ibgoedge.html

Delaunay三角形的网格剖分程序

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

<H1>Edge Computation</H1>

 <P>A remarkable property of a
 <A HREF="cogeometry.html">cogeometry</A> is that boundary edges -
for example, the edges 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 edges 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 edge does not intersect the planes of the octree, but
intersects some edges of the grid.  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 Problems:</H2>

 <A NAME="edge-problems"><hr></A>
 If the edges in the resulting grid are correct, ignore this warning.
 <A NAME="edge_computation_failure"><hr></A>

<H3>Edge Computation Failure</H3>

 <P>The edge computation has failed. That means, some edge points of
the geometry may have been not found. This usually leads to minor
errors near this edge.

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