Delaunay triangulation.

Delaunay mesh. More...

Classes
struct	Euclid::SplitSite< Mesh >
	The local mesh elements when splitting. More...
struct	Euclid::RemeshDelaunayVisitor< Mesh >
	A dumb remesh delaunay visitor. More...

Enumerations
enum	Euclid::RemeshDelaunayScheme { Euclid::RemeshDelaunayScheme::SimpleFlip, Euclid::RemeshDelaunayScheme::GeometryPreserving, Euclid::RemeshDelaunayScheme::FeaturePreserving }
	Schemes for remeshing a mesh to be Delaunay. More...

Functions
template<typename Mesh >
bool	Euclid::is_delaunay (const Mesh &mesh, double eps=1e-14)
	Test if a mesh is Delaunay. More...
template<typename Mesh >
bool	Euclid::is_delaunay (const Mesh &mesh, edge_t< Mesh > e, double eps=1e-14)
	Test if an edge is locally Delaunay. More...
template<typename Mesh >
void	Euclid::remesh_delaunay (Mesh &mesh, RemeshDelaunayScheme scheme=RemeshDelaunayScheme::SimpleFlip, double dihedral_angle=10.0)
	Remesh an arbitary mesh into Delaunay mesh. More...
template<typename Mesh , typename Visitor >
void	Euclid::remesh_delaunay (Mesh &mesh, Visitor &visitor, RemeshDelaunayScheme scheme=RemeshDelaunayScheme::SimpleFlip, double dihedral_angle=10.0)
	Remesh an arbitary mesh into Delaunay mesh. More...

Detailed Description

Reference

[1] Dyer, R., etc. Delaunay mesh construction.

Enumeration Type Documentation

enum Euclid::RemeshDelaunayScheme

strong

Enumerator
SimpleFlip	Just flip non-locally Delaunay edges untils they disappear. This will change the underlying geometry when flipping non-planar edges. Some edges cannot be flipped (cf. Fig 6 [1]), thus they output is not guaranteed to be Delaunay.
GeometryPreserving	Combine edge flip with edge split. This will keep the underlying geometry intact, since non-planar edges are not flipped. Instead, a lot more vertices will be inserted into the mesh.
FeaturePreserving	A combination of the simple flip and geometry presvering scheme. Do edge split only on edges with a dihedral angle larger than a threshold. Otherwise just flip that edge, which will incur a small geometric change.

Function Documentation

template<typename Mesh >

bool Euclid::is_delaunay	(	const Mesh &	mesh,
		double	eps = 1e-14
	)

Return true if all edges are locally Delaunay.

template<typename Mesh >

bool Euclid::is_delaunay	(	const Mesh &	mesh,
		edge_t< Mesh >	e,
		double	eps = 1e-14
	)

Return true if a1 + a2 <= PI, where a1, a2 are the angles of opposite corners.

template<typename Mesh >

void Euclid::remesh_delaunay	(	Mesh &	mesh,
		RemeshDelaunayScheme	scheme = RemeshDelaunayScheme::SimpleFlip,
		double	dihedral_angle = 10.0
	)

Parameters

mesh	Input mesh.
scheme	Remesh scheme.
dihedral_angle	The threshold used for FeaturePreserving scheme.

template<typename Mesh , typename Visitor >

void Euclid::remesh_delaunay	(	Mesh &	mesh,
		Visitor &	visitor,
		RemeshDelaunayScheme	scheme = RemeshDelaunayScheme::SimpleFlip,
		double	dihedral_angle = 10.0
	)

Parameters

mesh	Input mesh.
visitor	Remesh visitor.
scheme	Remesh scheme.
dihedral_angle	The threshold used for FeaturePreserving scheme.