Search results for "computational geometry"
showing 10 items of 139 documents
Representation of NURBS surfaces by Controlled Iterated Functions System automata
2019
Iterated Function Systems (IFS) are a standard tool to generate fractal shapes. In a more general way, they can represent most of standard surfaces like Bézier or B-Spline surfaces known as self-similar surfaces. Controlled Iterated Function Systems (CIFS) are an extension of IFS based on automata. CIFS are basically multi-states IFS, they can handle all IFS shapes but can also manage multi self-similar shapes. For example CIFS can describe subdivision surfaces around extraordinary vertices whereas IFS cannot. Having a common CIFS formalism facilitates the development of generic methods to manage interactions (junctions, differences...) between objects of different natures.This work focuses…
Efficient Implementation of Multiresolution Triangle Strips
2002
Triangle meshes are currently the most popular standard modelto represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphic engine. It has been shown that using drawing primitives, such as triangle fans or strips, dramatically reduces the amount of information. Multiresolution Triangle Strips (MTS) uses the connectivity information to represent a mesh as a set of multiresolution triangles strips. These strips are the basis of both the storage and rendering stages. They allow the efficient management of a wide range of levels of detail. In this paper, we have taken advantage of the coherence property betwee…
Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach
2008
We consider the three-dimensional rendezvous between two spacecraft: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular trave…
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
Classification of cat ganglion retinal cells and implications for shape-function relationship
2002
This article presents a quantitative approach to ganglion cell classification by considering combinations of several geometrical features including fractal dimension, symmetry, diameter, eccentricity and convex hull. Special attention is given to moment and symmetry-based features. Several combinations of such features are fed to two clustering methods (Ward's hierarchical scheme and K-Means) and the respectively obtained classifications are compared. The results indicate the superiority of some features, also suggesting possible biological implications.
Shape-Based Features for Cat Ganglion Retinal Cells Classification
2002
This article presents a quantitative and objective approach to cat ganglion cell characterization and classification. The combination of several biologically relevant features such as diameter, eccentricity, fractal dimension, influence histogram, influence area, convex hull area, and convex hull diameter are derived from geometrical transforms and then processed by three different clustering methods (Ward’s hierarchical scheme, K-means and genetic algorithm), whose results are then combined by a voting strategy. These experiments indicate the superiority of some features and also suggest some possible biological implications.
Denoising 3D Models with Attributes using Soft Thresholding
2004
International audience; Recent advances in scanning and acquisition technologies allow the construction of complex models from real world scenes. However, the data of those models are generally corrupted by measurement errors. This paper describes an efficient single pass algorithm for denoising irregular meshes of scanned 3D model surfaces. In this algorithm, the frequency content of the model is assessed by a multiresolution analysis that requires only 1-ring neighbourhood without any particular parameterization of the model faces. Denoising is achieved by applying the soft thresholding method to the detail coefficients given by the multiresolution analysis. Our method is suitable for irr…
An Efficient Algorithm for the Generation of Z-Convex Polyominoes
2014
We present a characterization of Z-convex polyominoes in terms of pairs of suitable integer vectors. This lets us design an algorithm which generates all Z-convex polyominoes of size n in constant amortized time.
Generation of Valid Labeled Binary Trees
2003
International audience; Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.
Efficient computation of the branching structure of an algebraic curve
2012
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant points of the curve are constructed via a minimal spanning tree of the discriminant points. This leads to paths of minimal length between the points, which is important for a later stage where these paths are used as integration contours to compute periods of the surface. The branching structure of the surface is obtained by analytically continuing the roots of the equation defining the algebraic curve along the constructed generators of the fundamental gro…