Star Delta Wiring Diagram With Timer Pdf Free
to Checkerboard and Voronoi meshes
Abstract:
The goal of this paper is to investigate a method of producing a mesh on a checkerboard
pattern on a smooth surface and the production of a Voronoi mesh on a relatively more
complex surface by combining the star delta method and the technique of merging
triangles to avoid self-overlapping triangles. The merging technique is to merge two
triangles which are
overlapped when they
are considered
with the orientation
which is
further away
from the
third vertex.
In this paper, we present some examples to
illustrate the proposed method and
produce the corresponding meshes.
Keywords:
1. Introduction
This paper aims to present a new mesh production method which is capable of producing
both a checkerboard mesh and a Voronoi mesh on relatively more complex surfaces by
combining the star delta method and the merging technique. In the literature, there are
already some works about the application of this method to different surface
configurations [1,2,3]. As mentioned in those papers, the star delta method is
based on a loop triangulation and can be implemented in an iterative way.
Let R be a surface and Q(R) be a mapping from the surface to a
unit square. For any point x of the surface R, Q(x) is defined as the
point (x, 1/2). The surface R can be represented in the form:
(1)
where A is an n x n matrix with n =
square
root(
number
of
vertices
+ 1),
C is a n x 1 vector with
Ci
= sqrt(
C
j
2), j = 1, 2,..., n,
E is an n x n
upper
triangle matrix whose
i-th column is
diag
(
E
)j = 1, 2,..., n, and
is a 1 x n
vector with each entry
= 1.
If there is no self-overlapping when a surface is represented by
(1),
then the surface is said to be checkerboard. If
R can be written as
(2):
(2)
, then the surface is called a Voronoi mesh
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