Interpolating triangular meshes by Loop subdivision scheme

Chongyang Deng

doi:10.1007/s11432-010-4049-y

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Interpolating triangular meshes by Loop subdivision scheme

2010-09-05

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Chongyang Deng *

Guozhao Wang

DOI：10.1007/s11432-010-4049-y

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Abstract

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Using the limit point formula of the Loop subdivision scheme, we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision scheme. The excellent properties of the method are: (1) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (2) Efficiency: the locations of new points can be computed with explicit formulae. (3) Easiness in implementation: only the geometric rule of the first step should be modified. (4) Freedom: for each edge, there is one degree of freedom to adjust the shape of the interpolation surface. (5) Easiness in generalization: it is easy to generalize our method to other approximation subdivision schemes with explicit formulae to compute limit point.

Keywords:

computer aided geometric design

subdivision surface

approximating subdivision scheme

Loop surface

surface interpolating

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