The Structure of C1 Spline Spaces on Freudenthal Partitions
Pages 347 - 367
Abstract
We analyze the structure of trivariate C1 splines on uniform tetrahedral partitions $\Delta$. The Freudenthal partitions $\Delta$ are obtained from uniform cube partitions by using three planes with a common line to subdivide every cube into six tetrahedra. This is a natural three-dimensional generalization of the well-known three-directional mesh in the plane. By using Bernstein--Bézier techniques, we construct minimal determining sets for C1 spline spaces on $\Delta$ of arbitrary degree and give explicit formulae for the dimension of the spaces.
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Published: 01 January 2006
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