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...

In the past decade, advances in electronics technology have made larger imaging sensors available to experimental fluid mechanics community. These advancements enabled measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible. However, due large size sensor, lens distortion needs be taken ...

Lower bounds, mandating a minimal number and degree of polynomial pieces, represent a major achievement in the theory of geometrically smooth (G) constructions. On one hand, they establish a floor when searching for optimal constructions, on the other they can be used to flag complex constructions for potential flaws. In particular, quadrilateral meshes of arbitrary topology can not in general ...

Based on the local refinement algorithm addressed in [18], we analyze the linear independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes.

Super-resolution techniques that process multiple images to achieve resolution enhancement for satellite images are very important. This work utilizes Vandewalle method to realize super-resolution for satellite images. Assuming the motions between images are all on the same plane, we estimate and stick images into the high resolution grid. Because of the huge size of satellite images, only part...