## Abstract

We discuss the following problem which arises in robot motion planning, NC machining and computer animation: Given are a fixed surface Ψ and N positions Φ_{i} of a moving surface Φ such that the Φ _{i} are in point contact with Ψ. Compute a smooth and fair Euclidean gliding motion Φ(t) of the surface Φ on the surface Ψ which interpolates (or approximates) the given positions Φ_{i} at time instances t_{i}. First we generalize interpolatory variational subdivision algorithms for curves to curves on surfaces. Second we study an unconstraint motion design algorithm which we then extend to the main contribution of this paper, an algorithm for the design of a motion constraint by a contacting surface pair. Both motion design algorithms use a feature point representation of the moving surface, subdivision algorithms for curves, instantaneous kinematics, and ideas from line geometry. Geometric methods are used for the numerical solution of the arising optimization problems.

Original language | English (US) |
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Pages (from-to) | 523-547 |

Number of pages | 25 |

Journal | Computer Aided Geometric Design |

Volume | 20 |

Issue number | 8-9 |

DOIs | |

State | Published - Nov 2003 |

Externally published | Yes |

## Keywords

- Gliding motion
- Kinematics
- Line geometry
- Motion design
- Variational subdivision

## ASJC Scopus subject areas

- Modeling and Simulation
- Automotive Engineering
- Aerospace Engineering
- Computer Graphics and Computer-Aided Design