# 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.