mirror of https://github.com/CGAL/cgal
Add polyline simplification to GIS tutorial + several fixes
This commit is contained in:
Simon Giraudot
parent
98faa60276
commit
345d22ae5a
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@ -0,0 +1,604 @@
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#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
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#include <CGAL/Projection_traits_xy_3.h>
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#include <CGAL/Delaunay_triangulation_2.h>
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#include <CGAL/Triangulation_vertex_base_with_info_2.h>
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#include <CGAL/Triangulation_face_base_with_info_2.h>
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#include <CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h>
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#include <CGAL/boost/graph/copy_face_graph.h>
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#include <CGAL/Point_set_3.h>
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#include <CGAL/Point_set_3/IO.h>
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#include <CGAL/compute_average_spacing.h>
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#include <CGAL/Surface_mesh.h>
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#include <CGAL/Polygon_mesh_processing/locate.h>
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#include <boost/graph/adjacency_list.hpp>
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#include <CGAL/boost/graph/split_graph_into_polylines.h>
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#include <CGAL/Constrained_Delaunay_triangulation_2.h>
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#include <CGAL/Constrained_triangulation_plus_2.h>
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#include <CGAL/Polyline_simplification_2/simplify.h>
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#include <CGAL/Polyline_simplification_2/Squared_distance_cost.h>
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#include <CGAL/Classification.h>
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#include <CGAL/Random.h>
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#include <fstream>
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#include <queue>
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#include "include/Color_ramp.h"
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///////////////////////////////////////////////////////////////////
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//! [TIN DS]
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using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
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using Projection_traits = CGAL::Projection_traits_xy_3<Kernel>;
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using Point_2 = Kernel::Point_2;
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using Point_3 = Kernel::Point_3;
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using Segment_3 = Kernel::Segment_3;
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// Triangulated Irregular Network
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using TIN = CGAL::Delaunay_triangulation_2<Projection_traits>;
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//! [TIN DS]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [TIN_with_info DS]
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// Triangulated Irregular Network (with info)
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using Point_set = CGAL::Point_set_3<Point_3>;
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using Vbi = CGAL::Triangulation_vertex_base_with_info_2 <Point_set::Index, Projection_traits>;
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using Fbi = CGAL::Triangulation_face_base_with_info_2<int, Projection_traits>;
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using TDS = CGAL::Triangulation_data_structure_2<Vbi, Fbi>;
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using TIN_with_info = CGAL::Delaunay_triangulation_2<Projection_traits, TDS>;
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//! [TIN_with_info DS]
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///////////////////////////////////////////////////////////////////
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namespace Classification = CGAL::Classification;
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#ifdef CGAL_LINKED_WITH_TBB
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using Concurrency_tag = CGAL::Parallel_tag;
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#else
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using Concurrency_tag = CGAL::Sequential_tag;
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#endif
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///////////////////////////////////////////////////////////////////
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//! [Contouring functions]
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bool face_has_isovalue (TIN_with_info::Face_handle fh, double isovalue)
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{
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bool above = false, below = false;
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for (int i = 0; i < 3; ++ i)
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{
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if (fh->vertex(i)->point().z() > isovalue)
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above = true;
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if (fh->vertex(i)->point().z() < isovalue)
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below = true;
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}
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return (above && below);
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}
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Segment_3 isocontour_in_face (TIN_with_info::Face_handle fh, double isovalue)
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{
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Point_3 source;
