From ae04f23077ad4225e57d784964dd6d0267a673a4 Mon Sep 17 00:00:00 2001 From: TANG ZhiXiong Date: Tue, 7 Mar 2023 16:19:21 +0800 Subject: [PATCH] Integrate point in polygon; Filter intersections by z, by self_intersection (#7) * fast point in polygon test * integrate fast point in polygon test * init benchmarks * not ready * benchmark matplotlib and cubao * not ready * shapely is slower than matplotlib (even 2.0.1 with PyGEOS) * filter by z, self intersection * not ready * filter by z * filter by polyline * not ready * fix * test point in polygon * update docs * ready to release --- Makefile | 15 ++ README.md | 10 + benchmarks/benchmark_point_in_polygon.py | 239 +++++++++++++++++++++++ docs/about/release-notes.md | 5 + docs/fast-crossing.png | Bin 0 -> 636818 bytes docs/index.md | 4 + docs/point-in-polygon.md | 97 +++++++++ mkdocs.yml | 2 + setup.py | 2 +- src/densify_polyline.hpp | 44 +++++ src/fast_crossing.hpp | 50 +++++ src/main.cpp | 10 + src/point_in_polygon.hpp | 226 +++++++++++++++++++++ src/pybind11_fast_crossing.hpp | 5 + tests/test_basic.py | 61 +++++- 15 files changed, 766 insertions(+), 4 deletions(-) create mode 100644 benchmarks/benchmark_point_in_polygon.py create mode 100755 docs/fast-crossing.png create mode 100644 docs/point-in-polygon.md create mode 100644 src/densify_polyline.hpp create mode 100644 src/point_in_polygon.hpp diff --git a/Makefile b/Makefile index c174da6..6f57d86 100644 --- a/Makefile +++ b/Makefile @@ -85,6 +85,21 @@ tar.gz: tar -cvz --exclude .git -f ../fast_crossing.tar.gz . ls -alh ../fast_crossing.tar.gz +benchmark_point_in_polygon: + python3 benchmarks/benchmark_point_in_polygon.py generate_test_data -o dist/point_in_polygon + python3 benchmarks/benchmark_point_in_polygon.py shapely \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy \ + dist/mask_shapely.npy + python3 benchmarks/benchmark_point_in_polygon.py matplotlib \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy \ + dist/mask_matplotlib.npy + python3 benchmarks/benchmark_point_in_polygon.py cubao \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy \ + dist/mask_cubao.npy +.PHONY: benchmark_point_in_polygon SYNC_OUTPUT_DIR := headers/include/cubao sync_headers: diff --git a/README.md b/README.md index 802ab49..990c82e 100644 --- a/README.md +++ b/README.md @@ -1,7 +1,13 @@ # fast crossing +![](docs/fast-crossing.png) + +(See jupyter notebook [here](https://github.com/cubao/index/blob/master/docs/notebooks/fast-crossing.ipynb)) + +Fast polyline (line segments) intersection (fast version of bentley-ottmann). + ## Installation ### via pip @@ -25,6 +31,10 @@ pip install git+https://github.com/cubao/fast-crossing.git (you can build wheels for later reuse by ` pip wheel git+https://github.com/cubao/fast-crossing.git`) +## Related + +Inspired by [anvaka/isect: Segments intersection detection library](https://github.com/anvaka/isect). + ## Usage & Tests diff --git a/benchmarks/benchmark_point_in_polygon.py b/benchmarks/benchmark_point_in_polygon.py new file mode 100644 index 0000000..9723ef5 --- /dev/null +++ b/benchmarks/benchmark_point_in_polygon.py @@ -0,0 +1,239 @@ +import math +import os +import random +import time +from typing import List, Tuple + +import numpy as np +from loguru import logger + + +def point_in_polygon_matplotlib(points: np.ndarray, polygon: np.ndarray) -> np.ndarray: + from matplotlib.path import Path + + tic = time.time() + path = Path(polygon) + mask = path.contains_points(points).astype(np.int32) + logger.info( + f"point_in_polygon_matplotlib, secs:{time.time() - tic:.9f} ({mask.sum():,}/{len(points)})" + ) + return mask + + +def