Mesh< ambient, topo > Struct Template Reference

#include <Mesh.h>

Inheritance diagram for Mesh< ambient, topo >:


Public Types
typedef ::SimplexData< ambient, topo >	SimplexData
typedef IncrementalDelaunay< ambient, topo, RefineVertex< ambient >, SimplexData >	Delaunay
typedef Delaunay::Complex	Complex
typedef Delaunay::Cavity	Cavity
typedef Delaunay::Star	Star
typedef Delaunay::Simplex	Simplex
typedef Delaunay::Vertex	Vertex
typedef MeshTypes< ambient >::Ball	Ball
typedef MeshTypes< ambient >::BallSet	BallSet
typedef MeshTypes< ambient >::GenericMesh	GenericMesh
typedef Geometry::CenterRadius< ambient >	CenterRadius
typedef Geometry::Point< ambient >	Point
typedef Geometry::Point< topo >	PPoint
typedef ::SplitData< ambient >	SplitData
Public Member Functions
	Mesh (Delaunay *del)
virtual unsigned	topological () const
const Delaunay *	getDelaunay () const
const Complex &	getSimplicialComplex () const
Delaunay *	getDelaunayDangerously ()
const Simplex &	getHandle () const
template<class DFSData>
void	dfs (DFSData &data) const
template<class output_iterator>
output_iterator	collectAllBalls (output_iterator out) const
Ball *	toBall (const Simplex &s) const
void	setBall (const Simplex &s, Ball *b)
bool	isMember (const Simplex &s) const
CenterRadius	circumcenter (const Simplex &s) const
double	radiusEdge2 (const Simplex &s) const
double	computeSigma (const Simplex &s) const
bool	encroachedBy (const Simplex &s, const Vertex *v) const
bool	inSphereExact (const Simplex &s, const Vertex *v) const
bool	isResolved (const Simplex &s) const
void	gatherUppers (const Simplex &s, BallSet &set) const
void	gatherLowers (const Simplex &s, BallSet &set) const
bool	approximatelyIntersects (const Simplex &s, const Ball *b) const
bool	split (const Simplex &s, SplitData &data, Vertex *inserthint=NULL, bool force=false)
bool	split (Vertex *v, SplitData &data)
bool	checkAddLower (const Simplex &s, Ball *b)
void	blindlyAddUpper (const Simplex &s, Ball *up)
void	blindlyAddLower (const Simplex &s, Ball *lower)
void	removeUpper (const Simplex &s, Ball *up)
void	removeLower (const Simplex &s, Ball *lower)
void	checkAddLowerToAll (Ball *b)
Static Public Attributes
static const size_t	ambient_dimension = ambient
static const size_t	topological_dimension = topo
Classes
struct	BallNotifier
struct	ConvertToBalls
struct	InitVertex
struct	WarpClosure

Detailed Description

template<size_t ambient, size_t topo>
struct Mesh< ambient, topo >

This class is a thin interface over a Delaunay triangulation, with functions specialized for our meshing application.

Member Typedef Documentation

template<size_t ambient, size_t topo>

typedef MeshTypes<ambient>::Ball Mesh< ambient, topo >::Ball

template<size_t ambient, size_t topo>

typedef MeshTypes<ambient>::BallSet Mesh< ambient, topo >::BallSet

template<size_t ambient, size_t topo>

typedef Delaunay::Cavity Mesh< ambient, topo >::Cavity

template<size_t ambient, size_t topo>

typedef Geometry::CenterRadius<ambient> Mesh< ambient, topo >::CenterRadius

template<size_t ambient, size_t topo>

typedef Delaunay::Complex Mesh< ambient, topo >::Complex

template<size_t ambient, size_t topo>

typedef IncrementalDelaunay<ambient, topo, RefineVertex<ambient>, SimplexData> Mesh< ambient, topo >::Delaunay

template<size_t ambient, size_t topo>

typedef MeshTypes<ambient>::GenericMesh Mesh< ambient, topo >::GenericMesh

template<size_t ambient, size_t topo>

typedef Geometry::Point<ambient> Mesh< ambient, topo >::Point

template<size_t ambient, size_t topo>

typedef Geometry::Point<topo> Mesh< ambient, topo >::PPoint

template<size_t ambient, size_t topo>

typedef Delaunay::Simplex Mesh< ambient, topo >::Simplex

template<size_t ambient, size_t topo>

typedef ::SimplexData<ambient, topo> Mesh< ambient, topo >::SimplexData

template<size_t ambient, size_t topo>

typedef ::SplitData<ambient> Mesh< ambient, topo >::SplitData

template<size_t ambient, size_t topo>

typedef Delaunay::Star Mesh< ambient, topo >::Star

template<size_t ambient, size_t topo>

typedef Delaunay::Vertex Mesh< ambient, topo >::Vertex

Constructor & Destructor Documentation

template<size_t ambient, size_t topo>

Mesh< ambient, topo >::Mesh ( Delaunay * del ) [inline]

Initialize the mesh.

The feature must be convex: the code breaks otherwise.
There should be O(1) boundary vertices: the code runs very slowly otherwise: O(n * initial triangles). In topo=2, init is n. In topo=3, init is n if we have good initial quality, but up to n^2 if we don't.
The Delaunay of the boundary vertices should have good quality. If so, the Delaunay is O(n) size (important for the prior point). If not, even assuming initial triangles is small, the code may run in a factor O(lg L/s) slower if we violate the quality assumption.

