Extended Abstract Summary: A convex quadrangulation with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is convex and has four points from S on its boundary. A minimum weight convex quadrangulation with respect to S is a convex quadrangula...

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...

Let G be an abelian group with n elements. Let S be a sequence of elements of G, where the repetition of elements is allowed. Let |S| be the cardinality, or the length of S. A sequence S ⊆ G with |S| ≥ 2 is barycentric or has a barycentric-sum if it contains one element aj such that ∑ ai∈S ai = |S|aj . This paper is a survey on the following three barycentric constants: the k-barycentric Olson ...

In 1988 the second author presented experimentally well-conditioned linear rational functions for global interpolation. We give here arrays of nodes for which one of these interpolants converges exponentially for analytic functions Introduction Let f be a complex function defined on an interval I of the real axis and let x0, x1, . . . , xn be n + 1 distinct points of I, which we do not assume e...

We propose an adaptive geometry compression method with labels 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. Labels are recorded in...

Surface constructions of polynomial degree (3,3) come in four flavours that complement each other: one pair extends the subdivision paradigm, the other the NURBS patch approach to free-form modeling. The first pair, Catmull-Clark (Catmull and Clark, 1978) and Polar subdivision (Karčiauskas and Peters, 2007) generalize bi-cubic subdivision: While Catmull-Clark subdivision is more suitable where ...

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...