Abstract

This paper deals with discrete computational geometry of motions and develops geometric construction algorithms for interpolating in-between rigid displacements. It combines concepts from the fields of kinematics and computational geometry and develops a computational framework for constructing motion interpolants useful in mechanical systems animation, robot trajectory planning and key framing in computer graphics.

A de Casteljau type algorithm is presented for constructing Bézier and rational Bézier motion interpolants. In addition, the problem of achieving higher order of continuity in piecing together motion interpolants is studied. A geometric construction algorithm is presented for designing C2 continuous motion interpolants.

Volume Subject Area:
22nd Biennial Mechanisms Conference: Mechanism Design and Synthesis
Keywords:
computer aided animation, quaternions, computational kinematics, computational geometry
Topics:
Computational geometry, Construction, Kinematics, Algorithms, Computer-aided engineering, Computers, Design, Framing (Construction), Robots, Structural frames, Trajectories (Physics)
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