Related papers: Analytical Methods for Squaring the Disc
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh inversion formulas were found in any dimension $n\geq2$ for recovering a smooth function with compact support in the unit ball from spherical means centered on…
We consider defining the embedding of a triangle mesh into $R^3$, up to translation, rotation, and scale, by its vector of dihedral angles. Theoretically, we show that locally, almost everywhere, the map from realizable vectors of dihedrals…
We study a functional, whose critical points couple Dirac-harmonic maps from surfaces with a two form. The critical points can be interpreted as coupling the prescribed mean curvature equation to spinor fields. On the other hand, this…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential…
Dynamics of rough discs in a rarified media is considered. We study possible trajectories of centers of discs. The main result of the paper is the following: any finite rectifiable curve can be approximated by trajectories of centers of…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
By presenting curved surfaces of various curvatures including edges to the fingertip, it is possible to reproduce the haptic sensation of object shapes that cannot be reproduced by flat surfaces alone, such as spheres and rectangular…
This is an elementary introduction to a method for studying harmonic maps into symmetric spaces, and in particular for studying constant mean curvature (CMC) surfaces, that was developed by J. Dorfmeister, F. Pedit and H. Wu. There already…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
In this paper, we introduce a new class of mappings, termed $(\rho,t)$-quasisymmetric mappings, which generalizes the classical concept of quasisymmetric mappings. Using this broader class of mappings, we provide an analytic…
In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.
In a spherically complete ultrametric space, a strictly contracting mapping has a fixed point. We indicate in this paper how this fixed point can either be reached or approximated.