point_in_polygon_cubao(points: np.ndarray, polygon: np.ndarray) -> np.ndarray: + """ + it's migrated from matplotlib + """ + from fast_crossing import point_in_polygon + + tic = time.time() + mask = point_in_polygon(points=points, polygon=polygon) + logger.info( + f"point_in_polygon_cubao, secs:{time.time() - tic:.9f} ({mask.sum():,}/{len(points)})" + ) + return mask + + +def point_in_polygon_polygons(points: np.ndarray, polygon: np.ndarray) -> np.ndarray: + """ + not ready + """ + import polygons + + polygon = polygon.tolist() + num_edges_children = 4 + num_nodes_children = 4 + tree = polygons.build_search_tree(polygon, num_edges_children, num_nodes_children) + mask = polygons.points_are_inside(tree, points).astype(np.int32) + return mask + + +def point_in_polygon_shapely(points: np.ndarray, polygon: np.ndarray) -> np.ndarray: + import shapely + from shapely.geometry import Polygon + + tic = time.time() + polygon = Polygon(polygon) + points = shapely.points(points) + mask = shapely.contains(polygon, points).astype(np.int32) + logger.info( + f"point_in_polygon_shapely, secs:{time.time() - tic:.9f} ({mask.sum():,}/{len(points)})" + ) + return mask + + +def load_points(path: str): + return np.load(path) + + +def load_polygon(path: str): + if path.endswith((".npy", ".pcd")): + return load_points(path) + pass + + +def write_mask(mask: np.ndarray, path: str): + os.makedirs(os.path.dirname(os.path.abspath(path)), exist_ok=True) + np.save(path, mask) + logger.info(f"wrote to {path}") + + +def wrapping(fn): + def wrapped_fn(input_points: str, input_polygon: str, output_path: str): + points = load_points(input_points)[:, :2] + polygon = load_polygon(input_polygon)[:, :2] + mask = fn(points, polygon) + write_mask(mask, output_path) + + return wrapped_fn + + +# https://stackoverflow.com/questions/8997099/algorithm-to-generate-random-2d-polygon +def generate_polygon( + center: Tuple[float, float], + avg_radius: float, + irregularity: float, + spikiness: float, + num_vertices: int, +) -> List[Tuple[float, float]]: + """ + Start with the center of the polygon at center, then creates the + polygon by sampling points on a circle around the center. + Random noise is added by varying the angular spacing between + sequential points, and by varying the radial distance of each + point from the centre. + + Args: + center (Tuple[float, float]): + a pair representing the center of the circumference used + to generate the polygon. + avg_radius (float): + the average radius (distance of each generated vertex to + the center of the circumference) used to generate points + with a normal distribution. + irregularity (float): + variance of the spacing of the angles between consecutive + vertices. + spikiness (float): + variance of the distance of each vertex to the center of + the circumference. + num_vertices (int): + the number of vertices of the polygon. + Returns: + List[Tuple[float, float]]: list of vertices, in CCW order. + """ + # Parameter check + if irregularity < 0 or irregularity > 1: + raise ValueError("Irregularity must be between 0 and 1.") + if spikiness < 0 or spikiness > 1: + raise ValueError("Spikiness must be between 0 and 1.") + + irregularity *= 2 * math.pi / num_vertices + spikiness *= avg_radius + angle_steps = random_angle_steps(num_vertices, irregularity) + + # now generate the points + points = [] + angle = random.uniform(0, 2 * math.pi) + for i in range(num_vertices): + radius = clip(random.gauss(avg_radius, spikiness), 0, 2 * avg_radius) + point = ( + center[0] + radius * math.cos(angle), + center[1] + radius * math.sin(angle), + ) + points.append(point) + angle += angle_steps[i] + + return points + + +def random_angle_steps(steps: int, irregularity: float) -> List[float]: + """Generates the division of a circumference in random angles. + + Args: + steps (int): + the number of angles to generate. + irregularity (float): + variance of the spacing of the angles between consecutive vertices. + Returns: + List[float]: the list of the random angles. + """ + # generate n angle steps + angles = [] + lower = (2 * math.pi / steps) - irregularity + upper = (2 * math.pi / steps) + irregularity + cumsum = 0 + for _ in range(steps): + angle = random.uniform(lower, upper) + angles.append(angle) + cumsum += angle + + # normalize the steps so that point 0 and point n+1 are the same + cumsum /= 2 * math.pi + for i in range(steps): + angles[i] /= cumsum + return angles + + +def clip(value, lower, upper): + """ + Given an interval, values outside the interval are clipped to the interval + edges. + """ + return min(upper, max(value, lower)) + + +def generate_test_data( + output_dir: str = ".", + *, + label: str = None, + num: int = 10000, + width: float = 800, + height: float = 600, + radius: float = 250, +): + os.makedirs(os.path.abspath(output_dir), exist_ok=True) + + if not label: + label = f"random_num_{num}__bbox_{width:.2f}x{height:.2f}__radius_{radius:.2f}" + xs = (np.random.random(num) - 0.5) * width + ys = (np.random.random(num) - 0.5) * height + xyzs = np.zeros((num, 2)) + xyzs[:, 0] = xs + xyzs[:, 1] = ys + path = f"{output_dir}/{label}__points.npy" + np.save(path, xyzs) + logger.info(f"wrote to {path}") + + polygon = np.array( + generate_polygon( + [0.0, 0.0], + avg_radius=radius, + irregularity=1.0, + spikiness=0.6, + num_vertices=60, + ) + ) + path = f"{output_dir}/{label}__polygon.npy" + np.save(path, polygon) + logger.info(f"wrote to {path}") + + +def point_in_polygon_all(): + pass + + +if __name__ == "__main__": + import fire + + fire.core.Display = lambda lines, out: print(*lines, file=out) + fire.Fire( + { + "all": point_in_polygon_all, + "matplotlib": wrapping(point_in_polygon_matplotlib), + "cubao": wrapping(point_in_polygon_cubao), + "polygons": wrapping(point_in_polygon_polygons), + "shapely": wrapping(point_in_polygon_shapely), + "generate_test_data": generate_test_data, + } + ) diff --git a/docs/about/release-notes.md b/docs/about/release-notes.md index f31efff..f89b99e 100644 --- a/docs/about/release-notes.md +++ b/docs/about/release-notes.md @@ -10,6 +10,11 @@ To upgrade `fast-crossing` to the latest version, use pip: pip install -U fast-crossing ``` +## Version 0.0.4 (2023-03-07) + +* Integrate `point_in_polygon` test +* Filter intersections by z, by self_intersection + ## Version 0.0.3 (2023-03-05) * Fix CI diff --git a/docs/fast-crossing.png b/docs/fast-crossing.png new file mode 100755 index 0000000000000000000000000000000000000000..d9c97821321d60477485e195fdaded9675936ebf GIT binary patch literal 636818 zcmZU)cQo7m`#+9G1x1WfwP(~G6?;>yt*Ba6dlO>sy=N(EmsYhZwZ*DEYSw72STUj~ zwW;-ex$pb^Ip=qNf90I~lXI>-uj_iOD^5pCm4xU%5e^Ox$&<&*PjPUFZE51K;;E`44swM47Y+_H&J$$?ecu<`t-8*PeQ!!l;vLlEmG$<;SstXpO5Ayc z?wj;6bCEoxkE_*4zGvaayDbr_G5{JKG3BeIX`aR*zD0Ux)ba~;K-ImWmo&9Q974~T zkLPuS=?C;bllQ7RNj)ria?g&62i2JIX9Qf%KeFx1HL{)Tje_6B>KahL|sk9PiE%?gjMk< 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zeci_i>(VCnua=7J%onVPkCvF?8-^B`g$W`b62D>_T$VVj#>$oe^ARVZMZ<|@<=VzZ z3U@jlsj%SuS;gIq%&kuawZ1vQyIs6$;BMGoc|?WS=J@(L_k0!=oH!