Topology

Topology. More...

Chain complex.
Vertex paths and loops.
template<typename Mesh >
using	Euclid::VertexChain = std::vector< vertex_t< Mesh >>
template<typename Mesh >
using	Euclid::VertexChains = std::vector< VertexChain< Mesh >>
template<typename Mesh >
bool	Euclid::is_chain (const Mesh &mesh, const VertexChain< Mesh > &chain)
	Test if the target is a valid chain. More...
template<typename Mesh >
bool	Euclid::is_loop (const Mesh &mesh, const VertexChain< Mesh > &chain)
	Test if the target is a valid loop. More...

Generator.
template<typename Mesh >
VertexChains< Mesh >	Euclid::greedy_homology_generators (const Mesh &mesh, double accept=0.05)
	Greedy homology generators. More...
template<typename Mesh >
VertexChains< Mesh >	Euclid::greedy_homotopy_generators (const Mesh &mesh, vertex_t< Mesh > v)
	Greedy homotopy generators. More...

Mesh topology.
Basic topological properties and operations.
template<typename Mesh >
int	Euclid::num_boundaries (const Mesh &mesh)
	The number of boundaries/holes.
template<typename Mesh >
std::vector< halfedge_t< Mesh > >	Euclid::boundary_components (const Mesh &mesh)
	Find the boundary components. More...
template<typename Mesh >
int	Euclid::euler_characteristic (const Mesh &mesh)
	Euler characteristic. More...
template<typename Mesh >
int	Euclid::genus (const Mesh &mesh)
	Genus. More...

Detailed Description

This package provides topology related operations.

Typedef Documentation

template<typename Mesh >

using Euclid::VertexChain = typedef std::vector<vertex_t<Mesh>>

Function Documentation

template<typename Mesh >

std::vector< halfedge_t< Mesh > > Euclid::boundary_components

(

const Mesh &

mesh

)

Each component can be retrived by a halfedge.

template<typename Mesh >

int Euclid::euler_characteristic

(

const Mesh &

mesh

)

\(X = V - E + F\)

template<typename Mesh >

int Euclid::genus

(

const Mesh &

mesh

)

\(2G = 2 - X - B\)

template<typename Mesh >

VertexChains< Mesh > Euclid::greedy_homology_generators	(	const Mesh &	mesh,
		double	accept = 0.05
	)

Reference

[1] Erickson, J., Whittlesey, K. Greedy Optimal Homotopy and Homology Generators.

[2] Crane, K. https://www.cs.cmu.edu/~kmcrane/Projects/LoopsOnSurfaces/

template<typename Mesh >

VertexChains< Mesh > Euclid::greedy_homotopy_generators	(	const Mesh &	mesh,
		vertex_t< Mesh >	v
	)

Reference

[1] Erickson, J., Whittlesey, K. Greedy Optimal Homotopy and Homology Generators.

template<typename Mesh >

bool Euclid::is_chain	(	const Mesh &	mesh,
		const VertexChain< Mesh > &	chain
	)

Consecutive vertices should be connected by a valid edge.

template<typename Mesh >

bool Euclid::is_loop	(	const Mesh &	mesh,
		const VertexChain< Mesh > &	chain
	)

A loop is a chain whose head and tail are connected.