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» Algebra and Geometry of Rewriting
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COMPGEOM
2004
ACM
15 years 3 months ago
Complete, exact, and efficient computations with cubic curves
The Bentley-Ottmann sweep-line method can be used to compute the arrangement of planar curves provided a number of geometric primitives operating on the curves are available. We d...
Arno Eigenwillig, Lutz Kettner, Elmar Schömer...
RTA
2010
Springer
14 years 10 months ago
Polynomial Interpretations over the Reals do not Subsume Polynomial Interpretations over the Integers
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and...
Friedrich Neurauter, Aart Middeldorp
COMPGEOM
2001
ACM
15 years 3 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...
ACS
2007
14 years 12 months ago
Directed Algebraic Topology, Categories and Higher Categories
Directed Algebraic Topology is a recent field, deeply linked with Category Theory. A ‘directed space’ has directed homotopies (generally non reversible), directed homology gro...
Marco Grandis
COMPGEOM
1994
ACM
15 years 3 months ago
Almost Tight Upper Bounds for the Single Cell and Zone Problems in Three Dimensions
We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of n low-degree algebraic surface patches in 3-space. We show that this complex...
Dan Halperin, Micha Sharir