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Point_3 target;
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bool source_found = false;
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for (int i = 0; i < 3; ++ i)
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{
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Point_3 p0 = fh->vertex((i+1) % 3)->point();
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Point_3 p1 = fh->vertex((i+2) % 3)->point();
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if ((p0.z() - isovalue) * (p1.z() - isovalue) > 0)
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continue;
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double zbottom = p0.z();
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double ztop = p1.z();
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if (zbottom > ztop)
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{
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std::swap (zbottom, ztop);
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std::swap (p0, p1);
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}
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double ratio = (isovalue - zbottom) / (ztop - zbottom);
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Point_3 p = CGAL::barycenter (p0, (1 - ratio), p1,ratio);
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if (source_found)
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target = p;
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else
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{
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source = p;
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source_found = true;
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}
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}
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return Segment_3 (source, target);
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}
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//! [Contouring functions]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [Contouring visitor]
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template <typename Graph>
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class Polylines_visitor
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{
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private:
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Graph& graph;
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std::vector<std::vector<Point_3> >& polylines;
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public:
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Polylines_visitor (Graph& graph, std::vector<std::vector<Point_3> >& polylines)
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: polylines (polylines), graph(graph) { }
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void start_new_polyline()
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{
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polylines.push_back (std::vector<Point_3>());
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}
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void add_node (typename Graph::vertex_descriptor vd)
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{
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polylines.back().push_back (graph[vd]);
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}
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void end_polyline()
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{
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// filter small polylines
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if (polylines.back().size() < 50)
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polylines.pop_back();
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}
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};
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//! [Contouring visitor]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [CDT]
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namespace PS = CGAL::Polyline_simplification_2;
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using CDT_vertex_base = PS::Vertex_base_2<Projection_traits>;
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using CDT_face_base = CGAL::Constrained_triangulation_face_base_2<Projection_traits>;
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using CDT_TDS = CGAL::Triangulation_data_structure_2<CDT_vertex_base, CDT_face_base>;
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using CDT = CGAL::Constrained_Delaunay_triangulation_2<Projection_traits, CDT_TDS>;
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using CTP = CGAL::Constrained_triangulation_plus_2<CDT>;
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//! [CDT]
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///////////////////////////////////////////////////////////////////
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int main (int argc, char** argv)
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{
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if (argc != 2)
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{
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std::cerr << "Usage: " << argv[0] << " points.ply" << std::endl;
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return EXIT_FAILURE;
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}
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///////////////////////////////////////////////////////////////////
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//! [Init TIN]
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// Read points
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std::ifstream ifile (argv[1], std::ios_base::binary);
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CGAL::Point_set_3<Point_3> points;
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ifile >> points;
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std::cerr << points.size() << " point(s) read" << std::endl;
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// Create TIN
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TIN tin (points.points().begin(), points.points().end());
