In this paper we propose a strategy for generating consistent hierarchical T–meshes which allow local refinement and offer a way to obtain spline basis functions with highest order smoothness incrementally. We describe the required ordering of line–segments during refinement and the construction of spline basis functions. We give our strategy for generating consistent hierarchical T–meshes over...

We present a method for producing quad-dominant subdivided meshes, which supports both adaptive refinement and adaptive coarsening. A hierarchical structure is stored implicitly in a standard half-edge data structure, while allowing us to efficiently navigate through the different level of subdivision. Subdivided meshes contain a majority of quad elements and a moderate amount of triangles and ...

An algorithm for adaptive refinement of 3D-meshes is outlined. This algorithm is very convenient for the generation of mesh hierarchies used for efficient volume visualization algorithms, e.g. iso-surface extraction or direct volume rendering, and for multilevel finite element computations. The aim was to construct an algorithm which generates as little congruence classes as possible. The main ...

In this paper, we construct a bijective mapping between biquadratic spline space over the hierarchical T-mesh and piecewise constant corresponding crossing-vertex-relationship graph (CVR graph). We propose novel structure, by which offer an effective easy operative method for constructing basis functions of space. The is isomorphism. hold properties such as linear independence, completeness pro...

We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a threedimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a certain assumption about the configurati...

In this paper we introduce a new algorithm for simplification of polygonal meshes. It generates a variable resolution structure called hierarchical 4-K mesh. This structure is a powerful representation for non-uniform level of detail that, among other things, allows simple and efficient extraction of conforming meshes.

Wavelet-based methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all waveletbased methods is a hierarchy of meshes that satisfies subdivisionconnectivity: this hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree unifor...

The theory and application of numerical methods for unstructured meshes have been improved significantly in recent years. Because the grids can be place arbitrarily in space, unstructured meshes can provide much higher spatial resolution than regular meshes. The built-in nature of mesh adaptivity for unstructured meshes gives one way to simulate highly dynamic, hierarchical problems involving b...

In this work a new multi-resolution model is proposed for polygonal meshes. It is based on the dual edge collapse, which performs face clustering instead of vertex clustering. The new hierarchical mesh representation combines a truly selective refinement scheme with a strict control of the two-sided Hausdorff distance. The proposed approach allows to build hierarchical meshes directly over non ...