Exact rotation minimizing frame via Moebius transformations

Michael Barton
Sunday, 23.12.2007, 13:00
Room 337-8 Taub Bld.

Rotation minimizing frames are useful for various applications in geometric modeling and computer graphics. For instance, the sweeping of one (cross-section) curve along the another one (spine curve) is well-known technique of surface construction in 3D shape modeling. In many applications, namely in the construction of canal surfaces, the minimal twist of the cross- section curve along the spine curve is required. For a general spine curve, the computation of the exact rotation minimizing frame is either very difficult or impossible.

We show that Moebius transformations preserve rotation minimizing frames. With the help of Pythagorean-hodograph curves we formulate an interpolation scheme which is able to produce rational space curves from given Hermite data, such that all segments have exact rational rotation minimizing frames

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