We propose a simple generalization of Shephard’s interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A...

We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, well-known in Harmonic Analysis, that the Laplacian operator commutes with orthogonal transformatio...

The parameters for a representative two-body Morse potential are determined for the solidified inert gases by fitting to O'K solid data. This is done using first the harmonic approximation and subsequently the first-order self-consistent harmonic approximation, which provides an upper limit to the anharmonic correction, to describe the solid at O'K. On comparing the two cases, the effect on the...

where E(x, y) > 0. The parametric curves x = const. and y = const. form an isothermal net on 1. It is well known that h(x, y) = c, where h is a harmonic function of (x, y), that is, h satisfies the Laplace equation, hA, + h,, = 0, defines an isothermal family of curves on Z. The constant c is called the isothermal parameter. The converse of the preceding statement is not valid. That is, if g(x,...

A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a “safe” domain. In the simple cases of a constant force, harmonic potential, and Kepler or Coulomb motion, the trajectories are conic curves whose envelope in a plane is another conic secti...

nowadays with increasing use of numerous nonlinear loads, voltage and current harmonics in power systems are one of the most important problems power engineers encounter. many of these nonlinear loads, because of their dynamic natures, inject time-varying harmonics into power system. common techniques applied for harmonics measurement and assessment such as fft have significant errors in presen...