Tiling

Functions
template<typename T , typename V , typename IS , class LSF >
void	IndSimpSet::tile (const BBox< 2, T > &domain, T length, const LSF &f, IndSimpSet< 2, 2, true, T, V, IS > *mesh)
	Tile the object with equilateral triangles.
template<typename T , typename V , typename IS >
void	IndSimpSet::tile (const BBox< 2, T > &domain, const T length, IndSimpSet< 2, 2, true, T, V, IS > *mesh)
	Tile the rectangular region with equilateral triangles.
template<typename T , typename V , typename IS , class LSF >
void	IndSimpSet::tile (const BBox< 3, T > &domain, const T length, const LSF &f, IndSimpSet< 3, 3, true, T, V, IS > *mesh)
	Tile the object with a body-centered cubic lattice.
template<typename T , typename V , typename IS >
void	IndSimpSet::tile (const BBox< 3, T > &domain, const T length, IndSimpSet< 3, 3, true, T, V, IS > *mesh)
	Tile the rectilinear region with a body-centered cubic lattice.

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Detailed Description

These functions use the cookie-cutter algorithm to mesh an object. The object is described implicitly with a level set function.

Future work: Tile inside and around the object. Refine the mesh near the boundary. Then apply the cookie cutter algorithm. This will increase fidelity at the boundary while maintaining the desired edge length in the interior.

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Function Documentation

template<typename T , typename V , typename IS >

void tile	(	const BBox< 3, T > &	domain,
		const T	length,
		IndSimpSet< 3, 3, true, T, V, IS > *	mesh
	)			[related, inherited]

Tile the rectilinear region with a body-centered cubic lattice.

Parameters:

	domain	is the rectilinear domain to tile.
	length	is the maximum tetrahedron edge length.
	mesh	is the indexed simplex set.

The template parameters can be deduced from the arguments.

• T is the number type.
• V is the vertex type, an 3-tuple of the number type. It must be subscriptable.
• IS is the indexed simplex type, a tuple of 4 integers. It must be subscriptable.

Note:

This function simply calls the above tiling function with a trivial level set function.

References IndSimpSet< _N, _M, _A, T, V, IS >::tile().

template<typename T , typename V , typename IS , class LSF >

void tile	(	const BBox< 3, T > &	domain,
		const T	length,
		const LSF &	f,
		IndSimpSet< 3, 3, true, T, V, IS > *	mesh
	)			[related, inherited]

Tile the object with a body-centered cubic lattice.

Parameters:

	domain	is the rectilinear domain to tile.
	length	is the maximum tetrahedron edge length.
	f	is the level set description of the object.
	mesh	is the indexed simplex set.

A BCC block with 12 tetrahedra.

The template parameters can be deduced from the arguments.

• T is the number type.
• V is the vertex type, an 3-tuple of the number type. It must be subscriptable.
• IS is the indexed simplex type, a tuple of 4 integers. It must be subscriptable.
• LSF is the level set function that describes the object. Negative values are inside.

template<typename T , typename V , typename IS >

void tile	(	const BBox< 2, T > &	domain,
		const T	length,
		IndSimpSet< 2, 2, true, T, V, IS > *	mesh
	)			[related, inherited]

Tile the rectangular region with equilateral triangles.

Parameters:

	domain	is the rectangular domain to tile.
	length	is the triangle edge length.
	mesh	is the indexed simplex set.

The template parameters can be deduced from the arguments.

• T is the number type.
• V is the vertex type, an 2-tuple of the number type. It must be subscriptable.
• IS is the indexed simplex type, a tuple of 3 integers. It must be subscriptable.

Note:

This function simply calls the above tiling function with a trivial level set function.

References IndSimpSet< _N, _M, _A, T, V, IS >::tile().

template<typename T , typename V , typename IS , class LSF >

void tile	(	const BBox< 2, T > &	domain,
		T	length,
		const LSF &	f,
		IndSimpSet< 2, 2, true, T, V, IS > *	mesh
	)			[related, inherited]

Tile the object with equilateral triangles.

Parameters:

	domain	is the rectangular domain that contains the object.
	length	is the triangle edge length.
	f	is the level set description of the object.
	mesh	is the indexed simplex set.

The template parameters can be deduced from the arguments.

• T is the number type.
• V is the vertex type, an 2-tuple of the number type. It must be subscriptable.
• IS is the indexed simplex type, a tuple of 3 integers. It must be subscriptable.
• LSF is the level set function that describes the object. Negative values are inside.

Referenced by tile(), and IndSimpSet< _N, _M, _A, T, V, IS >::tile().