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//! [Init TIN]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [Save TIN]
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CGAL::Surface_mesh<Point_3> tin_mesh;
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CGAL::copy_face_graph (tin, tin_mesh);
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std::ofstream tin_ofile ("tin.ply", std::ios_base::binary);
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CGAL::set_binary_mode (tin_ofile);
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CGAL::write_ply (tin_ofile, tin_mesh);
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//! [Save TIN]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [TIN_with_info]
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auto idx_to_point_with_info
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= [&](const Point_set::Index& idx) -> std::pair<Point_3, Point_set::Index>
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{
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return std::make_pair (points.point(idx), idx);
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};
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TIN_with_info tin_with_info
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(boost::make_transform_iterator (points.begin(), idx_to_point_with_info),
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boost::make_transform_iterator (points.end(), idx_to_point_with_info));
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//! [TIN_with_info]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [Components]
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double spacing = CGAL::compute_average_spacing<Concurrency_tag>(points, 6);
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spacing *= 2;
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auto face_height
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= [&](const TIN_with_info::Face_handle fh) -> double
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{
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double out = 0.;
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for (int i = 0; i < 3; ++ i)
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out = (std::max) (out, CGAL::abs(fh->vertex(i)->point().z() - fh->vertex((i+1)%3)->point().z()));
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return out;
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};
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// Initialize faces info
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for (TIN_with_info::Face_handle fh : tin_with_info.all_face_handles())
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if (tin_with_info.is_infinite(fh) || face_height(fh) > spacing) // Filtered faces are given info() = -2
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fh->info() = -2;
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else // Pending faces are given info() = -1;
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fh->info() = -1;
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// Flooding algorithm
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std::vector<int> component_size;
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for (TIN_with_info::Face_handle fh : tin_with_info.finite_face_handles())
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{
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if (fh->info() != -1)
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continue;
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std::queue<TIN_with_info::Face_handle> todo;
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todo.push(fh);
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int size = 0;
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while (!todo.empty())
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{
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TIN_with_info::Face_handle current = todo.front();
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todo.pop();
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if (current->info() != -1)
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continue;
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current->info() = component_size.size();
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++ size;
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for (int i = 0; i < 3; ++ i)
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todo.push (current->neighbor(i));
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}
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component_size.push_back (size);
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}
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std::cerr << component_size.size() << " connected component(s) found" << std::endl;
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//! [Components]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [Save TIN with info]
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using Mesh = CGAL::Surface_mesh<Point_3>;
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Mesh tin_colored_mesh;
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Mesh::Property_map<Mesh::Face_index, CGAL::Color>
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color_map = tin_colored_mesh.add_property_map<Mesh::Face_index, CGAL::Color>("f:color").first;
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CGAL::copy_face_graph (tin_with_info, tin_colored_mesh,
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CGAL::parameters::face_to_face_output_iterator
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(boost::make_function_output_iterator
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([&](const std::pair<TIN_with_info::Face_handle, Mesh::Face_index>& ff)
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{
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// Color unassigned faces grey
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if (ff.first->info() < 0)
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color_map[ff.second] = CGAL::Color(128, 128, 128);
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else
