4,140 research outputs found
Representations of polygons of finite groups
We construct discrete and faithful representations into the isometry group of
a hyperbolic space of the fundamental groups of acute negatively curved
even-sided polygons of finite groups.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper43.abs.htm
Ramification conjecture and Hirzebruch's property of line arrangements
The ramification of a polyhedral space is defined as the metric completion of
the universal cover of its regular locus.
We consider mainly polyhedral spaces of two origins: quotients of Euclidean
space by a discrete group of isometries and polyhedral metrics on the complex
projective plane with singularities at a collection of complex lines.
In the former case we conjecture that quotient spaces always have a CAT[0]
ramification and prove this in several cases. In the latter case we prove that
the ramification is CAT[0] if the metric is non-negatively curved. We deduce
that complex line arrangements in the complex projective plane studied by
Hirzebruch have aspherical complement.Comment: 19 pages 1 figur
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
Algebraic cubature on polygonal elements with a circular edge
We compute low-cardinality algebraic cubature formulas on convex or concave polygonal elements with a circular edge, by subdivision into circular quadrangles, blending formulas via subperiodic trigonometric Gaussian quadrature and final compression via Caratheodory\u2013Tchakaloff subsampling of discrete measures. We also discuss applications to the VEM (Virtual Element Method) in computational mechanics problems
Doctor of Philosophy
dissertationMany algorithms have been developed for synthesizing shaded images of three dimensional objects modeled by computer. In spite of widely differing approaches the current state of the art algorithms are surprisingly similar with respect to the richness of the scenes they can process. One attribute these algorithms have in common is the use of a conventional passive data base to represent the objects being modeled. This paper postulates and explores the use of an alternative modeling technique which uses procedures to represent the objects being modeled. The properties and structure of such "procedure models" are investigated and an algorithm based on them is presented
Design and loading of dragline buckets
Draglines are an expensive and essential part of open cut coal mining. Small improvements in performance can produce substantial savings. The design of the bucket and the way in which it fills with overburden are very important to the overall dragline performance. Here we use a numerical model to simulate this filling process and to differentiate between the flow patterns of two different buckets. Extensions to the model are explored
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
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