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# Rough quadrilateralation from a triangular mesh via layer-based decomposition

IP.com Disclosure Number: IPCOM000014271D
Original Publication Date: 2000-May-01
Included in the Prior Art Database: 2003-Jun-19
Document File: 4 page(s) / 88K

IBM

## Abstract

Disclosed is a system for generating rough quadrilateral meshes from finer triangular meshes. The quadrilateral meshes can be used for generating parametric curved surfaces that represent the geometry of the input triangular meshes (see Figure 1). This system first divides the region of a triangular elements into belt-like subregions (see Figure 2(a)(b)), and then divides each subregion into quadrilateral elements (see Figure 2(c)(d)). Figure 1. An example of the input triangular mesh, the output quadrilateral mesh, and the parametric curved surface. 1

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Page 1 of 4

Rough quadrilateralation from a triangular mesh via layer-based decomposition

Disclosed is a system for generating rough quadrilateral meshes from finer
triangular meshes.

The quadrilateral meshes can be used for generating parametric curved surfaces
that represent
the geometry of the input triangular meshes (see Figure 1). This system first
divides the region
of a triangular elements into belt-like subregions (see Figure 2(a)(b)), and then
divides each
subregion into quadrilateral elements (see Figure 2(c)(d)).

Figure 1. An example of the input triangular
mesh, the output quadrilateral mesh, and the
parametric curved surface.

1

Page 2 of 4

Figure 2. An example of processes in this
system.

Figure 3 denotes the flow of the processes in
this system.

Figure 3. The flowchart of this system.

Following is the explanation of each process:

(1) Offset distance calculation for each
triangular elements.

This process first extracts the boundary of the
given triangular mesh, and mark as A,B,C,...,
to the outer and inner boundaries. It then
extracts the triangular elements that are
to the boundaries, and mark as A-1, B-1, C-1,
..., to the elements. It then extracts the
triangular elements that are adjacent to the
A-1, B-1, C-1, ..., triangles, and mark as A-2,
B-2, C-2, ..., to the elements. Similarly it
marks triangular elements as A-(n+1), that are