We discuss the problem of adding features to a free form surface by applying one or several user deened surface curves. The curves are seen as editable parameters, while the surface is to be changed automatically, keeping a prede-ned set of constraints satissed, speciically the curve{surface incidence and derivatives. We review and update our approach presented earlier 18] and show, how the cur...

This paper presents an algorithm of modifying free-formed NURBS curve/surface for offsetting without local self-intersecting. The method consists of (1) sampling a number of points from a progenitor curve/surface based on second derivatives; (2) checking the curvature or maximum curvature of the progenitor curve/surface at the sampled points; (3) inserting corresponding knots of sampled points;...

Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint. Qualitative changes in that curve occur when the viewpoint crosses the visual event surface. We examine the components of this ruled surface, and observe that these co...

The action curve in Chara seems to depend (as in Nitella) on the outward movement of K(+) from the sap. Presumably the increase in permeability in the inner protoplasmic surface and the outward movement of K(+) destroy the concentration gradient of K(+) across the inner protoplasmic surface. Hence the outwardly directed P.D. disappears, causing the rise (spike) of the action curve. The outer pr...

Let S be a surface embedded in space in such a way that each point has a neighborhood within which the surface is a terrain. Then S projects to an immersed surface in the plane, the boundary of which is a (possibly self-intersecting) curve. Under what circumstances can we reverse these mappings algorithmically? Shor and van Wyk considered one such problem, determining whether a curve is the bou...

Contributions Parametric representation We come out a new smooth and convergent interpolation method called HOPI which exploits the derivative information based on Taylor Theorem. Our solution separates the derivative information (eg, normal) from neighborhood providing more freedom for user control and capability to represent very complicate curve/surface. The derivative information could be e...

The braid monodromy factorization of the branch curve of a surface of general type is known to be an invariant that completely determines the diffeomorphism type of the surface (see [2]). Calculating this factorization is of high technical complexity; computing the braid monodromy factorization of branch curves of surfaces uncovers new facts and invariants of the surfaces. Since finding the bra...

Given a point and a rational curve in the plane, their bisector curve is rational 2]. However, in general, the bisector of two rational curves in the plane is not rational 3]. Given a point and a rational space curve, this paper shows that the bisector surface is a rational ruled surface. Moreover, given two rational space curves, we show that the bisector surface is rational (except for the de...

We study the extension generated by the x-coordinates of the petorsion points of an elliptic curve over a function field of characteristic p. If S → C is a non-isotrivial elliptic surface in characteristic p with a pe-torsion section, then for pe > 11 our results imply restrictions on the genus, the gonality, and the p-rank of the base curve C, whereas for pe ≤ 11 such a surface can be construc...

The blade is one of the most critical parts of an aviation engine, and a small change in the blade geometry may significantly affect the dynamics performance of the aviation engine. Rapid advancements in 3D scanning techniques have enabled the inspection of the blade shape using a dense and accurate point cloud. This paper proposes a new method to achieving two common tasks in blade inspection:...