In this paper,we construct a bijective mapping between a biquadratic spline space over the hierarchical T-mesh and the piecewise constant space over the corresponding crossing-vertex-relationship graph(CVR graph).We p...In this paper,we construct a bijective mapping between a biquadratic spline space over the hierarchical T-mesh and the piecewise constant space over the corresponding crossing-vertex-relationship graph(CVR graph).We propose a novel structure,by which we offer an effective and easy operative method for constructing the basis functions of the biquadratic spline space.Themapping we construct is an isomorphism.The basis functions of the biquadratic spline space hold the properties such as linear independence,completeness and the property of partition of unity,which are the same as the properties for the basis functions of piecewise constant space over the CVR graph.To demonstrate that the new basis functions are efficient,we apply the basis functions to fit some open surfaces.展开更多
基金supported by the NSF of China(No.11771420,No.12001197).
文摘In this paper,we construct a bijective mapping between a biquadratic spline space over the hierarchical T-mesh and the piecewise constant space over the corresponding crossing-vertex-relationship graph(CVR graph).We propose a novel structure,by which we offer an effective and easy operative method for constructing the basis functions of the biquadratic spline space.Themapping we construct is an isomorphism.The basis functions of the biquadratic spline space hold the properties such as linear independence,completeness and the property of partition of unity,which are the same as the properties for the basis functions of piecewise constant space over the CVR graph.To demonstrate that the new basis functions are efficient,we apply the basis functions to fit some open surfaces.
