Related papers: Simple but not Simpler: A Surface-Sliding Method f…

A new method is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into several latitudinal bands of near-constant span with further division of each band into equal-area cells. It is…

In computer vision, camera pose estimation from correspondences between 3D geometric entities and their projections into the image has been a widely investigated problem. Although most state-of-the-art methods exploit low-level primitives…

This paper presents a collision avoidance method for elliptical agents traveling in a two-dimensional space. We first formulate a separation condition for two elliptical agents utilizing a signed distance from a supporting line of an agent…

This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…

When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to…

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…

The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For non-spherical particles, the distance of closest approach depends on orientation,…

The most direct measurement of adhesion is the pull-off force, i.e. the tensile force necessary to separate two solids in contact. For a given interface, it depends on various experimental parameters, including separation speed, contact age…

This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…

How many copies of a parallelepiped are needed to ensure that for every point in the parallelepiped a copy of each other point exists, such that the distance between them equals the distance of the pair of points when the opposite sites of…

Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…

It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…

We introduce a new type of distinct distances result: a lower bound on the number of distances between points on a line and points on a two-dimensional strip. This can be seen as a generalization of the well-studied problems of distances…

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse…

We use the $p$-Laplacian with large $p$-values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (2018) [1] computational results using the $p$-Laplacian for the distance-to-surface…

We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an…

In this paper, we discuss the mechanics and planning algorithms to slide an object on a horizontal planar surface via frictional patch contact made with its top surface. Here, we propose an asymmetric dual limit surface model to determine…

This paper proposes a minimal contractor and a minimal separator for an ellipse in the plane. The task is facilitated using actions induced by the hyperoctahedral group of symmetries. An application related to the localization of an object…

In this paper, we introduce the Method of Ellipcenters (ME) for unconstrained minimization. At the cost of two gradients per iteration and a line search, we compute the next iterate by setting it as the center of an elliptical…