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{
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// Random color seeded by the component ID
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CGAL::Random r (ff.first->info());
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color_map[ff.second] = CGAL::Color (r.get_int(64, 192),
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r.get_int(64, 192),
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r.get_int(64, 192));
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}
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})));
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std::ofstream tin_colored_ofile ("colored_tin.ply", std::ios_base::binary);
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CGAL::set_binary_mode (tin_colored_ofile);
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CGAL::write_ply (tin_colored_ofile, tin_colored_mesh);
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//! [Save TIN with info]
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///////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////
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//! [Filtering]
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int min_size = 100000;
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std::vector<TIN_with_info::Vertex_handle> to_remove;
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std::ofstream dbg ("dbg.xyz");
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dbg.precision(18);
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for (TIN_with_info::Vertex_handle vh : tin_with_info.finite_vertex_handles())
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{
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TIN_with_info::Face_circulator circ = tin_with_info.incident_faces (vh),
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start = circ;
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// Remove a vertex if it's only adjacent to components smaller than threshold
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bool keep = false;
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do
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{
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if (circ->info() >= 0 && component_size[std::size_t(circ->info())] > min_size)
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{
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keep = true;
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break;
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}
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}
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while (++ circ != start);
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if (!keep)
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{
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to_remove.push_back (vh);
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dbg << vh->point() << std::endl;
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}
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}
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std::cerr << to_remove.size() << " vertices(s) will be removed after filtering" << std::endl;
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for (TIN_with_info::Vertex_handle vh : to_remove)
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tin_with_info.remove (vh);
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//! [Filtering]
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///////////////////////////////////////////////////////////////////
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// Save as Mesh
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CGAL::Surface_mesh<Point_3> dsm_mesh;
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CGAL::copy_face_graph (tin_with_info, dsm_mesh);
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std::ofstream dsm_ofile ("dsm.ply", std::ios_base::binary);
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CGAL::set_binary_mode (dsm_ofile);
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CGAL::write_ply (dsm_ofile, dsm_mesh);
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///////////////////////////////////////////////////////////////////
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//! [Rastering]
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CGAL::Bbox_3 bbox = CGAL::bbox_3 (points.points().begin(), points.points().end());
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// Generate raster image 1920-pixels large
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std::size_t width = 1920;
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std::size_t height = std::size_t((bbox.ymax() - bbox.ymin()) * 1920 / (bbox.xmax() - bbox.xmin()));
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std::cerr << "Rastering with resolution " << width << "x" << height << std::endl;
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// Use PPM format (Portable PixMap) for simplicity
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std::ofstream raster_ofile ("raster.ppm", std::ios_base::binary);
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raster_ofile << "P6" << std::endl << width << " " << height << std::endl << 255 << std::endl;
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TIN_with_info::Face_handle location;
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// Use rainbow color ramp output
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Color_ramp color_ramp;
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for (std::size_t y = 0; y < height; ++ y)
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for (std::size_t x = 0; x < width; ++ x)
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{
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Point_3 query (bbox.xmin() + x * (bbox.xmax() - bbox.xmin()) / double(width),
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bbox.ymin() + y * (bbox.ymax() - bbox.ymin()) / double(height),
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0); // not relevant for location in 2D
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location = tin_with_info.locate (query, location);
