From extension of Loop's approximation scheme to interpolatory subdivisions

The minimum-supported bivariate C2-cubic spline on a 6-directional mesh constructed in our previous work [2] can be used to extend Loop's approximation subdivision scheme to introduce some parameter for controlling surface geometric shapes. This extension is achieved by considering matrix-valued subdivisions, resulting in subdivision templates of the same 1-ring template size as Loop's scheme, but with 2-dimensional matrix-valued weights. Another feature accomplished by considering such an extension is that the two components of the refinable vector-valued spline function can be reformulated, by taking certain linear combinations, to convert the approximation scheme to an interpolatory scheme, but at the expense of an increase in template size for the edge vertices. To maintain the 1-ring template size with guarantee of C2 smoothness for interpolatory surface subdivisions, a non-spline solution is needed, by applying some constructive scheme such as the procedure discussed i...

• Type: Journal
• Year: 2008
• Where: CAGD
• Authors: Charles K. Chui, Qingtang Jiang
• Keywords: Approximation Scheme, Approximation Subdivision Scheme, CAGD 2008, Interpolatory Scheme