We present a new interpolatory subdivision scheme for triangle meshes. Instead of splitting each edge and performing a 1-to-4 split for every triangle we compute a new vertex for every triangle and retriangulate the old and the new vertices. Using this refinement operator the number of triangles only triples in each step. New vertices are computed with a Butterfly like scheme. In order to obtai...

Subdivision started as a tool for eecient computation of spline functions, and is now an independent subject with many applications. It is used for developing new methods for curve and surface design, for approximation, for generating wavelets and mul-tiresolution analysis and also for solving some classes of functional equations. This paper reviews recent new directions and new developments in...

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...

Popular subdivision algorithms like Catmull-Clark and Loop are C almost everywhere, but suffer from shape artifacts and reduced smoothness exactly near the so-called “extraordinary vertices” that motivate their use. Subdivision theory explains that inherently, for standard stationary subdivision algorithms, curvature-continuity and the ability to model all quadratic shapes requires a degree of ...

3 Subdivision Algorithm 3 3.1 Centroid of Polyhedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Intersection of Ray with Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 Memory Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.4 Pseudocode for a Single Subdivision . . . . . ...

In [2, 3, 20, 21] the authors explored a construction to produce multiresolutions from given subdivisions. Certain assumptions carried through that work, two of which we wish to challenge: (1) that multiresolutions for irregular meshes have to be constructed on the fly rather than being prepared beforehand and (2) that the connectivity graph of the coarse mesh would have to be a subgraph of the...