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...

THE POLYPHOSPHOINOSITIDES, phosphatidyl inositol phosphate and bisphosphate, have been found as trace lipids in yeast (TALWALKAR & LESTER, 1973), protozoans (PALMER, 1973). and mammals (FOLCH, 1949). In mammals, these lipids are thought to be particularly enriched in neural tissue where they have been shown to undergo changes in metabolism with stimulation of the tissue (see MICHELL, 1975; HAWT...

This report mainly illustrates a way to compute the Laplace-Beltrami-Operator on a Riemannian Manifold and gives information to why and where it is used in the Analysis of 3D Shapes. After a brief introduction, an overview over the necessary properties of manifolds for calculating the Laplacian is given. Furthermore the two operators needed for defining the Laplace-Beltrami-Operator the gradien...

The relaxed state of a magnetized four-component partially ionized dusty (PID) plasma is explored. PID composed inertial electrons, positive ions, neutrals, and static negatively charged dust particles. When the neutrals are dragged along with steady-state solution vortex dynamic equations for electron ion species yields triple Beltrami state, which linear combination three single force-free fi...

Abstract We present an error bound for a least squares version of the kernel based meshless finite difference method elliptic differential equations on smooth compact manifolds arbitrary dimension without boundary. In particular, we obtain sufficient conditions convergence this method. Numerical examples are provided equation $$-\Delta _{\mathcal {M}} u + = f$$ <mml:math xmlns:mml="http://www.w...

This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by full algebraic (BAMG) setup algorithm that includes an AMG eigensolver, it is illustrated how can be simplified case a discretized equation (PDE), thereby developing geometric (BMG) approach. We illustrate numerically efficacy BMG metho...

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...