We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the √ 3-subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generate...

Thin plate splines are a well known entity of geometric design. They are defined as the minimizer of a variational problem whose differential operators approximate a simple notion of bending energy. Therefore, thin plate splines approximate surfaces with minimal bending energy and they are widely considered as the standard “fair” surface model. Such surfaces are desired for many modeling and de...

Interpolatory and non-interpolatory multivariate Hermite type subdivision schemes are introduced in [8, 7]. In their applications in free-form surfaces, symmetry properties play a fundamental role: one can essentially argue that a subdivision scheme without a symmetry property simply cannot be used for the purpose of modelling free-form surfaces. The symmetry properties defined in the article [...

A ternary 4-point interpolating subdivision scheme is proposed that generates the limiting curve of C1 continuity. Performance of the proposed subdivision scheme is improved using a tension parameter. The improved subdivision scheme generates a family of C1 limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the derivative continuity of the s...

One of the difficult task in subdivision is to create new effective subdivision schemes. Therefore, aim of this paper is a systematic analysis of affine combination of known subdivision masks to generate new subdivision schemes with enhanced properties. This will be done in the stationary and the non stationary case for the univariate and bivariate settings. © 2009 IMACS. Published by Elsevier ...

We propose an adaptive geometry compression method based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. In the meantime, we provide high-s...

As a general approach to procedural mesh definition we propose two mechanisms for mesh modification: generalized subdivision and rule based mesh growing. In standard subdivision, a specific subdivision rule is applied to a mesh to get a succession of meshes converging to a limit surface. A generalized approach allows different subdivision rules at each level of the subdivision process. By limit...

Recursive algorithms are generally not straightforward to be processed in parallel, particularly when an octree is involved. Some researchers have tried to process an octree in parallel, but this solution is restricted to recursive subdivision methods that guarantee surface containment in an octant. In this paper we show a whole class of recursive subdivision algorithms which does not fall into...

This paper gives applications of earlier work of the authors on the use of expansion complexes for studying conformality of finite subdivision rules. The first application is that a one-tile rotationally invariant finite subdivision rule (with bounded valence and mesh approaching 0) has an invariant conformal structure, and hence is conformal. The paper next considers one-tile single valence fi...

Abstract. We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. Starting with a triangulated set of scattered data with associated function values, our scheme applies linear, stationary subdivision rules resulting in a hierarchy of triangulations that converge rapidly to a smooth limit surface. The novelty of our scheme is that it applies su...