Member Function Documentation

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::approximatelyIntersects ( const Simplex & s,

const Ball * b

) const [inline]

Return whether the circumsphere of the simplex intersects the ball. Precision is not required here: we actually answer if the closed circumball of s intersects the closed ball b, up to floating-point accuracy.

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::blindlyAddLower ( const Simplex & s,

Ball * lower

) [inline]

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::blindlyAddUpper ( const Simplex & s,

Ball * up

) [inline]

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::checkAddLower ( const Simplex & s,

Ball * b

) [inline]

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::checkAddLowerToAll ( Ball * b ) [inline]

Iterate over the mesh, adding the ball as a lower to every simplex it approximatelyIntersects()

template<size_t ambient, size_t topo>

CenterRadius Mesh< ambient, topo >::circumcenter ( const Simplex & s ) const [inline]

Return the center and radius of the simplex.

template<size_t ambient, size_t topo>

template<class output_iterator>

output_iterator Mesh< ambient, topo >::collectAllBalls ( output_iterator out ) const [inline]

Convert the mesh into a list of balls. The output is done using an output iterator, so we can output a set, list, vector, count, etc.

template<size_t ambient, size_t topo>

double Mesh< ambient, topo >::computeSigma ( const Simplex & s ) const [inline]

template<size_t ambient, size_t topo>

template<class DFSData>

void Mesh< ambient, topo >::dfs ( DFSData & data ) const [inline]

Perform a depth-first-search in the mesh, starting at the global handle. Other DFS functions could easily be provided, but aren't necessary now.

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::encroachedBy ( const Simplex & s,

const Vertex * v

) const [inline]

Return whether the simplex would be encroached by the vertex. We use approximate arithmetic here, because precision is not required. Precision is necessary to make sure we don't count a vertex of the simplex as encroaching the simplex. But that can be checked combinatorially.

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::gatherLowers ( const Simplex & s,

BallSet & set

) const [inline]

Gather the set of lower-dimensional balls that s knows.

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::gatherUppers ( const Simplex & s,

BallSet & set

) const [inline]

Gather the set of balls that have down-pointers to this simplex.

template<size_t ambient, size_t topo>

const Delaunay* Mesh< ambient, topo >::getDelaunay ( ) const [inline]

Return the underlying mesh structure, with geometric information.

template<size_t ambient, size_t topo>

Delaunay* Mesh< ambient, topo >::getDelaunayDangerously ( ) [inline]

Return the underlying Delaunay, non-const. This is dangerous: changes to the underlying Delaunay can cause the Mesh structure to become invalid. Use this only in very prescribed locations, such at MeshConstructor.

template<size_t ambient, size_t topo>

const Simplex& Mesh< ambient, topo >::getHandle ( ) const [inline]

Return a handle into the mesh. Mostly just used internally, but there's not much reason not to provide it.

template<size_t ambient, size_t topo>

const Complex& Mesh< ambient, topo >::getSimplicialComplex ( ) const [inline]

Return the underlying mesh structure -- just the topology.

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::inSphereExact ( const Simplex & s,

const Vertex * v

) const [inline]

Exact test for encroachment by vertices in the plane of the mesh. We test the open ball; vertices of s do not encroach on s.

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::isMember ( const Simplex & s ) const [inline]

Return whether s is still in the mesh.

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::isResolved ( const Simplex & s ) const [inline]

Is this ball resolved in the top-dimensional mesh?

template<size_t ambient, size_t topo>

double Mesh< ambient, topo >::radiusEdge2 ( const Simplex & s ) const [inline]

Return the radius/edge ratio (squared) of the simplex.

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::removeLower ( const Simplex & s,

Ball * lower

) [inline]

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::removeUpper ( const Simplex & s,

Ball * up

) [inline]

template<size_t ambient, size_t topo>

void Mesh< ambient, topo >::setBall ( const Simplex & s,

Ball * b

) [inline]

TODO: restrict access here.

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::split ( Vertex * v,

SplitData & data

) [inline]

Split based on a vertex rather than on a simplex. The difference is simply that to split a vertex, we first need to find a simplex to split.

template<size_t ambient, size_t topo>

bool Mesh< ambient, topo >::split ( const Simplex & s,

SplitData & data,

Vertex * inserthint = NULL,

bool force = false

) [inline]

Try to split s, by inserting a point in its circumball. The insertion will either:

insert the circumcenter,
insert a lower-dimensional point,
fail due to encroachment.

Returns whether s was actually split (if not, it encroached).
If the insertion actually occurs, the upper/lower pointers are fixed.

template<size_t ambient, size_t topo>

Ball* Mesh< ambient, topo >::toBall ( const Simplex & s ) const [inline]

template<size_t ambient, size_t topo>

virtual unsigned Mesh< ambient, topo >::topological ( ) const [inline, virtual]

Get the topological dimension (required by GenericMesh).
Implements GenericMesh< ambient >.

Member Data Documentation

template<size_t ambient, size_t topo>

const size_t Mesh< ambient, topo >::ambient_dimension = ambient [static]

template<size_t ambient, size_t topo>

const size_t Mesh< ambient, topo >::topological_dimension = topo [static]

The documentation for this struct was generated from the following file:

feature-refine/Mesh.h

Generated on Thu Mar 27 19:04:15 2008 by

1.4.6

Mesh< ambient, topo > Struct Template Reference

Public Types

Public Member Functions

Static Public Attributes