Last edited 17jun01 by rshuttle@math.uiuc.edu
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document at http://new.math.uiuc.edu/im2001/mccreary
Proseminar Recap of Bishop Frames by
Paul McCreary on 14jun01
There are also files worth looking at in the following grafix directory:
/usr/people/paulmcc
The ability to "ride" along a three-dimensional space curve and illistrate the
properties of the curve, such as curvature and torsion, would be a great assett to
mathematicians. The classic Serret-Frenet frame (SF) provides such ability, however
the SF does is not defined for all points along every curve. A new frame is needed
for the kind of mathematical analysis that is typically done with computer graphics.
The Relatively Parallel Adapted Frame or Bishop Frame (BF) could provide the desired
means to ride along any given space curve. The BF has many properties that make it
ideal for mathematical research.
Annother area of intrested about the BF is so-called Normal Developement, or the
graph of the twisting motion of BF. This information along with the intial position
and orientation of the BF provide all of the information nescesary to define the
curve. Through the developement of an RTICA that can create curves based on their
Normal Developement it may be possible to learn new things both about space curves
and the BF itself.
The BF may have applications in the area of Biology and Computer Graphics. For
example it may be possible to compute information about the shape of sequences of
DNA using a curve defined by the BF. The BF may also provide a new way to control
virtual cameras in computer animations.
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