LatToPyr

DESCRIPTION

This module creates a pyramid from a 1D, 2D, or 3D lattice. Line segments are used as the building blocks for the 1D lattice. For the 2D lattice triangles or rectangles may be used; for the 3D lattice there is a choice of tetrahedra or cubes.

If triangles (tetrahedra) are selected, then each rectangle (cube) maps into two triangles (five tetrahedra). Note that there are two ways of decomposing a rectangle into triangles (cube into tetrahedra) and adjacent rectangles (cubes) will use different decompositions so that the edges will match up properly.

The pyramid formed will have one layer (for edges) if the lattice is 1D, two layers (for edges and faces) if the lattice is 2D, and three layers (for edges, faces, and cells) if the lattice is 3D.

If the lattice has a data component the pyramid's base lattice will include these data. In addition, the following will also be present:

1D lattice - the first layer includes a lattice with data at the centre of the edges, and the data values averaged over the vertices of each edge.

2D lattice - the second layer will have lattice data positioned at the centre of the polygons, and the data values averaged over the vertices of each polygon.

3D lattice - the third layer will have lattice data placed at the centre of the polyhedra, and the data values averaged over the vertices of each polyhedron.

This module is frequently used in conjunction with PyrToGeom or IsosurfacePyr.

INPUTS

Port: Input
Type: Lattice
Constraints: 1..3-D
This is the input lattice.

WIDGETS

Port: Output Type
Type: Radio Box
Menu Item: Tetrahedral (Triangular)
Menu Item: Cubical (Rectangular)

If the input lattice is 2D or 3D, this parameter allows selection between triangles and rectangles (2D), or between tetrahedra and cubes (3D).

OUTPUTS

Port: Output
Type: Pyramid
Constraints: 1..3-layer
Constraints: 1..-baseLat
Constraints: 1..3-D compression
Constraints: unique-compression type
This is the output pyramid.

KNOWN PROBLEMS

This module can create a tremendous amount of data from a seemingly simple lattice.

If the input lattice has curvilinear coordinates, then the user must take care when using triangles or tetrahedra as the pyramid's building blocks. The algorithm used to subdivide a rectangle into triangles (cube into tetrahedra), does not take into account if a diagonal actually lies totally inside the area that is subdivided. Rather, it alternates the type of decomposition for adjacent rectangles (cubes).

If triangles (tetrahedra) are selected, then each rectangle (cube) maps into two triangles (five tetrahedra). Note that there are two ways of decomposing a rectangle into triangles (cube into tetrahedra) and adjacent rectangles (cubes) will use different decompositions so that the edges will match up properly.

SEE ALSO

IsosurfacePyr, PyrToLat, PyrToGeom.
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© The Numerical Algorithms Group Ltd, Oxford UK. 2000