Dimensions of spline spaces over T-meshes
نویسندگان
چکیده
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 basis functions is briefly discussed. Furthermore, the dimension formulae for T-meshes after mesh operations, such as edge insertion and mesh merging, are also obtained. © 2005 Elsevier B.V. All rights reserved.
منابع مشابه
Dimensions of biquadratic spline spaces over T-meshes
This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key strategy is linear space embedding with the operator of mixed partial derivative. The dimension of the original space equals the difference between the dimension o...
متن کاملDimensions of Spline Spaces over 3 D Hierarchical T - Meshes ? Xin
A 3D T-mesh is basically a partition of a cuboid such that every part is a smaller cuboid. In this paper we define the spline spaces over 3D T-meshes, which would play an important role in adaptive and dynamic implicit surface reconstruction from unorganized point clouds, and present a dimension formula about the spline space over a special kind of T-mesh, i.e., 3D hierarchical T-mesh. The form...
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 کاملConstruction of polynomial spline spaces over quadtree and octree T-meshes
We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allows to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions ...
متن کاملNew Proof of Dimension Formula of Spline Spaces over T-meshes via Smoothing Cofactors
A T-mesh is basically a rectangular grid that allows T-junctions. Recently, Deng etal introduced splines over T-meshes, which are generalizations of T-splines invented by Sederberg etal, and proposed a dimension formula based on the B-net method. In this paper, we derive an equivalent dimension formula in a different form with the smoothing cofactor method. Mathematics subject classification:
متن کامل