دانلود رایگان مقاله قوانین طرح های فرعی درونیابی مبتنی بر چهارگانه

Abstract

This article deals with interpolatory subdivision schemes generalizing the tensor-product version of the Dubuc–Deslauriers 4-point scheme to quadrilateral meshes of arbitrary manifold topology. In particular, we focus our attention on an extension of the C1 regular stencils that respectively exploits (N+2)-point and (2N+8)-point stencils for the computation of an edge-point and a face-point in the vicinity of an extraordinary vertex of valence N≠4 not lying on a boundary. The aim of our work consists in identifying which constraints are required to be respected by the weights appearing in the above stencils in order to get closed limit surfaces that are C1-continuous at extraordinary points, have both principal curvatures bounded and at least one of them nonzero. The obtained constraints are used to easily check these features in the limit surfaces resulting from the application of special extraordinary rules proposed in the literature by different authors. Moreover, the conditions derived on the stencil weights are exploited to design new extraordinary rules that can produce closed limit surfaces of the same quality as the existing proposals, but at a reduced computational cost.

7. Conclusions

In this work we studied which constraints are required to be respected by the weights of the extraordinary stencils shown in Fig. 2 to obtain a limit surface that is C1-continuous and with bounded curvature at the extraordinary points. The necessary conditions defined by analyzing the eigenvalues of the subdivision matrix are summarized in Table 3 for all extraordinary points of valence N = 4. Moreover, a standard procedure that checks sufficient conditions for the regularity of the characteristic map has been presented in Subsection 5.3. These conditions allow one to define a large variety of C1-interpolatory schemes with bounded curvature. After proving that the schemes proposed in literature by Li–Ma–Bao and Deng–Ma satisfy all the above constraints, we have derived a new subdivision scheme characterized by a smaller and simplified face-point stencil, which behaves closely to Deng–Ma’s and Li–Ma–Bao’s schemes.