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The following two questions from univariate (curve) subdivision are not related to each other, but are both of current interest. (1) Is it possible for a non- stationary subdivision scheme to have as its limit an algebraic curve of genus higher than zero? (2) Is it possible to exploit the structure of a (stationary) univariate subdivision matrix to express the unit row eigenvector in closed form?...
This paper is concerned with the re-representation of a G1 composite rational Bézier curve. Although the rational Bézier curve segments that form the composite curve are G1 continuous at their joint points, their homogeneous representations may not be even C0 continuous in the homogeneous space. In this paper, an algorithm is presented to convert the G1 composite rational Bézier curve into a NURBS...
We provide estimates for the maximum error of polynomial tensor product interpolation on regular grids in $${\mathbb{R}^d}$$ . The set of partial derivatives required to form these bounds depends on the clustering of interpolation nodes. Also bounds on the partial derivatives of the error are derived.
We present an adaptive quasi-interpolating quartic spline construction for regularly sampled surface data. The method is based on a uniform quasi-interpolating scheme, employing quartic triangular patches with C1-continuity and optimal approximation order within this class. Our contribution is the adaption of this scheme to surfaces of varying geometric complexity, where the tiling resolution can...
An intermediate step in the construction of a polyhedron from a partial-view sketch is the derivation of a realizable wireframe sketch, i.e., a complete sketch which is guaranteed to be the projection of a polyhedron. This paper presents a robust realizability-test based on the classical “cross-section criterion” that was developed in a geometric “ruler-and-compass” framework.
We develop a scheme for constructing G1 triangular spline surfaces of arbitrary topological type. To assure that the scheme is local and singularity-free, we analyze the selection of scalar weight functions and the construction of the boundary curve network in detail. With the further requirements of interpolating positions, normals, and surface curvatures, we show that the minimum degree of such...
This paper considers the inverse 1-center location problem with edge length augmentation on a tree network T with n + 1 vertices. The goal is to increase the edge lengths at minimum total cost subject to given modification bounds such that a predetermined vertex s becomes an absolute 1-center under the new edge lengths. Using a set of suitably extended AVL-search trees we develop a combinatorial algorithm...
A mortar finite element discretization of the second order elliptic problem in three dimensions, on non-matching grids, using the 3D Crouzeix-Raviart (CR) finite element in each subdomain, is proposed in this paper. The overall discretization is based on using only the nodal values on the mortar side of a subdomain interface for the calculation of the mortar projection, as opposed to applying the...
We present an extension module for the Dune system. This module, called dune-subgrid, allows to mark elements of another Dune hierarchical grid. The set of marked elements can then be accessed as a Dune grid in its own right. dune-subgrid is free software and is available for download (External Dune Modules: www.dune-project.org/downloadext.html ). We describe the functionality and use of dune-subgrid,...
In this article, we present two new algorithms for solving given triangular systems in parallel on a shared memory architecture. Multilevel incomplete LU factorization based preconditioners, which have been very successful for solving linear systems iteratively, require these triangular solves. Hence, the algorithms presented here can be seen as parallelizing the application of these preconditioners...
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