Related papers: Circle and sphere blending with conformal geometri…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, and more. We present an abstract process of gluing model…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
We give a simple iterative procedure to compute the classical conformal blocks on the sphere to all order in the modulus.
We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
Curvature has received increased attention as an important alternative to length based regularization in computer vision. In contrast to length, it preserves elongated structures and fine details. Existing approaches are either inefficient,…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…
Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance…
Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility…