Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
441133 | Computer Aided Geometric Design | 2016 | 9 Pages |
Abstract
•There is a unique rational motion of minimal quaternion degree with given trajectory.•It can be computed by simple polynomial algebra over the ring of dual quaternions.•The minimal motion of Vivian's curve is a spherical circle rolling.
We give a constructive proof for the existence of a unique rational motion of minimal degree in the dual quaternion model of Euclidean displacements with a given rational parametric curve as trajectory. The minimal motion degree equals the trajectory's degree minus its circularity. Hence, it is lower than the degree of a trivial curvilinear translation for circular curves.
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Related Topics
Physical Sciences and Engineering
Computer Science
Computer Graphics and Computer-Aided Design
Authors
Z. Li, J. Schicho, H.-P. Schröcker,