Two Extensions of the Quadratic Nonuniform B-Spline Curve with Local Shape Parameter Series

Two extensions of the quadratic nonuniform B-spline curve with local shape parameter series, called the W3D3C1P2 spline curve and the W3D4C2P1 spline curve, are introduced in the paper. The new extensions not only inherit most excellent properties of the quadratic nonuniform B-spline curve but also can move locally toward or against the fixed control polygon by varying the shape parameter series. They are C1 and C2 continuous separately. Furthermore, the W3D3C1P2 spline curve includes the quadratic nonuniform B-spline curve as a special case. Two applications, the interpolation of the position and the corresponding tangent direction and the interpolation of a line segment, are discussed without solving a system of linear functions. Several numerical examples indicated that the new extensions are valid and can easily be applied.

Influence of Artificially Macroscopical Drilling on the Crystal Growth Orientation of Single Domain SmBCO Bulk Superconductor

A large drilled single domain SmBa2Cu3O7−δ (SmBCO) bulk superconductor with a diameter of 32 mm and different hole sizes was successfully fabricated using the modified top-seeded infiltration and growth (TSIG) process. The morphology, superconducting properties, and grain boundary orientation growth of the drilled SmBCO samples were investigated. It was found that not only are the properties of the drilled sample equivalent to those of normal SmBCO bulk superconductors, but also the NdBCO seed crystal can be well controlled because of the increase in the specific surface area in the solid phase pellet. In addition, the growth orientation along the tangent direction of the holes was first noticed in the drilled single domain SmBCO bulk superconductor. This conclusion is highly important for the accurate control of the growth temperature of high temperature bulk superconductors.

Buckling and Frequency Responses of a Graphene Nanoplatelet Reinforced Composite Microdisk

This is the first research on the vibration and buckling analysis of a graphene nanoplatelet composite (GPLRC) microdisk in the framework of a numerical based generalized differential quadrature method (GDQM). The stresses and strains are obtained using the higher-order shear deformable theory (HOSDT). Rule of the mixture is employed to obtain varying mass density, thermal expansion, and Poisson’s ratio, while the module of elasticity is computed by modified Halpin–Tsai model. Governing equations and boundary conditions of the GPLRC microdisk are obtained by implementing Extended Hamilton’s principle. The results show that outer to inner ratios of the radius ([Formula: see text], ratios of length scale and nonlocal to thickness [Formula: see text] and [Formula: see text], and GPL weight fraction [Formula: see text] have a significant influence on the frequency and buckling characteristics of the GPLRC microdisk. Another necessary consequence is that by increasing the value of the [Formula: see text], the distribution of the displacement field extends from radial to tangent direction, especially in the lower mode numbers, this phenomenon appears much more remarkable. A useful suggestion of this research is that, for designing the GPLRC microdisk at the low value of the [Formula: see text], more attention should be paid to the [Formula: see text] and [Formula: see text], simultaneously.

A relation between the curvature ellipse and the curvature parabola

At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geometry of the projection of the surface to ℝ3 at the singular point. In particular we relate the curvature ellipse of the surface to the curvature parabola of its singular projection.

Suns are convex in tangent directions

A direction d is called a tangent direction to the unit sphere S of a normed linear space s S and lin(s + d) is a tangent line to the sphere S at s imply that lin(s + d) is a one-sided tangent to the sphere S, i. e., it is the limit of secant lines at s. A set M is called convex with respect to a direction d if [x, y] M whenever x, y in M, (y - x) || d. We show that in a normed linear space an arbitrary sun (in particular, a boundedly compact Chebyshev set) is convex with respect to any tangent direction of the unit sphere.

A Robust Multi-Circle Detector Based on Horizontal and Vertical Search Analysis Fitting with Tangent Direction

In this paper, we propose an efficient Multi-Circle detector which follows the fixed search order. The method makes use of horizontal and vertical search to realize circle detection, which is named as HVCD. First, this method computes edge areas in a given image. The edge areas could be divided into some regions by means of region growing. Each of regions could be efficiently searched to achieve not only one-pixel wide edges but edge segments as well. Next, the candidate circles can be extracted from every edge segment. Finally, the circle candidates could be validated with the help of Helmholtz principle. Experimental results demonstrate that HVCD could effectively detect circles on synthetic and natural images on the one hand; on the other hand, HVCD here could solve the weakness in the process of circle Hough transform implementation and EDcircles implementation.

Three-Dimensional Curve Tracking for Particles Using Gyroscopic Control

Curve-tracking control is challenging and fundamental in many robotic applications for an autonomous agent to follow a desired path. In this paper, we consider a particle, representing a fully actuated autonomous robot, moving at unit speed under steering control in the three-dimensional (3D) space. We develop a feedback control law that enables the particle to track any smooth curve in the 3D space. Representing the 3D curve in the natural Frenet frame, we construct the control law under which the moving direction of the particle will be aligned with the tangent direction of the desired curve and the distance between the particle and the desired curve will converge to zero. We demonstrate the effectiveness of the proposed 3D curve-tracking control law in simulations.

Image Regularity and Fidelity Measure with a Two-Modality Potential Function

We define a strictly convex smooth potential function and use it to measure the data fidelity as well as the regularity for image denoising and cartoon-texture decomposition. The new model has several advantages over the well-known ROF or TV-L2 and the TV-L1 model. First, due to the two-modality property of the new potential function, the new regularity has strong regularizing properties in all directions and thus encourages removing noise in smooth areas, while, near edges, it smoothes the edge mainly along the tangent direction and thus can well preserve the edges. Second, the new potential function is very close to the L1 norm; thus using it to measure the data fidelity makes the new model perform very well in removing impulse noise and preserving the contrast. Lastly, the proposed fidelity and regularization term is strictly convex and smooth and thus allows a unique global minimizer and it can be solved by using the steepest descent method. Numerical experiments show that the proposed model outperforms TV-L2 and TV-L1 in removing impulse noise and mixed noise. It also outperforms some state-of-the-art methods specially designed for impulse noise. Tests on cartoon-texture decomposition show that our method is effective and performs better than TV-L1.