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std::array<unsigned char, 3> colors { 0, 0, 0 };
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if (!tin_with_info.is_infinite(location))
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{
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std::array<double, 3> barycentric_coordinates
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= CGAL::Polygon_mesh_processing::barycentric_coordinates
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(Point_2 (location->vertex(0)->point().x(), location->vertex(0)->point().y()),
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Point_2 (location->vertex(1)->point().x(), location->vertex(1)->point().y()),
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Point_2 (location->vertex(2)->point().x(), location->vertex(2)->point().y()),
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Point_2 (query.x(), query.y()),
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Kernel());
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double height_at_query
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= (barycentric_coordinates[0] * location->vertex(0)->point().z()
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+ barycentric_coordinates[1] * location->vertex(1)->point().z()
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+ barycentric_coordinates[2] * location->vertex(2)->point().z());
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double height_ratio = (height_at_query - bbox.zmin()) / (bbox.zmax() - bbox.zmin());
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colors = color_ramp.get(height_ratio);
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}
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raster_ofile.write ((char*)(&colors), 3);
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}
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//! [Rastering]
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///////////////////////////////////////////////////////////////////
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// Smooth heights with 5 successive Gaussian filters
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double gaussian_variance = 4 * spacing * spacing;
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for (std::size_t i = 0; i < 5; ++ i)
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for (TIN_with_info::Vertex_handle vh : tin_with_info.finite_vertex_handles())
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{
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double z = vh->point().z();
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double total_weight = 1;
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TIN_with_info::Vertex_circulator circ = tin_with_info.incident_vertices (vh),
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start = circ;
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do
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{
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if (!tin_with_info.is_infinite(circ))
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{
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double sq_dist = CGAL::squared_distance (vh->point(), circ->point());
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double weight = std::exp(- sq_dist / gaussian_variance);
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z += weight * circ->point().z();
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total_weight += weight;
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}
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}
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while (++ circ != start);
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z /= total_weight;
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vh->point() = Point_3 (vh->point().x(), vh->point().y(), z);
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}
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///////////////////////////////////////////////////////////////////
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//! [Contouring extraction]
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std::array<double, 50> isovalues; // Contour 50 isovalues
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for (std::size_t i = 0; i < isovalues.size(); ++ i)
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isovalues[i] = bbox.zmin() + ((i+1) * (bbox.zmax() - bbox.zmin()) / (isovalues.size() - 2));
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// First find on each face if they are crossed by some isovalues and
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// extract segments in a graph
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using Segment_graph = boost::adjacency_list<boost::listS, boost::vecS, boost::undirectedS, Point_3>;
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Segment_graph graph;
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using Map_p2v = std::map<Point_3, Segment_graph::vertex_descriptor>;
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Map_p2v map_p2v;
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for (TIN_with_info::Face_handle vh : tin_with_info.finite_face_handles())
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for (double iv : isovalues)
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if (face_has_isovalue (vh, iv))
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{
|
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Segment_3 segment = isocontour_in_face (vh, iv);
|
||||
for (const Point_3& p : { segment.source(), segment.target() })
|
||||
{
|
||||
Map_p2v::iterator iter;
|
||||
bool inserted;
|
||||
std::tie (iter, inserted) = map_p2v.insert (std::make_pair (p, Segment_graph::vertex_descriptor()));
|
||||
if (inserted)
|
||||
{
|
||||
iter->second = boost::add_vertex (graph);
|
||||
graph[iter->second] = p;
|
||||
}
|
||||
}
|
||||
boost::add_edge (map_p2v[segment.source()], map_p2v[segment.target()], graph);
|
||||
}
|
||||
|
||||
//! [Contouring extraction]
|
||||
///////////////////////////////////////////////////////////////////
|
||||
|
||||
