64 research outputs found
Regular triangulations of dynamic sets of points
The Delaunay triangulations of a set of points are a class of
triangulations which play an important role in a variety of
different disciplines of science. Regular triangulations are a
generalization of Delaunay triangulations that maintain both their
relationship with convex hulls and with Voronoi diagrams. In regular
triangulations, a real value, its weight, is assigned to each point.
In this paper a simple data structure is presented that allows
regular triangulations of sets of points to be dynamically updated,
that is, new points can be incrementally inserted in the set and old
points can be deleted from it. The algorithms we propose for
insertion and deletion are based on a geometrical interpretation of
the history data structure in one more dimension and use lifted
flips as the unique topological operation. This results in rather
simple and efficient algorithms. The algorithms have been
implemented and experimental results are given.Postprint (published version
Aproximació facetada de superfÃcies paramètriques retallades
Postprint (published version
Two triangulations methods based on edge refinement
In this paper two curvature adaptive methods of surface triangulation
are presented. Both methods are based on edge refinement to obtain a
triangulation compatible with the curvature requirements. The first
method applies an incremental and constrained Delaunay triangulation
and uses curvature bounds to determine if an edge of the triangulation
is admissible. The second method uses this function also in the edge
refinement process, i.e. in the computation of the location of a
refining point, and in the re-triangulation needed after the insertion
of this refining point. Results are presented, comparing both
approachesPostprint (published version
Skeletal representations of orthogonal shapes
In this paper we present two skeletal representations applied to orthogonal shapes of R^n : the cube axis and a family of skeletal representations provided by the scale cube axis. Orthogonal shapes are a subset of polytopes, where the hyperplanes of the bounding facets are restricted to be axis aligned. Both skeletal representations rely on the L∞ metric and are proven to be homotopically equivalent to its shape. The resulting skeleton is composed of n − 1 dimensional facets. We also provide an efficient and robust algorithm to compute the scale cube axis in the plane and compare the resulting skeleton with other skeletal representations.Postprint (published version
Funciones en el modelado de solidos y paradigmas de diseño
En este artÃculo se describen y analizan las diferentes
funciones de modelado de sólidos más comunes que ofrecen
los actuales sistemas de CAD. Se explican también las
limitaciones e inconsistencias a qué pueden dar lugar el
uso de dichas funciones. Por otro lado, también se analizan
y comparan los diferentes paradigmas de diseño con los que
trabajan los actuales sistemas. Se describe, evalúa y
compara el paradigma clásico basado en operaciones
booleanas, con los paradigmas basados en el diseño
paramétrico y el diseño basado en caracterÃsticas. También
se describe cual es la interrelación a través de la
interfaz de usuario entre los paradigmas de diseño y las
funciones de modelado.Postprint (published version
A practical and robust method to compute the boundary of three-dimensional axis-aligned boxes
The union of axis-aligned boxes results in a constrained structure that is advantageous for solving certain geometrical problems. A widely used scheme for solid modelling systems is the boundary representation (Brep). We present a method to obtain the B-rep of a union of axis-aligned boxes. Our method computes all boundary vertices, and additional information for each vertex that allows us to apply already existing methods to extract the B-rep. It is based on dividing the three-dimensional problem into two-dimensional boundary computations and combining their results. The method can deal with all geometrical degeneracies that may arise. Experimental results prove that our approach outperforms existing general methods, both in efficiency and robustness.)Peer ReviewedPostprint (author’s final draft
From Degenerate Patches to Triangular and Trimmed Patches
Postprint (published version
Splat representation of parametric surfaces
Point-based geometry representations and their splat-based
generalizations have become a suitable technique both for modeling and
rendering complex 3D shapes. So, it seems interesting to convert other
kind of models to a point or splat-based representations.
In this work, we present an approach to convert a parametric surface
to an elliptical splat-based representation. Although this conversion
supposes a loss of information going from an
analytical to an approximate model, it will allow to locally modify
zones with complex features, to mix surface and splat-based models and
to take advantage of the existing point-based rendering methods.
The presented approach works in the parametric space and performs an
adaptive sampling based on the surface curvature and a given error
tolerance. The goal is to obtain an optimized set of elliptical splats
that completely covers the surface. Two strategies are presented, one
based on a quadrangular subdivision of the parametric space and the
other on power Voronoi diagrams. Finally, some open problems are
enumerated.Postprint (published version
Skeleton computation of an image using a geometric approach
In this work we develop two algorithms to compute the skeleton of a binary 2D images. Both algorithms follow a geometric approach and work directly with the boundary of the image wich is an orthogonal polygon (OP). One of these algorithms processes the edges of the polygon while the other uses its vertices. Compared to a thinning method, the presented algorithms show a good performance.Postprint (published version
Computing directional constrained Delaunay triangulations
This work presents two generalizations of the algorithm for
obtaining a constrained Delaunay triangulation of a general planar
graph presented in [Vig97] and [Vig95]. While the first
generalization works with elliptical distances, the second one can
deal with a set of deforming ellipses associated to each point of
the plane. The pseudo-code of the procedures involved in the
algorithms is included, the suitability of the algorithms is
analyzed, and several examples are presented.Postprint (published version
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