Semi-regular 4–8 meshes are refinable triangulated quadrangulations. They provide a powerful hierarchical structure for multiresolution applications. In this paper, we show how to decompose the DooSabin and Catmull-Clark subdivision schemes using 4–8 refinement. The proposed technique makes it possible to use these classical subdivision surfaces with semi-regular 4–8 meshes. Additional

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For t...

This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementation of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction. The approach was tested by implementing hierarchical B-splines, truncated hierarchical B-splines, decoupled hierarchical B-splin...

A facile method is developed for the large-scale growth of hierarchical transition-metal (Cu, Fe, and Ni) vanadate nanosheets on corresponding metal mesh as supports. The hierarchical transition-metal vanadate nanosheets were in situ grown on the metal meshes through an orientational etching process and simultaneous nucleation and growth process. Interestingly, the morphologies of the vanadate ...

Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces generated by box splines. A family of box splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box spline, the optimal positioning of the wire-frame nodes is determined for each level...

In this paper, we propose a new scheme for sending three-dimensional (3-D) mesh models. In order to make a viewdependent representation of 3-D mesh models, we combine sequential and progressive mesh transmission techniques. After we partition a 3-D mesh model into a hierarchical tree, we determine the amount of information for each submesh. Then, we can send the 3-D model information by view-de...

Precise quality control for hierarchical lighting simulations is still a hard problem, due in part to the difficulty of analysing the source of error and to the close interactions between different components of the algorithm. In this paper we attempt to address this issue by examining two of the most central components of these algorithms: visibility computation and the mesh. We first present ...

We present a new method for computing the medial axis of a given closed smooth curve or surface. It is based on an algorithm for approximating the signed distance function using polynomial splines over hierarchical T-meshes, which has recently been presented in [36]. Since the signed distance function is not differentiable along the medial axis, the hierarchical T-meshes is automatically refine...