Related papers: Shape preservation behavior of spline curves

We study the surface shape of two-dimensional piles using experiments and a continuum theory for surface flows of granular materials (the BCRE equations). We first obtain an analytical solution to the BCRE equations with a simple…

In this dissertation, we concentrate on the challenging research issue of developing a spline-based modeling framework, which converts the conventional data (e.g., surface meshes) to tensor-product trivariate splines. This methodology can…

A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…

We study stable surfaces, i.e., second order minima of the area for variations of fixed volume, in sub-Riemannian space forms of dimension $3$. We prove a stability inequality and provide sufficient conditions ensuring instability of…

We reconsider some fundamental problems of the thin shell model. First, we point out that the "cut and paste" construction does not guarantee a well-defined manifold because there is no overlap of coordinates across the shell. When one…

Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear…

A fundamental control problem for autonomous vehicle formations is formation shape control, in which the agents must maintain a prescribed formation shape using only information measured or communicated from neighboring agents. While a…

In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…

Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…

Accurate segmentation of topological tubular structures, such as blood vessels and roads, is crucial in various fields, ensuring accuracy and efficiency in downstream tasks. However, many factors complicate the task, including thin local…

In this work, we provide explicit conditions for the coefficients of a symmetric truncated cubic to give a smooth tropical curve. We also examine non-smooth cases corresponding to some specific subdivision types.

We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…

We prove equivalent numerical conditions for a complete spherical variety to admit a toric structure, and for the smoothness of an arbitrary spherical variety along any given G-orbit. The conditions are in terms of spherical skeletons, a…

We discuss the direct use of cubic-matrix splines to obtain continuous approximations to the unique solution of matrix models of the type $Y''(x) = f(x,Y(x))$. For numerical illustration, an estimation of the approximation error, an…

The distinctive feature of a polynomial parametric speed let polynomial Pythagorean-hodograph (PH) curves be attractive for the design of accurate and efficient application algorithms. We propose a robust path following scheme for the…

Here we perform a systematic analysis of equilibrium solutions for Neel and Bloch skyrmions on a cylindrical shell and demonstrate that both experience curvature-induced deformation. Considering the curvature as a small perturbation and…

In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…

Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…