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» Arrangement Computation for Planar Algebraic Curves
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CAD
2008
Springer
13 years 7 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
13 years 11 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»
14 years 1 months 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»
14 years 10 days 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»
13 years 2 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...