Abstract
This paper offers a general formula for surface subdivision rules for quad meshes by using 2-D Lagrange interpolating polynomial [1]. We also see that the result obtained is equivalent to the tensor product of (2N + 4)-point n-ary interpolating curve scheme for N ≥ 0 and n ≥ 2. The simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented by L. Kobbelt [2], which can be directly calculated from the proposed formula. Furthermore, some characteristics and applications of the proposed work are also discussed.
Highlights
There are two general classes of subdivision schemes, namely, approximating and interpolating schemes
The limit curve of an approximating scheme usually does not pass through the control points of control polygon
All vertices in the control polygon are located on the limit curve of the interpolation scheme, which facilitates and simplifies the graphics algorithms and engineering designs
Summary
There are two general classes of subdivision schemes, namely, approximating and interpolating schemes. Ko [6] presented explicitly a new formula for the mask of (2N + 4)-point binary interpolating and approximating subdivision schemes with two parameters. Using all the above mentioned identities Ko [6] presented the general formula for the mask of (2N + 4) -point binary interpolating symmetric subdivision schemes.
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