Heat Method Reference

Keenan Crane, Christina Vaz, and Andreas Fabri

The package provides an algorithm that solves the single- or multiple-source shortest path problem by returning an approximation of the geodesic distance for all vertices of a triangle mesh to the closest vertex in a given set of source vertices.

Introduced in: CGAL 4.14
Depends on: CGAL and Solvers
BibTeX: cgal:cvf-hm3-24b
License: GPL
Windows Demo: CGAL Lab

Classified Reference Pages

Concepts

• HeatMethodTraits_3

Classes

• CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3
• CGAL::Heat_method_3::Direct
• CGAL::Heat_method_3::Intrinsic_Delaunay

Functions

• CGAL::Heat_method_3::estimate_geodesic_distances()

Modules
	Concepts

Classes
class	CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3< TriangleMesh, Mode, VertexPointMap, LA, Traits >
	Class Surface_mesh_geodesic_distances_3 computes estimated geodesic distances for a set of source vertices where sources can be added and removed. More...

Functions
template<typename TriangleMesh , typename VertexDistanceMap , typename Mode >
void	CGAL::Heat_method_3::estimate_geodesic_distances (const TriangleMesh &tm, VertexDistanceMap vdm, typename boost::graph_traits< TriangleMesh >::vertex_descriptor source, Mode)
	computes for each vertex of the triangle mesh tm the estimated geodesic distance to a given source vertex.
template<typename TriangleMesh , typename VertexDistanceMap , typename VertexConstRange , typename Mode >
void	CGAL::Heat_method_3::estimate_geodesic_distances (const TriangleMesh &tm, VertexDistanceMap vdm, const VertexConstRange &sources, Mode)
	computes for each vertex of the triangle mesh tm the estimated geodesic distance to a given set of source vertices.

Function Documentation

estimate_geodesic_distances() [1/2]

template<typename TriangleMesh , typename VertexDistanceMap , typename VertexConstRange , typename Mode >

void CGAL::Heat_method_3::estimate_geodesic_distances	(	const TriangleMesh &	tm,
		VertexDistanceMap	vdm,
		const VertexConstRange &	sources,
		Mode
	)

#include <CGAL/Heat_method_3/Surface_mesh_geodesic_distances_3.h>

computes for each vertex of the triangle mesh tm the estimated geodesic distance to a given set of source vertices.

This function is provided only if Eigen 3.3 (or greater) is available and CGAL_EIGEN3_ENABLED is defined.

Template Parameters

TriangleMesh	a triangulated surface mesh, model of FaceListGraph and HalfedgeListGraph It must have an internal vertex point property map with the value type being a 3D point from a cgal Kernel model
VertexDistanceMap	a property map model of WritablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and double as value type.
VertexConstRange	a model of the concept ConstRange with value type boost::graph_traits<TriangleMesh>::vertex_descriptor
Mode	either the tag Direct or Intrinsic_Delaunay, which determines if the geodesic distance is computed directly on the mesh or if the intrinsic Delaunay triangulation is applied first. The default is Intrinsic_Delaunay.

Precondition

If Mode is Direct, tm mesh does not have any degenerate faces

Warning

The return type is double even when used with an exact kernel.

See also

CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3

estimate_geodesic_distances() [2/2]

template<typename TriangleMesh , typename VertexDistanceMap , typename Mode >

void CGAL::Heat_method_3::estimate_geodesic_distances	(	const TriangleMesh &	tm,
		VertexDistanceMap	vdm,
		typename boost::graph_traits< TriangleMesh >::vertex_descriptor	source,
		Mode
	)

#include <CGAL/Heat_method_3/Surface_mesh_geodesic_distances_3.h>

computes for each vertex of the triangle mesh tm the estimated geodesic distance to a given source vertex.

This function is provided only if Eigen 3.3 (or greater) is available and CGAL_EIGEN3_ENABLED is defined.

Template Parameters

TriangleMesh	a triangulated surface mesh, model of FaceListGraph and HalfedgeListGraph. It must have an internal vertex point property map with the value type being a 3D point from a cgal Kernel model
VertexDistanceMap	a property map model of WritablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and double as value type.
Mode	either the tag Direct or Intrinsic_Delaunay, which determines if the geodesic distance is computed directly on the mesh or if the intrinsic Delaunay triangulation is applied first. The default is Intrinsic_Delaunay.

Precondition

If Mode is Direct, tm does not have any degenerate faces

Warning

The return type is double even when used with an exact kernel.

See also

CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3

Examples

Heat_method_3/heat_method.cpp, and Heat_method_3/heat_method_polyhedron.cpp.