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/********************************************************************** * * GEOS - Geometry Engine Open Source * http://geos.osgeo.org * * Copyright (C) 2021 Paul Ramsey * * This is free software; you can redistribute and/or modify it under * the terms of the GNU Lesser General Public Licence as published * by the Free Software Foundation. * See the COPYING file for more information. * **********************************************************************/ #pragma once #include #include #include #include #include #include #include namespace geos { namespace geom { class Coordinate; class Geometry; class GeometryFactory; } namespace triangulate { namespace quadedge { class Quadedge; class QuadEdgeSubdivision; } } } using geos::geom::Coordinate; using geos::geom::Geometry; using geos::geom::GeometryFactory; using geos::geom::Triangle; using geos::triangulate::quadedge::QuadEdge; using geos::triangulate::quadedge::QuadEdgeSubdivision; using geos::triangulate::quadedge::TriangleVisitor; using geos::triangulate::tri::Tri; using geos::triangulate::tri::TriList; namespace geos { namespace algorithm { // geos::algorithm namespace hull { // geos::algorithm::hull typedef std::priority_queue, HullTri::HullTriCompare> HullTriQueue; /** * Constructs a concave hull of a set of points. * The hull is constructed by removing border triangles * of the Delaunay Triangulation of the points * as long as their "size" is larger than the target criterion. * The target criteria are: * * * Maximum Edge Length Ratio - determines the Maximum Edge Length * by a fraction of the difference between * the longest and shortest edge lengths * in the Delaunay Triangulation. This normalizes the * Maximum Edge Length to be scale-independent. * * Maximum Area Ratio - the ratio of the concave hull area to the convex * hull area will be no larger than this value * * Alpha - produces Alpha-shapes, by removing border triangles * with a circumradius greater than alpha. * Large values produce the convex hull; a value of 0 * produces maximum concaveness. * * The preferred criterium is the Maximum Edge Length Ratio, since it is * scale-free and local (so that no assumption needs to be made about the * total amount of concavity present. * * Other length criteria can be used by setting the Maximum Edge Length. * For example, use a length relative to the longest edge length * in the Minimum Spanning Tree of the point set. * Or, use a length derived from the uniformGridEdgeLength() value. * * The computed hull is always a single connected geom::Polygon * (unless it is degenerate, in which case it will be a geom::Point or a geom::LineString). * This constraint may cause the concave hull to fail to meet the target criteria. * * Optionally the concave hull can be allowed * to contain holes by calling setHolesAllowed(boolean). * * @author mdavis */ class GEOS_DLL ConcaveHull { public: ConcaveHull(const Geometry* geom); /** * Computes the approximate edge length of * a uniform square grid having the same number of * points as a geometry and the same area as its convex hull. * This value can be used to determine a suitable length threshold value * for computing a concave hull. * A value from 2 to 4 times the uniform grid length * seems to produce reasonable results. * * @param geom a geometry * @return the approximate uniform grid length */ static double uniformEdgeLength(const Geometry* geom); /** * Computes the concave hull of the vertices in a geometry * using the target criteria of maximum edge length. * * @param geom the input geometry * @param maxLength the target maximum edge length * @return the concave hull */ static std::unique_ptr concaveHullByLength( const Geometry* geom, double maxLength); static std::unique_ptr concaveHullByLength( const Geometry* geom, double maxLength, bool isHolesAllowed); /** * Computes the concave hull of the vertices in a geometry * using the target criteria of maximum edge length ratio. * The edge length ratio is a fraction of the length difference * between the longest and shortest edges * in the Delaunay Triangulation of the input points. * * @param geom the input geometry * @param lengthRatio the target edge length factor * @return the concave hull */ static std::unique_ptr concaveHullByLengthRatio( const Geometry* geom, double lengthRatio); /** * Computes the concave hull of the vertices in a geometry * using the target criterion of maximum edge