+Og(HdNSQGE8 zg0_jQUV%CJg55RcdGLRL=)T-Afq984QG7Yi+Mn5qwYA}cjyTWD3xZ**;+_hEN6F7d zd@^MjboH}Etbz|`mN>vILVUADWh! zsOeCwx_WVb8e)t@$l0Fv%Mi%z8&}(BSz23%UjPyO1R$Dm=9wPP1Q>;V&f{mR$%JRr z)=uc$Z!jYMNrA+SPw2ry;Hg7Hv71cF*AJ>m^9W(OIO5)T}Q0JA1t5;V@WZ!0G< zg_21a1bl@=Q8Xz_H*CU)`$}jtKx*UmAA#tx=PMs$xkQ*^EuFdzZ@~xsi|+~tta(h zP}l7c(251s4@XfX_X>+kCD2UTO8H+mNSQeOp`QUn)NOmcF*R9>Ql-kdvZf^zmx4VK zWS&|0_jubWLh)W#n^9j?B5yl03K<0!R4R$$Oqz7OUB>Seb0d;B{N%3$Fwr(1IIoaY z#XqVUEPIrDi>MD7?xpLAIw7lPR$$8PCK5Jx=Z}TyP~}<_&81@dZvkr;g-CCHI>Bw$ z`-EuM)^n)_=U}taVmO>ikPMUgD-@(34yOM)dm8gN(Sc3kgRRaz{4I8BvE#dsp-;z*cZiNpz5 z;e`3N$=rt8dd{_QRyY^e4i*OHW6}JQ6I(OmxP1>h&dLyj82!}8!p*bQ2gW In computational geometry, the point-in-polygon (PIP) problem asks whether +> a given point in the plane lies inside, outside, or on the boundary of a +> polygon. It is a special case of point location problems and finds +> applications in areas that deal with processing geometrical data, such as +> computer graphics, computer vision, geographic information systems (GIS), +> motion planning, and computer-aided design (CAD). + +## super-fast implementation from matplotlib + +[`shapely`](https://shapely.readthedocs.io) (>=2.0.1 already integrated C++ GEOS) version: + +```python +import shapely +from shapely.geometry import Polygon +polygon = Polygon(polygon) +points = shapely.points(points) +mask = shapely.contains(polygon, points).astype(np.int32) +``` + +[`matplotlib`](https://matplotlib.org/stable/api/path_api.html) version: + +```python +from matplotlib.path import Path +path = Path(polygon) +mask = path.contains_points(points).astype(np.int32) +``` + +matplotlib version is 50x faster than shapely version. Why??? + +> Need to mention that, shapely version can handle multi-polygon (thought that's not a quite common need) + +We integrated matplotlib version: + +```python +from fast_crossing import point_in_polygon +mask = point_in_polygon(points=points, polygon=polygon) +``` + +It's a little bit faster than matplotlib. (Maybe because I used `-O3` compile flag?) + +## benchmarks + +code: + +```python +{% + include-markdown "../benchmarks/benchmark_point_in_polygon.py" + comments=false +%} +``` + +test: + +```makefile +{% + include-markdown "../Makefile" + start="benchmark_point_in_polygon:" + end=".PHONY: benchmark_point_in_polygon" + comments=false +%} +``` + +result: + +``` +python3 benchmarks/benchmark_point_in_polygon.py generate_test_data -o dist/point_in_polygon +2023-03-07 16:04:39.661 | INFO | __main__:generate_test_data:206 - wrote to dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy +2023-03-07 16:04:39.661 | INFO | __main__:generate_test_data:219 - wrote to dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy +python3 benchmarks/benchmark_point_in_polygon.py shapely \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy \ + dist/mask_shapely.npy +2023-03-07 16:04:39.911 | INFO | __main__:point_in_polygon_shapely:59 - point_in_polygon_shapely, secs:0.114556074 (3,207/10000) +2023-03-07 16:04:39.912 | INFO | __main__:write_mask:78 - wrote to dist/mask_shapely.npy +python3 benchmarks/benchmark_point_in_polygon.py matplotlib \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy \ + dist/mask_matplotlib.npy +2023-03-07 16:04:40.086 | INFO | __main__:point_in_polygon_matplotlib:17 - point_in_polygon_matplotlib, secs:0.001869917 (3,207/10000) +2023-03-07 16:04:40.086 | INFO | __main__:write_mask:78 - wrote to dist/mask_matplotlib.npy +python3 benchmarks/benchmark_point_in_polygon.py cubao \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__points.npy \ + dist/point_in_polygon/random_num_10000__bbox_800.00x600.00__radius_250.00__polygon.npy \ + dist/mask_cubao.npy +2023-03-07 16:04:40.224 | INFO | __main__:point_in_polygon_cubao:31 - point_in_polygon_cubao, secs:0.001556635 (3,207/10000) +2023-03-07 16:04:40.225 | INFO | __main__:write_mask:78 - wrote to dist/mask_cubao.npy +``` + +| implementation | time (seconds) | speed up | +| :-- | :-- | :-- | +| shapely | 0.114556074 | | +| matplotlib | 0.001869917 | x61 | +| cubao | 0.001556635 | x73 | diff --git a/mkdocs.yml b/mkdocs.yml index 1d9788e..3f45b04 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -10,6 +10,8 @@ theme: readthedocs nav: - Home: index.md - Usage: usage.md + - MISC: + - point-in-polygon-test: point-in-polygon.md - About: - Release Notes: about/release-notes.md - License: about/license.md diff --git a/setup.py b/setup.py index e392e2a..4740242 100644 --- a/setup.py +++ b/setup.py @@ -124,7 +124,7 @@ def build_extension(self, ext): # logic and declaration, and simpler if you include description/version in a file. setup( name="fast_crossing", - version="0.0.3", + version="0.0.4", author="tzx", author_email="dvorak4tzx@gmail.com", url="https://github.com/cubao/fast-crossing", diff --git a/src/densify_polyline.hpp b/src/densify_polyline.hpp new file mode 100644 index 0000000..a321d6e --- /dev/null +++ b/src/densify_polyline.hpp @@ -0,0 +1,44 @@ +#ifndef CUBAO_DENSIFY_POLYLINE_HPP +#define CUBAO_DENSIFY_POLYLINE_HPP + +#include + +namespace cubao +{ +inline RowVectors densify_polyline(const Eigen::Ref &coords, + double max_gap) +{ + if (coords.rows() < 2 || max_gap <= 0) { + return coords; + } + std::vector xyzs; + const int N = coords.rows(); + xyzs.reserve(N); + for (int i = 0; i < N - 1; i++) { + const Eigen::RowVector3d &curr = coords.row(i); + const Eigen::RowVector3d &next = coords.row(i + 1); + Eigen::RowVector3d dir = next - curr; + double gap = dir.norm(); + if (gap == 0) { + continue; + } + dir /= gap; + if (gap <= max_gap) { + xyzs.push_back(curr); + continue; + } + RowVectors pos(1 + int(std::ceil(gap / max_gap)), 3); + pos.col(0) = Eigen::ArrayXd::LinSpaced(pos.rows(), curr[0], next[0]); + pos.col(1) = Eigen::ArrayXd::LinSpaced(pos.rows(), curr[1], next[1]); + pos.col(2) = Eigen::ArrayXd::LinSpaced(pos.rows(), curr[2], next[2]); + int M = pos.rows() - 1; + int N = xyzs.size(); + xyzs.resize(N + M); + Eigen::Map(&xyzs[N][0], M, 3) = pos.topRows(M); + } + xyzs.push_back(coords.row(N - 1)); + return Eigen::Map(&xyzs[0][0], xyzs.size(), 3); +} +} // namespace cubao + +#endif diff --git a/src/fast_crossing.hpp b/src/fast_crossing.hpp index 61c2e08..9beee61 100644 --- a/src/fast_crossing.hpp +++ b/src/fast_crossing.hpp @@ -6,6 +6,8 @@ #include #include #include +#include +#include namespace cubao { @@ -109,6 +111,54 @@ struct FastCrossing return ret; } + std::vector intersections( + const std::tuple &z_offset_range, + // 2: no check, 1: only self intersection, 0: no self intersection + int self_intersection = 2) const + { + double z_min = std::get<0>(z_offset_range); + double z_max = std::get<1>(z_offset_range); + if (std::isinf(z_max)) { + z_max = std::numeric_limits::max(); + } + if (z_min > z_max || z_max < 0) { + return {}; + } + + auto v = this->intersections(); + // filter by intersection + if (self_intersection == 0) { + v.erase(std::remove_if(v.begin(), v.end(), + [](const auto &inter) { + return std::get<2>(inter)[0] == + std::get<3>(inter)[0]; + }), + v.end()); + } else if (self_intersection == 1) { + v.erase(std::remove_if(v.begin(), v.end(), + [](const auto &inter) { + return std::get<2>(inter)[0] != + std::get<3>(inter)[0]; + }), + v.end()); + } + + // filter by z + if (z_min > 0 || z_max < std::numeric_limits::max()) { + v.erase(std::remove_if(v.begin(), v.end(), + [&](auto &inter) { // + auto p0 = this->coordinates(inter, true); + auto p1 = + this->coordinates(inter, false); + double zz = std::fabs(p0[2] - p1[2]); + return zz < z_min || zz > z_max; + }), + v.end()); + } + + return v; + } + std::vector intersections(const Eigen::Vector2d &p0, const Eigen::Vector2d &p1, bool dedup = true) const diff --git a/src/main.cpp b/src/main.cpp index 9896256..c3137ed 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -20,6 +20,9 @@ #include "pybind11_flatbush.hpp" #include "pybind11_polyline_ruler.hpp" +#include "point_in_polygon.hpp" +#include "densify_polyline.hpp" + #define STRINGIFY(x) #x #define MACRO_STRINGIFY(x) STRINGIFY(x) @@ -32,6 +35,13 @@ PYBIND11_MODULE(fast_crossing, m) cubao::bind_flatbush(m); cubao::bind_polyline_ruler(m); + m.def("point_in_polygon", &cubao::point_in_polygon, // + py::kw_only(), "points"_a, "polygon"_a, + "point-in-polygon test, returns 0-1 mask"); + m.def("densify_polyline", &cubao::densify_polyline, // + "polyline"_a, py::kw_only(), "max_gap"_a, + "densify polyline, interpolate to satisfy max_gap"); + #ifdef VERSION_INFO m.attr("__version__") = MACRO_STRINGIFY(VERSION_INFO); #else diff --git a/src/point_in_polygon.hpp b/src/point_in_polygon.hpp new file mode 100644 index 0000000..b16f193 --- /dev/null +++ b/src/point_in_polygon.hpp @@ -0,0 +1,226 @@ +#ifndef CUBAO_POINT_IN_POLYGON_HPP +#define CUBAO_POINT_IN_POLYGON_HPP + +#include + +namespace cubao +{ +using RowVectorsNx2 = Eigen::Matrix; +namespace agg +{ +enum path_commands +{ + path_cmd_stop = 0, //----path_cmd_stop + path_cmd_move_to = 1, //----path_cmd_move_to + path_cmd_line_to = 2, //----path_cmd_line_to + path_cmd_curve3 = 3, //----path_cmd_curve3 + path_cmd_curve4 = 4, //----path_cmd_curve4 + path_cmd_curveN = 5, //----path_cmd_curveN + path_cmd_catrom = 6, //----path_cmd_catrom + path_cmd_ubspline = 7, //----path_cmd_ubspline + path_cmd_end_poly = 0x0F, //----path_cmd_end_poly + path_cmd_mask = 0x0F //----path_cmd_mask +}; +} + +// https://github.com/matplotlib/matplotlib/blob/7303d81eb2390208d3bac67dd51d390b585e411f/src/_path.h#L67-L233 +// 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. +inline Eigen::VectorXi +point_in_polygon(const Eigen::Ref &points, + const Eigen::Ref &polygon // or polyline +) +{ + if (!points.rows() || !polygon.rows()) { + throw std::invalid_argument("invalid polygon, or empty points"); + } + + size_t n = points.rows(); + Eigen::VectorXi inside_flag(n); + inside_flag.setZero(); + const int N = polygon.rows(); + + uint8_t yflag1; + double vtx0, vty0, vtx1, vty1; + double tx, ty; + double sx, sy; + double x, y; + bool all_done; + + std::vector yflag0(n); + std::vector subpath_flag(n); + unsigned path_id = 0; + unsigned code = 0; + unsigned vertex; + + do { + if (code != agg::path_cmd_move_to) { + if (path_id >= N) { + x = 0.0; + y = 0.0; + vertex = agg::path_cmd_stop; + } else { + x = polygon(path_id, 0); + y = polygon(path_id, 1); + vertex = path_id == 0 ? agg::path_cmd_move_to + : agg::path_cmd_line_to; + ++path_id; + } + code = vertex; + 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 (size_t 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 { + if (path_id >= N) { + x = 0.0; + y = 0.0; + vertex = agg::path_cmd_stop; + } else { + x = polygon(path_id, 0); + y = polygon(path_id, 1); + vertex = path_id == 0 ? agg::path_cmd_move_to + : agg::path_cmd_line_to; + ++path_id; + } + code = vertex; + + // 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 (size_t 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 (size_t 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); + return inside_flag; +} +} // namespace cubao + +#endif diff --git a/src/pybind11_fast_crossing.hpp b/src/pybind11_fast_crossing.hpp index