This paper presents two automatic fairing algorithms for parametric C-continuous bi-cubic B-spline surfaces. The fairing method consists of a knot removal and knot reinsertion step which locally smooths the surface. Search strategies like best-first-search and simulated-annealing are searching for the global minimum of the fairing measure. The best-first-search algorithm constructs only partial...

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...

We use an inverse scattering approach to study multi-peakon solutions of the Degasperis–Procesi (DP) equation, an integrable PDE similar to the Camassa–Holm shallow water equation. The spectral problem associated to the DP equation is equivalent under a change of variables to what we call the cubic string problem, which is a third order non-selfadjoint generalization of the well-known equation ...

highly crystalline bi3+-doped cadmium oxide (cdo) sub-micron structures were synthesized by calcination the obtained precursor from a sol-gel reaction. the reaction was carried out with cadmium nitrate (cd(no3)2.4h2o), bismuth nitrate (bi(no3)3.5h2o) and ethylene glycol (c2h6o2) reactants without any additives at 80°c for 2h. resulting gel was calcined at 900 °c with increasing temperature rate...

In this paper we disprove the belief widespread within the computer graphics community that Catmull-Clark subdivision surfaces cannot be evaluated directly without explicitly subdividing. We show that the surface and all its derivatives can be evaluated in terms of a set of eigenbasis functions which depend only on the subdivision scheme and we derive analytical expressions for these basis func...

Polyhedral meshes consisting of triangles, quads, and pentagons and polar configurations cover all major sampling and modeling scenarios. We give an algorithm for efficient local, parallel conversion of such meshes to an everywhere smooth surface consisting of low-degree polynomial pieces. Quadrilateral facets with 4-valent vertices are ‘regular’ and are mapped to bi-cubic patches so that adjac...

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 ...

This paper presents a novel image interpolation method, extended linear interpolation, which is a low-cost and high-speed architecture with interpolation quality compatible to that of bi-cubic convolution interpolation. The method of reducing computational complexity of generating weighting coefficients is proposed. Based on the approach, the efficient hardware architecture is designed under re...

introduction 3d reconstruction of an object from its 2d cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. in order to perform 3d reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. mate...