کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
440621 | 691195 | 2013 | 15 صفحه PDF | دانلود رایگان |
This paper discusses the dimension of spline spaces S(m,n,m−1,n−1,T)S(m,n,m−1,n−1,T) over a certain type of hierarchical T-mesh. The key step is to establish a bijection between the spline space S(m,n,m−1,n−1,T)S(m,n,m−1,n−1,T) and a univariate spline space defined in terms of the l-edges of the extended T-mesh with respect to bi-degree (m,n)(m,n). We decompose the univariate spline space into an isomorphic direct sum using the theory of short exact sequences from homological algebra. Using this decomposition, we can obtain a formula for the dimension of the spline space S(m,n,m−1,n−1,T)S(m,n,m−1,n−1,T) over the required type of hierarchical T-mesh. We also construct a set of basis functions for the spline space.
► This paper shows the dimension of spline spaces with highest order smoothness over certain type of hierarchical T-mesh.
► The paper presents a method to compute the dimension of the spline space in an explicit way.
► A set of basis functions is constructed.
Journal: Computer Aided Geometric Design - Volume 30, Issue 1, January 2013, Pages 20–34