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We present an explicit formula for the orthogonal projection onto the subspace of analytic polynomials of degree at most $n$ in the local Dirichlet space $D_\mu$ , where the positive measure $\mu$ consists of a finite number of Dirac…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
Existing electromagnetic inverse design methods are often established in the spacial domain. This communication presents an inverse design method, which can design aperture field for the desired phaseless radiation pattern, from the…
Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed…
Generalizable 3D Gaussian Splatting reconstruction showcases advanced Image-to-3D content creation but requires substantial computational resources and large datasets, posing challenges to training models from scratch. Current methods…
Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
We show how spectral submanifold theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predictions include an explicit criterion for the existence of…
In computational 3D geometric problems involving rotations, it is often that people have to convert back and forth between a rotational matrix and a rotation described by an axis and a corresponding angle. For this purpose, Rodrigues'…
We present a certified algorithm that takes a smooth algebraic curve in $\mathbb{R}^n$ and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}^2$. Our algorithm is designed for curves given implicitly…
We consider the numerical approximation of surfaces of prescribed Gaussian curvature via the solution of a fully nonlinear partial differential equation of Monge-Amp\`ere type. These surfaces need not be continuous up to the boundary of the…
Contour integrals of rational functions over ${\cal M}_{0,n}$, the moduli space of $n$-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…
We develop a boundary only method for computing weak gravitational deflection angles at finite source and receiver distances within the Gauss-Bonnet theorem formulation of optical geometry. Exploiting the fact that the relevant equatorial…
In this paper we study constant angle surfaces in Euclidean 3-space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the…
The classical result of Cauchy's surface area formula states that the surface area of the boundary $\partial K=\Sigma$ of any $n$-dimensional convex body in the $n$-dimensional Euclidean space $\mathbb{R}^n$ can be obtained by the average…
In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection…
A Woods-Saxon equivalent to a double folding potential in the surface region is obtained for the heavy-ion scattering potential. The Woods-Saxon potential has fixed geometry and was applied as a bare potential in the analysis of…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…