6533b861fe1ef96bd12c4d78
RESEARCH PRODUCT
An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
Elmar SchömerNicola WolpertEric BerberichLutz KettnerMichael Hemmersubject
Discrete mathematicsCombinatoricssymbols.namesakeGeometric designQuadricDegenerate energy levelsAlgebraic surfaceFamily of curvessymbolsGravitational singularityAlgebraic curveMathematicsPlanar graphdescription
We present the first exact, complete and efficient implementation that computes for a given set P=p1,...,pn of quadric surfaces the planar map induced by all intersection curves p1∩ pi, 2 ≤ i ≤ n, running on the surface of p1. The vertices in this graph are the singular and x-extreme points of the curves as well as all intersection points of pairs of curves. Two vertices are connected by an edge if the underlying points are connected by a branch of one of the curves. Our work is based on and extends ideas developed in [20] and [9].Our implementation is complete in the sense that it can handle all kind of inputs including all degenerate ones where intersection curves have singularities or pairs of curves intersect with high multiplicity. It is exact in that it always computes the mathematical correct result. It is efficient measured in running times.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-06-06 | Proceedings of the twenty-first annual symposium on Computational geometry |