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» Arrangement Computation for Planar Algebraic Curves
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CAD
2008
Springer
15 years 6 months ago
Self-intersection detection and elimination in freeform curves and surfaces
We present several algorithms for self-intersection detection, and possible elimination, in freeform planar curves and surfaces. Both local and global self-intersections are elimi...
Diana Pekerman, Gershon Elber, Myung-Soo Kim
COMPGEOM
2001
ACM
15 years 10 months ago
PRECISE: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation
: Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitive...
Shankar Krishnan, Mark Foskey, Tim Culver, John Ke...
ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
16 years 24 days ago
Fast and exact geometric analysis of real algebraic plane curves
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert
GMP
2010
IEEE
190views Solid Modeling» more  GMP 2010»
15 years 11 months ago
A Subdivision Approach to Planar Semi-algebraic Sets
Abstract. Semi-algebraic sets occur naturally when dealing with implicit models and boolean operations between them. In this work we present an algorithm to efficiently and in a ce...
Angelos Mantzaflaris, Bernard Mourrain
MICS
2010
128views more  MICS 2010»
15 years 1 months ago
Arrangements on Parametric Surfaces II: Concretizations and Applications
We describe the algorithms and implementation details involved in the concretizations of a generic framework that enables exact construction, maintenance, and manipulation of arran...
Eric Berberich, Efi Fogel, Dan Halperin, Michael K...