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...

This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offe...

We establish several fundamental properties of analysis-suitable Tsplines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended T-mesh of an analysis-suitable T-spline, is contained in the corresponding analysis-suitable T-spline space. This is accomplished through the theory of pertu...

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...

in the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. nurbs and t-splines are two different computational geometry technologies which are studied in this work. among features of b-spline basis functions the possibility of enhancing a b-spline basis with discontinuities b...

Data fitting is a fundamental tool in scientific research and engineering applications. Generally, there are two ingredients in solving data fitting problems. One is the fitting representation, and the other is the fitting method. Nowadays, the fitting of larger and larger quantities of data sets requires more compact fitting representation and faster fitting methods. The T-spline is a recently...

T-splines is a recently developed surface modelling technique which is a generalization of B-splines and allows true local refinement. Another well established method supporting local refinement is hierarchical B-splines. This paper presents algorithms for transformation between T-splines and hierarchical (rational) B-splines. With the transformation, a surface expressed in terms of T-splines c...