ÐCurved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys. Existing curvature estimators fail here. The characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvaturedependent confidence measure. Using parameterized curvilinear models we measure the amount of loc...

In this paper it is shown that the space of metrics of positive scalar curvature on a manifold is, when nonempty, homotopy equivalent to a space of metrics of positive scalar curvature that restrict to a fixed metric near a given submanifold of codimension greater or equal than 3. Our main tool is a parameterized version of the Gromov-Lawson construction, which was used to show that the existen...

In curve design such as highway design andmotion planning of autonomous vehicles, it may be important to minimize the maximum curvature. In this paper we address the problem of minimizing the maximum curvature of a quadratic Bézier curve within a boundary constraint determined by a tetragonal concave polygon. The curve is parameterized by lengths between its control points, called the ‘‘control...

Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field’s planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associat...

A path deviation equation in the Parameterized Absolute Parallelism (PAP) geometry is derived. This equation includes curvature and torsion terms. These terms are found to be naturally quantized. The equation represents the deviation from a general path equation, in the PAP-geometry, derived by the author in a previous work. It is shown that, as the effect of the torsion, on the deviation, incr...

We prove that C∞ curves of constant curvature satisfy, in the sense of Gromov, the relative C-dense h-principle in the space of immersed curves in Euclidean space Rn≥3. In particular, in the isotopy class of any given C knot f there exists a C∞ knot e f of constant curvature which is C-close to f . More importantly, we show that if f is C, then the curvature of e f may be set equal to any const...