Re: Finding edges of a given polyhedra in 3D

Patricia Shanahan wrote:
[snip]
How can I find the edges of a polyhedra in 3D having only coordinates
of its vertices?
All the pairs of the vertices constitute corresponding line segments.
Some of them are diTetrahedronagonals and some of them are edges. I have to
distinguish them based only on the vertices data.
[snip]


A simple way of representing the polyhedron is as union of tetrahedra. You might take the middle of each pair of the vertices and check whether it is in the interior any tetrahedron (taking all four-tuples). This should give an (quite slow) algorithm to start with.
hth
Klaus


Are there any limitations on the polyhedron, such as that it must be convex?

If not, a tetrahedron with four of the points as vertices could enclose
space that is outside the polyhedron.

Similarly, for the 2D polygon, I don't think the original diagonal
crossing idea works for non-convex:

A------B
| |
| C--D
| |
| E--F
| |
G------H

The lines CF and DE intersect outside the area of the polygon, but
neither is an edge.

Patricia
The OP has only the corners of a 3d-polyhedron. I don't know how they specify a nonconvex figure

.

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