a691685..c999cb5 100644 --- a/src/pybind11_fast_crossing.hpp +++ b/src/pybind11_fast_crossing.hpp @@ -52,6 +52,11 @@ CUBAO_INLINE void bind_fast_crossing(py::module &m) .def("intersections", py::overload_cast<>(&FastCrossing::intersections, py::const_), "all segment intersections in tree") + .def("intersections", + py::overload_cast &, int>( + &FastCrossing::intersections, py::const_), + py::kw_only(), "z_offset_range"_a, "self_intersection"_a = 2, + "segment intersections in tree, filter by some condition") .def("intersections", py::overload_cast(&FastCrossing::intersections, py::const_), diff --git a/tests/test_basic.py b/tests/test_basic.py index 2bcf634..2a02628 100644 --- a/tests/test_basic.py +++ b/tests/test_basic.py @@ -1,6 +1,6 @@ import numpy as np import pytest -from fast_crossing import FastCrossing +from fast_crossing import FastCrossing, densify_polyline, point_in_polygon def test_fast_crossing(): @@ -143,9 +143,12 @@ def test_fast_crossing_filter_by_z(): assert len(ret) == 1 assert fc.coordinates(ret[0])[2] == 0 - ret = fc.intersections([[0.5, -1, 10], [0.5, 1, 10]], z_min=-1, z_max=1) + ret = fc.intersections([[0.5, -1, 10.5], [0.5, 1, 10.5]], z_min=-1, z_max=1) assert len(ret) == 1 - assert fc.coordinates(ret[0])[2] == 10 + assert np.all(fc.coordinates(ret[0]) == [0.5, 0, 10]) + assert np.all(fc.coordinates(ret[0], second=True) == [0.5, 0, 10]) + # don't do this, first point is not in fc!!! + # assert np.all(fc.coordinates(ret[0], second=False) == [0.5, 0, 10.5]) ret = fc.intersections([[0.5, -1, 20], [0.5, 1, 20]], z_min=-1, z_max=1) assert len(ret) == 1 @@ -156,6 +159,10 @@ def test_fast_crossing_filter_by_z(): assert fc.coordinates(ret[0])[2] == 10 assert fc.coordinates(ret[1])[2] == 20 + assert 3 == len(fc.intersections()) # 3 == C(3,2): choose 2 from 3 + # for row in fc.intersections(): + # print(row) + def test_fast_crossing_dedup(): # should be stable @@ -175,3 +182,51 @@ def test_fast_crossing_dedup(): # for idx, row in enumerate(ret): # print(idx, row) assert len(ret) == 4 + + +def test_fast_crossing_single_polyline(): + fc = FastCrossing() + fc.add_polyline([[0, 0, 0], [1, 0, 0], [2, 0, 0]]) + assert not fc.intersections() + + +def test_fast_crossing_single_polyline_self_intersection(): + fc = FastCrossing() + fc.add_polyline([[0, 0, 0], [1, 0, 0], [1, 1, 0], [-1, -1, 0]]) + assert len(fc.intersections()) == 1 + assert not fc.intersections(z_offset_range=[0.0, 10.0], self_intersection=0) + assert fc.intersections(z_offset_range=[0.0, 0.0]) + assert not fc.intersections(z_offset_range=[1e-15, 1.0]) + + fc = FastCrossing() + fc.add_polyline([[0, 0, 0], [1, 0, 0], [1, 1, 0], [-1, -1, 0]]) + fc.add_polyline(np.array([[0.0, 0.0], [5.0, 0.0]])) # AB + fc.add_polyline(np.array([[2.5, 2.0], [2.5, 1.0], [2.5, -2.0]])) # CDE + self_inter = fc.intersections(z_offset_range=[-1.0, 1e10], self_intersection=1) + assert len(self_inter) == 1 + + +def test_densify(): + coords = np.array( + [ + [0, 0, 0], + [2, 0, 0], + [5, 0, 0], + ], + dtype=np.float64, + ) + dense = densify_polyline(coords, max_gap=1.0) + assert len(dense) == 6 + dense = densify_polyline(coords, max_gap=2.0) + assert len(dense) == 4 + dense = densify_polyline(coords, max_gap=3.0) + assert len(dense) == 3 + assert 3 == len(densify_polyline(coords, max_gap=3.0 + 1e-3)) + assert 4 == len(densify_polyline(coords, max_gap=3.0 - 1e-3)) + + +def test_point_in_polygon(): + polygon = [[0, 0], [1, 0], [1, 1], [0, 1]] + points = [[0.5, 0.5], [10, 0]] + mask = point_in_polygon(points=points, polygon=polygon) + assert np.all(mask == [1, 0])

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