We investigate the properties of a special kind of frame, which we call the Euler–Rodrigues frame (ERF), defined on the spatial Pythagorean-hodograph (PH) curves. It is a frame that can be naturally constructed from the PH condition. It turns out that this ERF enjoys some nice properties. In particular, a close examination of its angular velocity against a rotation-minimizing frame yields a cha...

A straight-line drawing of a graph is an open weak rectangleof-influence (RI) drawing, if there is no vertex in the relative interior of the axis-parallel rectangle induced by the end points of each edge. No algorithm is known to test whether a graph has a planar open weak RI-drawing, not even for inner triangulated graphs. In this paper, we study RI-drawings that must have a non-aligned frame,...

We introduce nite relational structures called sketches, that represent edge crossings in drawings of nite graphs. We consider the problem of characterizing sketches in Monadic Second-Order logic. We answer positively the question for framed sketches, i.e., for those representing drawings of graphs consisting of a planar connected spanning subgraph (the frame) augmented with additional edges th...

A video sequence can be represented as a trajectory curve in a high dimensional feature space. This video curve can be analyzed by tools similar to those developed for planar curves. In particular, the classic binary curve splitting algorithm has been found to be a useful tool for video analysis. With a splitting condition that checks the dimensionality of the curve segment being split, the vid...

The paper deals with the identification of planar anisotropic diffusion properties carbon-epoxy composite materials for aircraft applications, based on exploitation short-time gravimetric tests. method consists in performing short time tests composites samples and measuring initial slope their mass uptake curve respect to t. is performed by minimizing sum squared residuals, residual being diffe...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...