ibgovertex.html

Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: Vertex computation</TITLE>

<H1>Vertex Computation</H1>

 <P>A remarkable property of a
 <A HREF="cogeometry.html">cogeometry</A> is that boundary vertices -
for example, the corners of a cube - are not part of the geometry
description.  They have to be computed, usually based on a nontrivial
iteration. This allows to create grids in a situation where the
information about these vertices is not available.

 <P>On the other hand, this procedure may fail. Especially it tends to
fail because of rounding errors in degenerated cases.  A "degenerated
case" means the corner is not inside a cell of the octree, but on the
boundary. Unfortunately, such "degenerated cases" are very common,
because people tend to use integer numbers as input data as for the
geometry, as for the coarse grid.

<H2>Known Errors:</H2>

<A NAME="vertex-problems"><hr></A>
 <P> If the corners in the resulting grid are correct, ignore this warning.
<A NAME="vertex_computation_failure"><hr></A>

<H3>Vertex Computation Failure</H3>

 <P>The vertex computation has failed. That means, corner points of
the geometry may have been not found. This results in a minor error
near this corner: the corner point itself is not part of the resulting
grid.

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