This paper shows how to construct a rational Bezier model of a swept surface that interpolates N frames (i.e., N position/orientation pairs) of a fixed rational space curve c(s) and maintains the shape of the curve at all intermediate points of the sweep. Thus, the surface models an exact sweep of the curve, consistent with the given data. The primary novelty of the method is that this exact mo...

Voronoi based interpolation employs the concept of natural neighbors to define an interpolating function over discrete data known at scattered sample points. In this work we review the two main concepts for improving interpolation continuity inside the convex hull of the sample domain and compare four natural neighbor interpolants of C and C continuity. We give a visual presentation of all inte...

LET K C R3 be a simple closed curve, and K be its convex hull. In [l], Almgren and Thurston define the (oriented) convex hull genus of K to be the minimal genus of an (oriented) surface contained in g and bounded by K. They give examples showing that even if K is unknotted both the orientable and non-orientable convex hull genus of K may be arbitrarily large. In 43 of this paper we show that th...

This short article explains my joint research with J. Scott Carter and Joachim Rieger, \A combinatorial description of knotted surfaces and their isotopies" 3]. For other topics in knotted surface theory that I am interested, see the book with J. Scott Carter \Knotted Surfaces and Their Diagrams" 4]. Please also check publication list in my home page for more details. This article is intended f...

This note continues the study initiated in 2006 by P.L. Papini, R. R. Phelps and the author on some classical notions from finite-dimensional convex geometry in spaces of continuous functions. Let H be the family of all closed, convex and bounded subsets of a Banach space endowed with the Hausdorff metric. A completion of A ∈ H is a diametrically maximal set D ∈ H satisfying A ⊂ D and diamA = d...

The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We express the degree of this surface in terms of the degree, genus and singularities of the curve. We present algorithms for computing their defining polynomia...

The solid hulls of the Hardy–Lorentz spaces Hp,q , 0 < p < 1, 0 < q 6∞ and Hp,∞ 0 , 0 < p < 1, as well as of the mixed norm space H p,∞,α 0 , 0 < p 6 1, 0 < α <∞, are determined. Introduction In [JP1] the solid hull of the Hardy space H, 0 < p < 1, is determined. In this article we determine the solid hulls of the Hardy–Lorentz spaces H, 0 < p < 1, 0 < q 6 ∞ and H 0 , 0 < p < 1, as well as of t...

Fixed a bounded open set Ω of R , we completely characterize the weak* lower semicontinuity of functionals of the form F (u,A) = ess sup x∈A f(x, u(x), Du(x)) defined for every u ∈ W 1,∞(Ω) and for every open subset A ⊂ Ω. Without a continuity assumption on f(·, u, ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it can be represented through a level conv...

Linear Hull is a phenomenon that there are a lot of linear paths with the same data mask but different key masks for a block cipher. In 1994, K. Nyberg presented the effect on the key-recovery attack such as Algorithm 2 with linear hull, in which the required number of the known plaintexts can be decreased compared with that in the attack using an individual linear path. In 2009, S. Murphy prov...

We consider the following problem: Given a point set in space find a largest subset that is in convex position and whose convex hull is empty. We show that the (decision version of the) problem is W[1]-hard.