louis@aerospace.aero.org (Louis M. McDonald) (10/24/89)
Given two overlapping bezier patches (16 control pts each) that are fitted
to the same surface, but are arbitrarily oriented relative to each other within
that surface, how does one find the mapping function that transforms a
point from the (s,t) parameter space of one of them to the (s',t') parameter
space of the other?
+-----------------------------------------------------------+
\ +---------------------------------------+ /
\ | | /
\ | | /
\ | | /
\ | | /
\ | | /
\| | /
\ | /
|\ | /
| \ | /
| \ |/
| \ /
| \ /|
| \ / |
| \ / |
| \ / |
+--------\-------------------------/----+
\ /
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For example: both are in a plane, and one is square, but the other could be
a segment of circle. It seems that there might be an analytic function that
converts between the parameter spaces.
I realize that there may be no exact mapping in cases where the surface is
too general for one or the other patches to fit it accurately, but then an
approximate map would have to do. Any pointers?
P.S.:
We plan to use this parameter map to maintain tolerance between the surfaces
during distortions. Might we be barking up the wrong tree?
--
Louis McDonald
The Aerospace Corporation
louis@aerospace.aero.org