Related papers: Fast Geometric Fit Algorithm for Sphere Using Exac…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
In this paper, we consider a problem of covering a straight line segment by equal circles that are initially arbitrarily placed on a plane by moving their centers on a segment or on a straight line containing a segment so that the segment…
Recently, a new geometric approach which is called the fixed-circle problem has been gained to fixed-point theory. The problem is introduced and studied using different techniques on metric spaces. In this paper, we consider the…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…
Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…
The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the…
Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF),…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
Reconstructing a 3D scene from unordered images is pivotal in computer vision and robotics, with applications spanning crowd-sourced mapping and beyond. While global Structure-from-Motion (SfM) techniques are scalable and fast, they often…
The paper describes a novel real-time algorithm for finding 3D geometric primitives (cylinders, cones and spheres) from 3D range data. In its core, it performs a fast model fitting with a model update in constant time (O(1)) for each new…
The paper presents two edge grouping algorithms for finding a closed contour starting from a particular edge point and enclosing a fixation point. Both algorithms search a shortest simple cycle in \textit{an angularly ordered graph} derived…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in…
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
In this article we propose a new efficient strategy to construct exact solutions of Einstein gravities with a minimally coupled self-interacting scalar field. The strategy is to use the symmetry of the equations of motion (EOMs) to give a…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…