Showing papers by "John Keyser published in 1998"

Efficient and Reliable Computation with Algebraic Numbers for Geometric Algorithms

Abstract: Many geometric algorithms involve dealing with numeric data corresponding to high degree algebraic numbers. They come up in computing generalized Voronoi diagrams of lines and planes, medial axis of a polyhedron and geometric computation on non-linear primitives described using algebraic functions. Earlier algorithms dealing with algebraic numbers either use xed precision arithmetic or techniques from symbolic computation. While the former can be inaccurate, the latter is too slow in practice. We present e cient representations and algorithms for reliable computations with algebraic numbers. We use these representations to e ciently perform geometric queries like inside/outside tests, which-side or orientation tests. The overall approach combines di erent techniques from symbolic computation based on exact arithmetic with oating point arithmetic. We demonstrate its applications to e cient and reliable computation of curve and surface intersections. In practice, it is about one order of magnitude faster as compared to earlier implementations that produce reliable results. Supported in part by a Sloan fellowship, ARO Contract P-34982-MA, NSF grant CCR-9319957, NSF grant CCR-9625217 and ONR Young Investigator Award. Currently at AT & T Research Labs