teoria malla hexahedral

1Primal and Dual Representations of

Hexahedral Meshes

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United

States Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL85000.

2Quadrilateral

Dual Representation

The elemental

representation of a

mesh, composed of

elements, edges, and

nodes, is known as the

primal.

Quadrilateral meshes

have a dual

representation, similar

to the voroni skeleton

of a triangular

delaunay mesh.

3A dual vertex, vi, is

defined at the

centroid of each

quadrilateral

element.

A dual vertex is also

placed at the

centroid of every

boundary edge.

Quadrilateral

Dual Representation

4Connecting the dual

vertices through

adjacent elements

creates the edges of

the dual.

Quadrilateral

Dual Representation

5Quadrilateral meshes

have an inherent row

structure. The red

quads illustrate one

row.

Each row

corresponds to one

dual chord.

Quadrilateral

Dual Representation

6Matt Staten

The set of all dual

edges which connect

quads in each row

forms a dual chord,

ci.

Quadrilateral

Dual Representation

7Matt Staten

Each dual edge is

part of exactly one

dual chord.

The vertex at the

centroid of a quad is

the intersection of 2

dual chords.

Quadrilateral

Dual Representation

8Dual chords must be either circular, or connect two boundaries.

Quadrilateral

Dual Representation

CircularConnects two

boundaries

9Dual chords can be self-intersecting or self-touching or both.

Quadrilateral

Dual Representation

Self-touchingSelf-intersecting

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The union of all dual

chords is the dual.

For quadrilateral

meshes, the dual is

set of all chords and

vertices.

D2D = (C, V)

Quadrilateral

Dual Representation

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Another way to

define a chord is

through edge

traversal.

Create a group of

edges by

propagating from a

single edge through

adjacent

quadrilaterals and

through their

topologically

opposite edges.

Connecting

midpoints of edges

forms the chord.

Quadrilateral

Dual Representation

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Dual Chord Extraction

Dual chords can be

extracted from a quad mesh

by collapsing each edge

defining it.

To maintain an all-quad

mesh, the entire chord must

be extracted.

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Dual chords can be



defining it.



be extracted.

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Dual chords can be



defining it.



be extracted.

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Dual Chord Modifications

The path of a dual chord can

be altered by performing

local operations on the quad

mesh:

Edge Swapping Face Collapsing Face Open Doublet Insertion

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Hexahedral

Dual Representation

The elemental

representation of a

hexahedral mesh,

composed of

hexahedra, faces,

edges, and nodes, is

known as the primal.

Hexahedral meshes

also have a dual

representation, similar

to the voroni skeleton

of a triangular

delaunay mesh.

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Hexahedral

Dual Representation

A dual vertex, vi, is

defined at the

centroid of each

hexahedral element,

boundary quad face,

and boundary edge.

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Hexahedral

Dual Representation

Connecting the dual

vertices through

adjacent elements

creates the edges and

faces of the dual.

teoria malla hexahedral

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