///////////////////////////////////////////////////////////////////
|
||||
//! [Contouring split]
|
||||
|
||||
// Split segments into polylines
|
||||
std::vector<std::vector<Point_3> > polylines;
|
||||
Polylines_visitor<Segment_graph> visitor (graph, polylines);
|
||||
CGAL::split_graph_into_polylines (graph, visitor);
|
||||
|
||||
std::cerr << polylines.size() << " polylines computed, with "
|
||||
<< map_p2v.size() << " vertices in total" << std::endl;
|
||||
|
||||
// Output to polyline file
|
||||
std::ofstream contour_ofile ("contour.polylines.txt");
|
||||
contour_ofile.precision(18);
|
||||
for (const std::vector<Point_3>& poly : polylines)
|
||||
{
|
||||
contour_ofile << poly.size();
|
||||
for (const Point_3& p : poly)
|
||||
contour_ofile << " " << p;
|
||||
contour_ofile << std::endl;
|
||||
}
|
||||
|
||||
//! [Contouring split]
|
||||
///////////////////////////////////////////////////////////////////
|
||||
|
||||
///////////////////////////////////////////////////////////////////
|
||||
//! [Contouring simplify]
|
||||
|
||||
// Construct constrained Delaunay triangulation with polylines as constraints
|
||||
CTP ctp;
|
||||
for (const std::vector<Point_3>& poly : polylines)
|
||||
ctp.insert_constraint (poly.begin(), poly.end());
|
||||
|
||||
// Simplification algorithm with limit on distance
|
||||
PS::simplify (ctp, PS::Squared_distance_cost(), PS::Stop_above_cost_threshold (16 * spacing * spacing));
|
||||
|
||||
// Output to file
|
||||
std::ofstream simplified_ofile ("simplified.polylines.txt");
|
||||
simplified_ofile.precision(18);
|
||||
std::size_t nb_vertices = 0;
|
||||
for (CTP::Constraint_id cid : ctp.constraints())
|
||||
{
|
||||
simplified_ofile << ctp.vertices_in_constraint (cid).size();
|
||||
nb_vertices += ctp.vertices_in_constraint (cid).size();
|
||||
for (CTP::Vertex_handle vh : ctp.vertices_in_constraint(cid))
|
||||
simplified_ofile << " " << vh->point();
|
||||
simplified_ofile << std::endl;
|
||||
}
|
||||
|
||||
std::cerr << nb_vertices << " vertices remaining after simplification ("
|
||||
<< 100. * (nb_vertices / double(map_p2v.size())) << "%)" << std::endl;
|
||||
|
||||
|
||||
//! [Contouring simplify]
|
||||
///////////////////////////////////////////////////////////////////
|
||||
|
||||
///////////////////////////////////////////////////////////////////
|
||||
//! [Classification]
|
||||
|
||||
// Get training from input
|
||||
Point_set::Property_map<int> training_map;
|
||||
bool training_found;
|
||||
std::tie (training_map, training_found) = points.property_map<int>("training");
|
||||
|
||||
if (training_found)
|
||||
{
|
||||
std::cerr << "Classifying ground/vegetation/building" << std::endl;
|
||||
|
||||
// Create labels
|
||||
Classification::Label_set labels ({ "ground", "vegetation", "building" });
|
||||
|
||||
// Generate features
|
||||
Classification::Feature_set features;
|
||||
Classification::Point_set_feature_generator<Kernel, Point_set, Point_set::Point_map>
|
||||
generator (points, points.point_map(), 5); // 5 scales
|
||||
|
||||
#ifdef CGAL_LINKED_WITH_TBB
|
||||
// If TBB is used, features can be computed in parallel
|
||||
features.begin_parallel_additions();
|
||||
generator.generate_point_based_features (features);
|
||||
features.end_parallel_additions();
|
||||
#else
|
||||
generator.generate_point_based_features (features);
|
||||
#endif
|
||||
|
||||
// Train a random forest classifier
|
||||
Classification::ETHZ::Random_forest_classifier classifier (labels, features);
|
||||
classifier.train (points.range(training_map));
|
||||
|
||||
// Classify with graphcut regularization
|
||||
Point_set::Property_map<int> label_map = points.add_property_map<int>("labels").first;
|
||||
Classification::classify_with_graphcut<Concurrency_tag>
|
||||
(points, points.point_map(), labels, classifier,
|
||||
generator.neighborhood().k_neighbor_query(12), // regularize on 12-neighbors graph
|
||||
0.5f, // graphcut weight
|
||||
12, // Subdivide to speed-up process
|
||||
label_map);
|
||||
|
||||
// Evaluate
|
||||
std::cerr << "Mean IoU on training data = "
|
||||
<< Classification::Evaluation(labels,
|
||||
points.range(training_map),
|
||||
points.range(label_map)).mean_intersection_over_union() << std::endl;
|
||||
|
||||
// Save the classified point set
|
||||
std::ofstream classified_ofile ("classified.ply");
|
||||
CGAL::set_binary_mode (classified_ofile);
|
||||
classified_ofile << points;
|
||||
}
|
||||
|
||||
//! [Classification]
|
||||
///////////////////////////////////////////////////////////////////
|
||||
|
||||
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,45 @@
|
|||
#ifndef COLOR_RAMP_H
|
||||
#define COLOR_RAMP_H
|
||||
|
||||
class Color_ramp
|
||||
{
|
||||
typedef std::array<unsigned char, 3> Color;
|
||||
typedef std::pair<double, Color> Step;
|
||||
|
||||
std::vector<Step> m_steps;
|
||||
|
||||
public:
|
||||
|
||||
Color_ramp()
|
||||
{
|
||||
m_steps.push_back (std::make_pair (0, Color{ 192, 192, 255}));
|
||||
m_steps.push_back (std::make_pair (0.2, Color{ 0, 0, 255}));
|
||||
m_steps.push_back (std::make_pair (0.4, Color{ 0, 255, 0}));
|
||||
m_steps.push_back (std::make_pair (0.6, Color{ 255, 255, 0}));
|
||||
m_steps.push_back (std::make_pair (0.8, Color{ 255, 0, 0}));
|
||||
m_steps.push_back (std::make_pair (1.0, Color{ 128, 0, 0}));
|
||||
}
|
||||
|
||||
Color get (double value) const
|
||||
{
|
||||
std::size_t idx = 0;
|
||||
while (m_steps[idx+1].first < value)
|
||||
++ idx;
|
||||
|
||||
double v0 = m_steps[idx].first;
|
||||
double v1 = m_steps[idx+1].first;
|
||||
const Color& c0 = m_steps[idx].second;
|
||||
const Color& c1 = m_steps[idx+1].second;
|
||||
|
||||
double ratio = (value - v0) / (v1 - v0);
|
||||
|
||||
Color out;
|
||||
for (std::size_t i = 0; i < 3; ++ i)
|
||||
out[i] = (unsigned char)((1 - ratio) * c0[i] + ratio * c1[i]);
|
||||
|
||||
return out;
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
#endif // COLOR_RAMP_H
|
||||
|
|
@ -18,6 +18,7 @@
|
|||
#include <CGAL/Classification/Label_set.h>
|
||||
|
||||
#include <boost/iterator/zip_iterator.hpp>
|
||||
#include <CGAL/Iterator_range.h>
|
||||
|
||||
#include <map>
|
||||
#include <cmath> // for std::isnan
|
||||
|
|
|
|||
|
|
@ -139,21 +139,42 @@ light blue for low values to dark red for high values.