length factor, * and optionally allowing holes. * The edge length factor is a fraction of the length difference * between the longest and shortest edges * in the Delaunay Triangulation of the input points. * * @param geom the input geometry * @param lengthRatio the target maximum edge length * @param isHolesAllowed whether holes are allowed in the result * @return the concave hull */ static std::unique_ptr concaveHullByLengthRatio( const Geometry* geom, double lengthRatio, bool isHolesAllowed); /** * Computes the alpha shape of a geometry as a polygon. * The alpha parameter is the radius of the eroding disc. * * @param geom the input geometry * @param alpha the radius of the eroding disc * @param isHolesAllowed whether holes are allowed in the result * @return the alpha shape polygon */ static std::unique_ptr alphaShape( const Geometry* geom, double alpha, bool isHolesAllowed); /** * Sets the target maximum edge length for the concave hull. * The length value must be zero or greater. * * * The value 0.0 produces the concave hull of smallest area * that is still connected. * * Larger values produce less concave results. * A value equal or greater than the longest Delaunay Triangulation edge length * produces the convex hull. * * The uniformGridEdgeLength value may be used as * the basis for estimating an appropriate target maximum edge length. * * @param edgeLength a non-negative length */ void setMaximumEdgeLength(double edgeLength); /** * Sets the target maximum edge length ratio for the concave hull. * The edge length ratio is a fraction of the length delta * between the longest and shortest edges * in the Delaunay Triangulation of the input points. * A value of 1.0 produces the convex hull. * A value of 0.0 produces a concave hull of minimum area * that is still connected. * * @param edgeLengthRatio a length ratio value between 0 and 1 */ void setMaximumEdgeLengthRatio(double edgeLengthRatio); /** * Sets whether holes are allowed in the concave hull polygon. * * @param holesAllowed true if holes are allowed in the result */ void setHolesAllowed(bool holesAllowed); /** * Sets the alpha parameter to compute an alpha shape of the input. * Alpha is the radius of the eroding disc. * Border triangles with circumradius greater than alpha are removed. * * @param newAlpha the alpha radius */ void setAlpha(double newAlpha); /** * Gets the computed concave hull. * * @return the concave hull */ std::unique_ptr getHull(); private: // Constants static constexpr int PARAM_EDGE_LENGTH = 1; static constexpr int PARAM_ALPHA = 2; // Members const Geometry* inputGeometry; double maxEdgeLengthRatio; double alpha; bool isHolesAllowed; int criteriaType; double maxSizeInHull; const GeometryFactory* geomFactory; // Methods static double computeTargetEdgeLength( TriList& triList, double edgeLengthFactor); void computeHull(TriList& triList); void computeHullBorder(TriList& triList); void createBorderQueue(HullTriQueue& queue, TriList& triList); /** * Adds a Tri to the queue. * Only add tris with a single border edge. * since otherwise that would risk isolating a vertex if * the tri ends up being eroded from the hull. * Sets the tri size according to the threshold parameter being used. * * @param tri the Tri to add * @param queue the priority queue */ void addBorderTri(HullTri* tri, HullTriQueue& queue); void computeHullHoles(TriList& triList); void setSize(HullTri* tri); /** * Finds tris which may be the start of holes. * Only tris which have a long enough edge and which do not touch the current hull * boundary are included. * This avoids the risk of disconnecting the result polygon. * The list is sorted in decreasing order of edge length. * The list is sorted in decreasing order of size. * * @param triList * @param maxSizeInHull maximum tri size which is not in a hole * @return */ static std::vector findCandidateHoles( TriList& triList, double maxSizeInHull); void removeHole(TriList& triList, HullTri* triHole); void setSize(TriList& triList); /** * Tests if a tri is included in the hull. * Tris with size less than the maximum are included in the hull. * * @param tri the tri to test * @return true if the tri is included in the hull */ bool isInHull(const HullTri* tri) const; bool isRemovableBorder(const HullTri* tri) const; bool isRemovableHole(const HullTri* tri) const; std::unique_ptr toGeometry( TriList& triList, const GeometryFactory* factory); }; } // geos::algorithm::hull } // geos::algorithm } // geos