1,416 research outputs found
QuickCSG: Fast Arbitrary Boolean Combinations of N Solids
QuickCSG computes the result for general N-polyhedron boolean expressions
without an intermediate tree of solids. We propose a vertex-centric view of the
problem, which simplifies the identification of final geometric contributions,
and facilitates its spatial decomposition. The problem is then cast in a single
KD-tree exploration, geared toward the result by early pruning of any region of
space not contributing to the final surface. We assume strong regularity
properties on the input meshes and that they are in general position. This
simplifying assumption, in combination with our vertex-centric approach,
improves the speed of the approach. Complemented with a task-stealing
parallelization, the algorithm achieves breakthrough performance, one to two
orders of magnitude speedups with respect to state-of-the-art CPU algorithms,
on boolean operations over two to dozens of polyhedra. The algorithm also
outperforms GPU implementations with approximate discretizations, while
producing an output without redundant facets. Despite the restrictive
assumptions on the input, we show the usefulness of QuickCSG for applications
with large CSG problems and strong temporal constraints, e.g. modeling for 3D
printers, reconstruction from visual hulls and collision detection
QuickCSG: Fast Arbitrary Boolean Combinations of N Solids
QuickCSG computes the result for general N-polyhedron boolean expressions
without an intermediate tree of solids. We propose a vertex-centric view of the
problem, which simplifies the identification of final geometric contributions,
and facilitates its spatial decomposition. The problem is then cast in a single
KD-tree exploration, geared toward the result by early pruning of any region of
space not contributing to the final surface. We assume strong regularity
properties on the input meshes and that they are in general position. This
simplifying assumption, in combination with our vertex-centric approach,
improves the speed of the approach. Complemented with a task-stealing
parallelization, the algorithm achieves breakthrough performance, one to two
orders of magnitude speedups with respect to state-of-the-art CPU algorithms,
on boolean operations over two to dozens of polyhedra. The algorithm also
outperforms GPU implementations with approximate discretizations, while
producing an output without redundant facets. Despite the restrictive
assumptions on the input, we show the usefulness of QuickCSG for applications
with large CSG problems and strong temporal constraints, e.g. modeling for 3D
printers, reconstruction from visual hulls and collision detection
A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings
We provide algorithmic methods to check the Cohen--Macaulayness,
Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are
constructed from the dilation of bounded convex polyhedrons of .
Some families of semigroup rings are given satifying these properties
A-Tint: A polymake extension for algorithmic tropical intersection theory
In this paper we study algorithmic aspects of tropical intersection theory.
We analyse how divisors and intersection products on tropical cycles can
actually be computed using polyhedral geometry. The main focus of this paper is
the study of moduli spaces, where the underlying combinatorics of the varieties
involved allow a much more efficient way of computing certain tropical cycles.
The algorithms discussed here have been implemented in an extension for
polymake, a software for polyhedral computations.Comment: 32 pages, 5 figures, 4 tables. Second version: Revised version, to be
published in European Journal of Combinatoric
Linear bilevel problems: Genericity results and an efficient method for computing local minima
The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for computing efficiently local minimizers. The method is based on the given structural analysis and combines ideas of the Simplex method with projected gradient steps
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