|
|||
\section TutorialGIS_Contour Contouring
|
||||
|
||||
Extracting isolevels of a function defined on a TIN is another
|
||||
application that can be done with \cgal. The following example does
|
||||
the following:
|
||||
application that can be done with \cgal. We demonstrate here how to
|
||||
extract isolevels of height to build a topographic map.
|
||||
|
||||
1. Smooth the height values in order to generate less noisy
|
||||
isocontours
|
||||
2. Compute 50 isovalues evenly distributed between the minimum and
|
||||
maximum heights of the point cloud
|
||||
3. Output the contours found in a polyline file
|
||||
\subsection TutorialGIS_Contour_Extraction Building Contour Graph
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp Contouring
|
||||
|
||||
The functions used for this contouring algorithm are the following:
|
||||
The first step is to extract, from all faces of the triangulation, the
|
||||
section of each isolevel that goes through that face, in the form of a
|
||||
segment. The following functions allow to test if one isovalue does
|
||||
cross a face, and to extract it then:
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp Contouring functions
|
||||
|
||||
From these functions, we can create a graph of segments to process
|
||||
later into a set of polylines. To do so, we use the `adjacency_list`
|
||||
structure from boost and keep track of a mapping from the positions of
|
||||
the end points to the vertices of the graph.
|
||||
|
||||
The following code computes 50 isovalues evenly distributed between
|
||||
the minimum and maximum heights of the point cloud and creates a graph
|
||||
containing all the segment sections of all isolevels:
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp Contouring extraction
|
||||
|
||||
\subsection TutorialGIS_Contour_Splitting Splitting Into Polylines
|
||||
|
||||
Once the graph is created, splitting it into polylines is easily
|
||||
performed using the function `CGAL::split_graph_into_polylines()`:
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp Contouring split
|
||||
|
||||
This function requires a visitor which is called when starting a
|
||||
polyline, when adding a point to it and when ending it. Defining such
|
||||
a class is straightforward in our case:
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp Contouring visitor
|
||||
|
||||
An example of contouring using 50 isovalues is given on Figure
|
||||
\cgalFigureRef{TutorialGISFigContour}.
|
||||
|
||||
|
|
@ -161,6 +182,31 @@ An example of contouring using 50 isovalues is given on Figure
|
|||
Contouring using 50 isovalues evenly spaced.
|
||||
\cgalFigureEnd
|
||||
|
||||
\subsection TutorialGIS_Contour_Simplifying Simplifying
|
||||
|
||||
Because the output is quite noisy, users may want to simplify the
|
||||
polylines. \cgal provides a polyline simplification algorithm that
|
||||
guarantees that two polylines won't intersect after
|
||||
simplification. This algorithm takes advantage of the Constrained
|
||||
Delaunay Triangulation 2 Plus, which embeds polylines as a set of
|
||||
constraints:
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp CDT
|
||||
|
||||
The following code simplies the polyline set based on the squared
|
||||
distance to the original polylines, stopping when no more vertex can
|
||||
be removed without going farther than 4 times the average spacing.
|
||||
|
||||
\snippet Classification/gis_tutorial_example.cpp Contouring simplify
|
||||
|
||||
An example of simplified contouring is given on Figure
|
||||
\cgalFigureRef{TutorialGISFigSimplified}.
|
||||
|
||||
\cgalFigureBegin{TutorialGISFigSimplified, contour_simplified.jpg}
|
||||
Simplified contour which only uses less than 2\% of the original
|
||||
vertices.
|
||||
\cgalFigureEnd
|
||||
|
||||
\section TutorialGIS_Classify Classifying
|
||||
|
||||
\cgal provides a Classification package which can be used to segment a
|
||||
|
|
|
|||
Loading…
Reference in New Issue