Algorithms for Planar Geometric Models

We consider planar geometric models given by an explicit boundary of 0 en) algebraic curve segments of maximum degree d. We present an 0 en"dO(l) time algorithm to compute its convex hull and an 0 (nlog logn +K) . dO(l) 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. ... Research supported in part by NSF grant MIP-85-21356, ARO contract DAAG29-85-eOOI8 under Cornell MSI and a David Ross Fellowship. Proc. of 15th ICALP, Tampere, Finland, LIeS Springer Verlag, to appear 1988 Algorithms for Planar Geometric Models' Chanderjit Bajaj and Myung-Soo Kim Department of Computer Science Purdue University West Lafayette, IN 47907. Abstract We consider planar geometric models given by an e>...plicit boundary of O(n) algebraic curve segments of maximum degree d. We present an O(n.dO(l») time algorithm to compute its convex hull and an O«n log logn +]() . dO(l)) 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 geomet.ric models.We consider planar geometric models given by an e>...plicit boundary of O(n) algebraic curve segments of maximum degree d. We present an O(n.dO(l») time algorithm to compute its convex hull and an O«n log logn +]() . dO(l)) 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 geomet.ric models.