Dimensions of Spline Spaces over 3 D Hierarchical T - Meshes ? Xin
نویسندگان
چکیده
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 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 briefly discussed.
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