Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to PDEs. A...

This paper presents a method to determine the shape of a space object while simultaneously recovering the observed space object’s inertial orientation. This paper employs an Adaptive Hamiltonian Markov Chain Monte Carlo estimation approach, which uses light curve data to infer the space object’s orientation, shape, and surface parameters. This method is shown to work well for relatively high di...

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

This paper presents a new multiscale curvature-based shape representation technique with application to curve data compression using B-spline wavelets. The evolution of the curve is implemented in the B-spline scale-space, which enjoys a number of advantages over the classical Gaussian scale-space, for instance, the availability of fast algorithms. The B-spline wavelet transforms are used to ef...

This paper presents a new multiscale curvaturebased shape representation technique with application to curve data compression using B-spline wavelets. The evolution of the curve is implemented in the B-spline scale-space, which enjoys a number of advantages over the classical Gaussian scale-space, for instance, the availability of fast algorithms. The B-spline wavelet transforms are used to eff...

The size of the Gaussian kernel defines the "width" of the curve which determines in turn how much the data is smoothed. The width is not expressed in terms of the standard deviation ?, as customary in statistics, but with the Full Width at Half Maximum (FWHM). In this case the FWHM would be 2.35: The maximum of this curve is y = 0.4 at x = 0. The half maximum is y = 0.2 at x = -1.175 and at x ...

The size of the Gaussian kernel defines the "width" of the curve which determines in turn how much the data is smoothed. The width is not expressed in terms of the standard deviation ?, as customary in statistics, but with the Full Width at Half Maximum (FWHM). In this case the FWHM would be 2.35: The maximum of this curve is y = 0.4 at x = 0. The half maximum is y = 0.2 at x = -1.175 and at x ...

We present a curve approximation method which approximates each planar algebraic curve segment by discrete curve points at each of which the curve has its gradient from a set of uniformly distributed normals. This method, called Gaussian Approximation (GAP), provides efficient algorithms for various primitive geometric operations, especially for those related with gradients such as common tange...

The size of the Gaussian kernel defines the "width" of the curve which determines in turn how much the data is smoothed. The width is not expressed in terms of the standard deviation ?, as customary in statistics, but with the Full Width at Half Maximum (FWHM). In this case the FWHM would be 2.35: The maximum of this curve is y = 0.4 at x = 0. The half maximum is y = 0.2 at x = -1.175 and at x ...

The gravitational evolution of the genus of the density field in large-scale structure is analytically studied in a weakly nonlinear regime using second-order perturbation theory. Weakly nonlinear evolution produces asymmetry in the symmetric genus curve for Gaussian initial density field. The effect of smoothing the density field in perturbation theory on the genus curve is also evaluated and ...