# Algorithms for planar geometric models

Conference paper

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## Abstract

We consider planar geometric models given by an explicit boundary of *O*(*n*) algebraic curve segments of maximum degree *d*. We present an *O*(*n · d*^{O(1)}) time algorithm to compute its convex hull and an *O*((*n* loglog*n*+*K*) · *d*^{O(1)}) time algorithms to compute various decompositions of an object, where *K* is the characteristic number of this object. Both operations, besides being solutions to interesting computational geometry problems, prove useful in motion planning with planar geometric models.

## Keywords

Convex Hull Geometric Model Algebraic Curf Curve Segment Simple Polygon## Preview

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1988