Search results for "Computer Science::Computational Geometry"
showing 10 items of 70 documents
Counter-complementarity control of the weak exchange interaction in a bent {Ni(ii)3 complex with a μ-phenoxide-μ-carboxylate double bridge
2019
We have prepared and structurally characterized a novel {Ni3} bent complex bearing a double μ-phenoxide-μ-carboxylate bridge. Both terminal Ni(ii) sites are symmetry related, offering a simplified exchange interaction scheme. DC magnetic data is consistent with a weak antiferromagnetic interaction between the central and terminal Ni(ii) ions. As expected for a Ni(ii) system, local zero-field splitting is observed, which can be experimentally established. Broken symmetry quantum chemical calculations, as well as ab initio CASSCF-SA-SOC computations that support the magnetic experimental data, were also performed. From the analysis of other reported closely related Ni(ii) systems, a counter-c…
An efficient upper bound of the rotation distance of binary trees
2000
A polynomial time algorithm is developed for computing an upper bound for the rotation distance of binary trees and equivalently for the diagonal-flip distance of convex polygons triangulations. Ordinal tools are used.
Bézier surfaces of minimal area: The Dirichlet approach
2004
The Plateau-Bezier problem consists in finding the Bezier surface with minimal area from among all Bezier surfaces with prescribed border. An approximation to the solution of the Plateau-Bezier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bezier surfaces obtained by the use of masks related with minimal surfaces are studied.
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
2020
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Efficiently using connectivity information between triangles in a mesh for real-time rendering
2004
Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Triangle Strips (MTS) represent a triangle mesh as a collection of multiresolution triangles strips. These strips are the basis of both the storage and the rendering stage. The coherence between the extraction of two levels of detail is used in the model in order to decrease the visualisation time.
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…
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.