This paper proposes a new method of Visual Secret Sharing using Zigzag Scan approach. Non-expanded shares are generated by this scheme. This overcomes the drawback of Hilbert Curve approach, that is, the input should be a square image of size which is an integral power of 2.

A topological approach of determining the best one out of four solutions of the Hermitian interpolation problem for quintic Pythagorean hodograph curves is presented. An existence theorem is proved together with complete analysis of uniqueness/nonuniqueness properties. A simple formula of obtaining the best solution without using any curve fairing or curvature integral is also presented.

We derive asymptotic formuli for two dimensional steady state voltage potentials associated with thin, “curve-like” conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formuli (rigorously) derived in [3] for imperfections of small diameter, these new formuli cover the generic imperfe...

Feature-based visualization of flow fields has proven as an effective tool for flow analysis. While most flow visualization techniques operate on vector field data, our visualization techniques make use of a different simulation output: Particle Tracers. Our approach solely relies on integral lines that can be easily obtained from most simulation software. The task is the visualization of dense...

The problem of the form of the 'arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the em...

(4) v′ r(s) = c(xr(s), yr(s), vr(s)). Note that here the subscript r denotes a parameter, not a derivative! We may equally well write xr(s) = x(r, s), yr(s) = y(r, s), and we will do so; we adopted the subscript notation to emphasize that along each integral curve r is fixed, i.e. is a constant. Which parameterization should we use? We are normally also given initial conditions along a curve Γ ...

Pythagorean hodograph curves (PH curves) have a number of advantages over other splines commonly used in planar robot path planning: (i) the integral of curvature is small; (ii) the curve, its length, curvature and total “bending energy” are known in closed-form; (iii) start and end positions and directions are straightforwardly usable as boundary conditions; and (iv) length can be traded off a...

In this paper, for one-parameter closed dual spherical motions, we define the dual versions of the area vector of a given closed space curve, and the area projection of this curve in the direction of a given unit vector. The relationship between the above dual versions and the dual Steiner vector of the motion is used to give a generalization for Holditch’s theorem of planar kinematics into spa...

Pythagorean hodograph curves (PH curves) have a number of advantages over other splines commonly used in planar robot path planning: (i) the integral of curvature is small; (ii) the curve, its length, curvature and total \bending energy" are known in closed-form; (iii) start and end positions and directions are straightforwardly usable as boundary conditions; and (iv) length can be traded oo ag...

Clothoids, i.e. curves Z(s) in RI whoem curvatures xes) are linear fitting functions of arclength ., have been nued for some time for curve fitting purposes in engineering applications. The first part of the paper deals with some basic interpolation problems for lothoids and studies the existence and uniqueness of their solutions. The second part discusses curve fitting problems for clothoidal ...