60 research outputs found
Quasi-Splines and their moduli
We study what we call quasi-spline sheaves over locally Noetherian schemes.
This is done with the intention of considering splines from the point of view
of moduli theory. In other words, we study the way in which certain objects
that arise in the theory of splines can be made to depend on parameters. In
addition to quasi-spline sheaves, we treat ideal difference-conditions, and
individual quasi- splines. Under certain hypotheses each of these types of
objects admits a fine moduli scheme. The moduli of quasi-spline sheaves is
proper, and there is a natural compactification of the moduli of ideal
difference-conditions. We include some speculation on the uses of these moduli
in the theory of splines and topology, and an appendix with a treatment of the
Billera-Rose homogenization in scheme theoretic language
Stable splitting of bivariate spline spaces by Bernstein-Bézier methods
We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer's method for solving fully nonlinear elliptic PDEs on polygonal domains
Almost- splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems
Isogeometric Analysis generalizes classical finite element analysis and
intends to integrate it with the field of Computer-Aided Design. A central
problem in achieving this objective is the reconstruction of analysis-suitable
models from Computer-Aided Design models, which is in general a non-trivial and
time-consuming task. In this article, we present a novel spline construction,
that enables model reconstruction as well as simulation of high-order PDEs on
the reconstructed models. The proposed almost- are biquadratic splines on
fully unstructured quadrilateral meshes (without restrictions on placements or
number of extraordinary vertices). They are smooth almost everywhere,
that is, at all vertices and across most edges, and in addition almost (i.e.
approximately) smooth across all other edges. Thus, the splines form
-nonconforming analysis-suitable discretization spaces. This is the
lowest-degree unstructured spline construction that can be used to solve
fourth-order problems. The associated spline basis is non-singular and has
several B-spline-like properties (e.g., partition of unity, non-negativity,
local support), the almost- splines are described in an explicit
B\'ezier-extraction-based framework that can be easily implemented. Numerical
tests suggest that the basis is well-conditioned and exhibits optimal
approximation behavior
Parametric Interpolation To Scattered Data [QA281. A995 2008 f rb].
Dua skema interpolasi berparameter yang mengandungi interpolasi global untuk data tersebar am dan interpolasi pengekalan-kepositifan setempat data tersebar positif dibincangkan.
Two schemes of parametric interpolation consisting of a global scheme to interpolate general scattered data and a local positivity-preserving scheme to interpolate positive scattered data are described
Filling holes under non-linear constraints
Publisher Copyright:
© 2023, The Author(s).In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C1-smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.publishersversionpublishe
Filling holes under non-linear constraints
In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C1-smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.Funding for open access publishing: Universidad de Granada/CBUANational funds through the FCT - Fundação
para a Ciência e a TecnologiaProjects UIDB/00297/2020 and UIDP/00297/2020
(Center for Mathematics and Applications
Five-axis tool path generation using piecewise rational bezier motions of a flat-end cutter
Master'sMASTER OF ENGINEERIN
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