Dimension of spline spaces with highest order smoothness over hierarchical T-meshes
نویسندگان
چکیده
منابع مشابه
Dimension of spline spaces with highest order smoothness over hierarchical T-meshes
This paper discusses the dimension of spline spaces S(m,n,m−1, n−1,T ) over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space S(m,n,m− 1, n− 1,T ) and a univariate spline space whose definition depends on the l-edges of the extended T-mesh. We decompose the univariate spline space into direct sums in the sense of isomorphism using the theory...
متن کاملIterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness
In this paper we propose a strategy for generating consistent hierarchical T–meshes which allow local refinement and offer a way to obtain spline basis functions with highest order smoothness incrementally. We describe the required ordering of line–segments during refinement and the construction of spline basis functions. We give our strategy for generating consistent hierarchical T–meshes over...
متن کاملBases of Biquadratic Polynomial Spline Spaces over Hierarchical T-meshes
Basis functions of biquadratic polynomial spline spaces over hierarchical T-meshes are constructed. The basis functions are all tensor-product B-splines, which are linearly independent, nonnegative and complete. To make basis functions more efficient for geometric modeling, we also give out a new basis with the property of unit partition. Two preliminary applications are given to demonstrate th...
متن کاملDimensions of spline spaces over T-meshes
A T-mesh is basically a rectangular grid that allows T-junctions. In this paper, we propose a method based on Bézier nets to calculate the dimension of a spline function space over a T-mesh. When the order of the smoothness is less than half of the degree of the spline functions, a dimension formula is derived which involves only the topological quantities of the T-mesh. The construction of bas...
متن کاملOn the dimension of spline spaces on planar T-meshes
We analyze the space Sr m,m (T ) of bivariate functions that are piecewise polynomial of bi-degree 6 (m,m) and of smoothness r along the interior edges of a planar T-mesh T . We give new combinatorial lower and upper bounds for the dimension of this space by exploiting homological techniques. We relate this dimension to the weight of the maximal interior segments of the T-mesh, defined for an o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 2013
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2012.09.002