phyllis@utcsrgv.UUCP (Phyllis Eve Bregman) (04/06/84)
**** UofT Department of Computer Science Seminar Schedule for the week of April 9th, 1984 Tuesday, April 10th, 2:00 P.M., SF1105: Professor J. Nievergelt, ETH, Zurich, Switzerland: "Algorithms and data structures for geometric computation". ABSTRACT: The growing importance of computer applications that involve geometric objects (e.g. CAD, graphics, geographic data processing) creates a need for libraries of geometric software, much as earlier computer applications led to numerical subroutine libraries. What geometric software is sufficiently general to be included in a general purpose program library for geometric computation? We present two candidates: a class of algorithms and a data structure. Sweep algorithms solve many geometric problems in 2 or more dimensions in time O((n+s) log n), where n measures the amount of data (e.g. the number of line segments), and s its intricacy (e.g. the number of unknown intersections). Realistic configurations are often characterized by s = O(n), thus many practical geometric problems can be solved at the asymptotic cost of sorting. Data structures suitable for storing geometric objects should treat all space dimensions in a symmetric way and support range and intersection queries. The grid file has been designed to meet these requirements with the goal of minimizing disk accesses. A transformation of geometric objects to points in higher-dimensional spaces reduces intersection queries to sweeping simple regions called search cones. -- Phyllis Eve Bregman CSRG, Univ. of Toronto {decvax,linus,ihnp4,uw-beaver,allegra,utzoo}!utcsrgv!phyllis CSNET: phyllis@toronto (416) 978 6985