A Unified Interpolatory and Approximation sqrt-3 Subdivision Scheme

Abstract

We have found that there is a relationship between the cubic B-spline and four-point curve subdivision method. In the paper it is used to deduce interpolatory subdivision schemes from cubic B-spline based approximation subdivision schemes directly and construct unified schemes for compositing approximation and interpolatory subdivision. A new interpolatory p3 subdivision scheme and a interpolatory and approximation blended p3 subdivision scheme are created by this straightforward method. The former produces C1 limit surface and avoids the problem in the exsiting interpolatory p3 subdivision mask where the weight coefficients on extraordinary vertices can not be described by explicit formulation. The latter can be used to solve the "popping effect" problem when switching between meshes at different levels of resolution, provide the possibility to locally choose an interpolating variant of the conventionally approximating subdivision scheme, and give more flexibility for feature modeling. These are realized by only changing the value of a parameter. The method is thoroughly simple without needs of constructing and solving equations.