Find this document at http://new.math.uiuc.edu/im2001/bishop/index.html

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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