7,576 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
Experiments with a Convex Polyhedral Analysis Tool for Logic Programs
Convex polyhedral abstractions of logic programs have been found very useful
in deriving numeric relationships between program arguments in order to prove
program properties and in other areas such as termination and complexity
analysis. We present a tool for constructing polyhedral analyses of
(constraint) logic programs. The aim of the tool is to make available, with a
convenient interface, state-of-the-art techniques for polyhedral analysis such
as delayed widening, narrowing, "widening up-to", and enhanced automatic
selection of widening points. The tool is accessible on the web, permits user
programs to be uploaded and analysed, and is integrated with related program
transformations such as size abstractions and query-answer transformation. We
then report some experiments using the tool, showing how it can be conveniently
used to analyse transition systems arising from models of embedded systems, and
an emulator for a PIC microcontroller which is used for example in wearable
computing systems. We discuss issues including scalability, tradeoffs of
precision and computation time, and other program transformations that can
enhance the results of analysis.Comment: Paper presented at the 17th Workshop on Logic-based Methods in
Programming Environments (WLPE2007
Software for Exact Integration of Polynomials over Polyhedra
We are interested in the fast computation of the exact value of integrals of
polynomial functions over convex polyhedra. We present speed ups and extensions
of the algorithms presented in previous work. We present the new software
implementation and provide benchmark computations. The computation of integrals
of polynomials over polyhedral regions has many applications; here we
demonstrate our algorithmic tools solving a challenge from combinatorial voting
theory.Comment: Major updat
The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems
Since its inception as a student project in 2001, initially just for the
handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library
has been continuously improved and extended by joining scrupulous research on
the theoretical foundations of (possibly non-convex) numerical abstractions to
a total adherence to the best available practices in software development. Even
though it is still not fully mature and functionally complete, the Parma
Polyhedra Library already offers a combination of functionality, reliability,
usability and performance that is not matched by similar, freely available
libraries. In this paper, we present the main features of the current version
of the library, emphasizing those that distinguish it from other similar
libraries and those that are important for applications in the field of
analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table
- …