
+        while (*c == '0') {
+            --c;
+        }
+        if (*c == '.') {
+            --c;
+        }
+        try {
+            buffer.append(str, c + 1);
+        } catch (std::bad_alloc& e) {
+            PyMem_Free(str);
+            throw e;
+        }
+        PyMem_Free(str);
+    }
+}
+
+
+template <class PathIterator>
+bool __convert_to_string(PathIterator &path,
+                         int precision,
+                         char **codes,
+                         bool postfix,
+                         std::string& buffer)
+{
+    const char format_code = 'f';
+
+    double x[3];
+    double y[3];
+    double last_x = 0.0;
+    double last_y = 0.0;
+
+    unsigned code;
+
+    while ((code = path.vertex(&x[0], &y[0])) != agg::path_cmd_stop) {
+        if (code == CLOSEPOLY) {
+            buffer += codes[4];
+        } else if (code < 5) {
+            size_t size = NUM_VERTICES[code];
+
+            for (size_t i = 1; i < size; ++i) {
+                unsigned subcode = path.vertex(&x[i], &y[i]);
+                if (subcode != code) {
+                    return false;
+                }
+            }
+
+            /* For formats that don't support quad curves, convert to
+               cubic curves */
+            if (code == CURVE3 && codes[code - 1][0] == '\0') {
+                quad2cubic(last_x, last_y, x[0], y[0], x[1], y[1], x, y);
+                code++;
+                size = 3;
+            }
+
+            if (!postfix) {
+                buffer += codes[code - 1];
+                buffer += ' ';
+            }
+
+            for (size_t i = 0; i < size; ++i) {
+                __add_number(x[i], format_code, precision, buffer);
+                buffer += ' ';
+                __add_number(y[i], format_code, precision, buffer);
+                buffer += ' ';
+            }
+
+            if (postfix) {
+                buffer += codes[code - 1];
+            }
+
+            last_x = x[size - 1];
+            last_y = y[size - 1];
+        } else {
+            // Unknown code value
+            return false;
+        }
+
+        buffer += '\n';
+    }
+
+    return true;
+}
+
+template <class PathIterator>
+bool convert_to_string(PathIterator &path,
+                       agg::trans_affine &trans,
+                       agg::rect_d &clip_rect,
+                       bool simplify,
+                       SketchParams sketch_params,
+                       int precision,
+                       char **codes,
+                       bool postfix,
+                       std::string& buffer)
+{
+    size_t buffersize;
+    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;
+    typedef Sketch<curve_t> sketch_t;
+
+    bool do_clip = (clip_rect.x1 < clip_rect.x2 && clip_rect.y1 < clip_rect.y2);
+
+    transformed_path_t tpath(path, trans);
+    nan_removal_t nan_removed(tpath, true, path.has_codes());
+    clipped_t clipped(nan_removed, do_clip, clip_rect);
+    simplify_t simplified(clipped, simplify, path.simplify_threshold());
+
+    buffersize = (size_t) path.total_vertices() * (precision + 5) * 4;
+    if (buffersize == 0) {
+        return true;
+    }
+
+    if (sketch_params.scale != 0.0) {
+        buffersize *= 10;
+    }
+
+    buffer.reserve(buffersize);
+
+    if (sketch_params.scale == 0.0) {
+        return __convert_to_string(simplified, precision, codes, postfix, buffer);
+    } else {
+        curve_t curve(simplified);
+        sketch_t sketch(curve, sketch_params.scale, sketch_params.length, sketch_params.randomness);
+        return __convert_to_string(sketch, precision, codes, postfix, buffer);
+    }
+
+}
+
+template<class T>
+bool is_sorted_and_has_non_nan(PyArrayObject *array)
+{
+    char* ptr = PyArray_BYTES(array);
+    npy_intp size = PyArray_DIM(array, 0),
+             stride = PyArray_STRIDE(array, 0);
+    using limits = std::numeric_limits<T>;
+    T last = limits::has_infinity ? -limits::infinity() : limits::min();
+    bool found_non_nan = false;
+
+    for (npy_intp i = 0; i < size; ++i, ptr += stride) {
+        T current = *(T*)ptr;
+        // The following tests !isnan(current), but also works for integral
+        // types.  (The isnan(IntegralType) overload is absent on MSVC.)
+        if (current == current) {
+            found_non_nan = true;
+            if (current < last) {
+                return false;
+            }
+            last = current;
+        }
+    }
+    return found_non_nan;
+};
+
+
+#endif