Prof. Rida T. Farouki, Rational Rotation-Minimizing Frames on Space Curves: Theory, Algorithms, and Applications

Berliner Colloquium für wissenschaftliche Visualisierung

Montag, 27. August 2018, 17:15 Uhr
Zuse-Institut Berlin (ZIB)
Takustrasse 7, 14195 Berlin
Großer Hörsaal (Rundbau, Erdgeschoss)

Prof. Rida T. Farouki

University of California, Davis

An adapted orthonormal frame along a space curve incorporates the curve tangent at each point as one basis vector, and the frame is said to  be rotation-minimizing if its angular velocity maintains a zero component in the tangent direction, i.e., the two normalplane  vectors exhibit no instantaneous rotation about the tangent. Such frames are important in applications such as computer animation, swept surface constructions, path planning for robotics, and 5-axis CNC machining.

The theory of polynomial space curves with rational rotation-minimizing  adapted frames (which form a proper subset of the spatial Pythagorean-hodograph curves) is presented, together with algorithms for their construction and examples of their applications. Some generalizations to other types of rotation-  minimizing frames are also briefly discussed.