Despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continue to be the standard motions of modern CNC machines. However, the increasing industrial demand for parts with intricate shapes cannot be satisfied with only these standard motions. The proportion of parts which are not covered by the standard CNC motions is certain...

hile painless for the guest editor, these introductions might cause readers some pain. Still, I don’t want to waste this opportunity to tell you about interesting developments in computer-aided geometric design by giving you reason to hastily skim past these opening paragraphs. So, I abstracted a “top ten” list of what’s happening in CAGD based on ideas from recent conferences, technical papers...

In this paper, we present an effective algorithm for reassembling three-dimensional apictorial jigsaw puzzles obtained by dividing a curved surface into a finite number of interlocking pieces. As such, our algorithm does not make use of any picture or design that may be painted on the surface; nor does it require a priori knowledge of the overall shape of the original surface. A motivating exam...

Transonic airfoil design problems are solved using a Genetic Algorithm (GA) based optimizer. At the desired operating point, the minimum drag and constant lift targets are achieved through either a scalarized objective function, involving an arbitrary weighting factor, or the Pareto technique. For the optimization of an airfoil at two operating points, similar approaches are used. The CPU cost ...

Black-on-white images can be represented either as a bitmap or as a vector outline. A bitmap represents an image as a grid of black or white pixels. A vector outline describes an image via an algebraic description of its contours, typically in the form of Bezier curves. The advantage of representing an image as a vector outline is that it can be scaled to any size without loss of quality. Outli...

A gr'oup-theor'etic analysis is applied to find th e transf01'11wtion of the homogeneous control points of kdim ensional B ezier simplices {such as two dim ensional triangles and three dim ensional tetrah edra} under' a kdim ensional projec tive reparam eterization, This transf ormation has applications in the perspec tive projec ti on of textur'es represented as triangular spline intensity sur...

In order to reduce the dependence on fossil fuels, concept of distributed electric propulsion (DEP) has been introduced. At present, there are a few studies small engines DEP vertical take-off and landing (VTOL) UAVs. According design requirements VTOL UAV ducted fans, aerodynamic fan is carried out in this paper. Firstly, initial model established by referring theoretical derivations. Then, Be...

Recursive evaluation procedures based on spherical linear interpolation and stationary subdivision algorithms based on geodesic midpoint averaging are used to construct the analogues on spheres of arbitrary dimension of Lagrange and Hermite interpolation and Bezier and B-spline approximation.

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...