Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342-avoiding permutations of length n as well as an exact formula for their number Sn(1342). While achieving this, we bijectively prove that the number of indecomposable 1342avoiding permutations of length n equals that of labeled plane trees of a certain t...

This work has been contributed on the visualization of curves and surfaces for constrained data. A rational cubic function, with free shape parameters in its description, has been introduced and used. This function has been constrained to visualize the preservation of shape of the data by imposing constraints on free parameters. The rational cubic curve case has also been extended to a rational...

Compact surface descriptions like higher-order surfaces are popular representations for both modeling and animation. However, for fast graphics-hardware-assisted rendering, they usually need to be converted to triangle meshes. In this paper, we introduce a new framework for performing on-the-fly crack-free adaptive tessellation of surface primitives completely on the GPU. Utilizing CUDA and its...

Recently, it was shown that a bi-cubic patch complex with n-sided holes can be completed into a curvature-continuous (G) surface by n-sided caps of degree bi-5 that offer good and flexible shape [KP13]. This paper further explores the space of n-sided caps of degree bi-5 but focusing on functionals to set degrees of freedom and to optimally propagate and average out curvature from the bi-cubic ...

We explore a class of polynomial tensor-product spline surfaces on 3-6 polyhedra, whose vertices have valence n = 3 or n = 6. This restriction makes it possible to exclusively use rational linear transition maps between the pieces: transitions between the bi-cubic tensor-product spline pieces are either C1 or they are G1 (tangent continuous) based on one single rational linear reparameterizatio...

Many papers describe techniques for evaluating spline curves and surfaces. While each paper provides some theoretical or empirical evidence with which to compare techniques, there exist few global comparisons Peters94]. Also, papers describing particular algorithms often provide few details, making implementation of the technique presented diicult or impossible. This report attempts to illumina...

For many design applications, where multiple primary surface pieces meet, the distribution of curvature is more important than formally achieving exact curvature continuity. For parametric spline surfaces, when constructing a multi-sided surface cap, we demonstrate a strong link between the uniform variation of the re-parameterization between (boundary) data of the joining pieces and a desirabl...

This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In particular, when one bicubic tensor-product B-spline patch is associated with each facet of a quadrilateral mesh with n-valent vertices and we do not want seg...