The convergence property of the discrete Laplace-Beltrami operator is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. The aim of this paper is to review several already used discrete Laplace-Beltrami operators over triangulated surface and study numerically as well as theoretically their conv...

In this work, we propose a fast and simple approach to obtain a spherical parameterization of a certain class of closed surfaces without holes. Our approach relies on empirical findings that can be mathematically investigated, to a certain extent, by using Laplace-Beltrami Operator and associated geometrical tools. The mapping proposed here is defined by considering only the three first non-tri...

The Laplace Beltrami operator, known as an elliptic operator for functions defined on surfaces, appears in some applications in sciences and engineerings. In this paper we consider the Laplace Beltrami operator ∆Γ on surfaces Γ defined as graphs of C2 functions on a flat domain Ω ⊂ Rd−1 (d ≥ 2), ∆Γu = f on Γ, u = 0 on ∂Γ. Based on some properties of differential geometry, we transformed the Lap...

We define a discrete Laplace-Beltrami operator for simplicial surfaces (Definition 16). It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called “cotan formula”) except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new ...

We propose Steklov geometry processing, an extrinsic approach to spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace–Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, while many previous extrinsic methods lack theoretical justi cation. Instead, we propose a systematic approach by considering the Steklov eigenva...

This note presents an elementary numerical scheme for discretizing the Laplace-Beltrami operator on smooth manifolds, as a difference operator of arbitrary high order. The method is coordinate-free, and involves very little geometry.

We exploit the Laplace-Beltrami operator to represent shapes which in turn is used for designing a shape based transfer function for volume rendering. Laplace-Beltrami spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. Isosurfaces are extracted from the volume data and the Laplace-Beltrami operator is applied on these extr...

einstein, möbius, and proper velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper lorentz group in the real minkowski space-time $bbb{r}^n$. using the gyrolanguage we study their gyroharmonic analysis. although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. our study focus ...

We introduce a Laplace-Beltrami type operator on the Fock space of symmetric functions and show that the Jack symmetric functions are the only family of eigenvectors of the differential operator, thus giving a new characterization of Jack polynomials. This was achieved by explicit computation of its action on generalized homogeneous symmetric functions. Using this new method we give a combinato...

Generalization of the harmonic superposition rule for the case of dependent choice of harmonic functions is given. Dependence of harmonic functions from all (relative and overall) transverse coordinates is considered using the BeltramiLaplace operator. Supersymmetry of IIB 10D supergravity solutions with only non-vanished 5-form field and 11D supergravity solutions is discussed.