58 research outputs found
Threadable Curves
We define a plane curve to be threadable if it can rigidly pass through a
point-hole in a line L without otherwise touching L. Threadable curves are in a
sense generalizations of monotone curves. We have two main results. The first
is a linear-time algorithm for deciding whether a polygonal curve is
threadable---O(n) for a curve of n vertices---and if threadable, finding a
sequence of rigid motions to thread it through a hole. We also sketch an
argument that shows that the threadability of algebraic curves can be decided
in time polynomial in the degree of the curve. The second main result is an O(n
polylog n)-time algorithm for deciding whether a 3D polygonal curve can thread
through hole in a plane in R^3, and if so, providing a description of the rigid
motions that achieve the threading.Comment: 16 pages, 12 figures, 12 references. v2: Revised with brief addendum
after Mikkel Abrahamsen pointed us to a relevant reference on "sweepable
polygons." v3: Major revisio
Abstracts for the twentyfirst European workshop on Computational geometry, Technische Universiteit Eindhoven, The Netherlands, March 9-11, 2005
This volume contains abstracts of the papers presented at the 21st European Workshop on Computational Geometry, held at TU Eindhoven (the Netherlands) on March 9–11, 2005. There were 53 papers presented at the Workshop, covering a wide range of topics. This record number shows that the field of computational geometry is very much alive in Europe. We wish to thank all the authors who submitted papers and presented their work at the workshop. We believe that this has lead to a collection of very interesting abstracts that are both enjoyable and informative for the reader. Finally, we are grateful to TU Eindhoven for their support in organizing the workshop and to the Netherlands Organisation for Scientific Research (NWO) for sponsoring the workshop
Unstructured surface and volume decimation of tessellated domains
A general algorithm for decimating unstructured discretized data sets is presented. The discretized space may be a planar triangulation, a general 3D surface triangulation, or a 3D tetrahedrization. The decimation algorithm enforces Dirichlet boundary conditions, uses only existing vertices, and assumes manifold geometry. Local dynamic vertex removal is performed without history information while preserving the initial topology and boundary geometry. The tessellation at each step of the algorithm is preserved and, in the pathological case, every interior vertex is a candidate for removal. The research focuses on how to remove a vertex from an existing unstructured n-dimensional tessellation, not on the formulation of decimation criteria. Criteria for removing a candidate vertex may be based on geometric properties or any scalar governing function specific to the application. Use of scalar functions to adaptively control or optimize tessellation resolution is particularly applicable to the computer graphics, computational fluids, and structural analysis disciplines. Potential applications in the geologic exploration and medical or industrial imaging fields are promising
Collection of abstracts of the 24th European Workshop on Computational Geometry
International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by Erd˝os
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n ≥ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version
- …