Related papers: Computation of Circular Area and Spherical Volume …
In this paper, we propose two methods of calculating theoretically maximal metamer mismatch volumes. Unlike prior art techniques, our methods do not make any assumptions on the shape of spectra on the boundary of the mismatch volumes. Both…
We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…
We give an explicit slice formula for a surface invariant of generic immersions in $\mathbb{R}^3$, expressed in terms of curve invariants arising from planar slices. Using a motion-picture viewpoint, we introduce differential measures that…
The conformal nature of smooth curves in $\mathbb{R}^3$ is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges .…
Inspired by piecewise polynomiality results of double Hurwitz numbers, Ardila and Brugall\'e introduced an enumerative problem which they call double Gromov--Witten invariants of Hirzebruch surfaces. These invariants serve as a…
We analyze human poses and motion by introducing three sequences of easily calculated surface descriptors that are invariant under reparametrizations and Euclidean transformations. These descriptors are obtained by associating to each…
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
For a finite planar graph, it associates with some metric spaces, called (regular) spherical polyhedral surfaces, by replacing faces with regular spherical polygons in the unit sphere and gluing them edge-to-edge. We consider the class of…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
Given $r_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq 0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq r_0$ and with the supremum of absolute sectional curvature at most $K_0$, and let…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ of dual unitarily invariant curvature measures. Building on the recent results from integral…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…
We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell…
We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of…