Dimensions of Spline Spaces over 3D Hierarchical T-Meshes ?

A 3D T-mesh is basically a partition of a cuboid such that every part is a smaller cuboid. In this paper we deflne 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 formula holds when the smoothness is less than half of the degree of the spline functions, and it involves only the topological quantities of the T-meshes. The construction of basis functions of the spline space is brie∞y discussed.