Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. Especially, curvature estimation of a mesh is an active research area [GI04, CSM03, CP03] with many applications. The most important curvature measures on a surface are the mean curvature H, the Gaussian curvature K, and the curv...

This paper presents an algorithm of modifying free-formed NURBS curve/surface for offsetting without local self-intersecting. The method consists of (1) sampling a number of points from a progenitor curve/surface based on second derivatives; (2) checking the curvature or maximum curvature of the progenitor curve/surface at the sampled points; (3) inserting corresponding knots of sampled points;...

Consider a two-dimensional surface in an Alexandrov space of curvature bounded above by k. Assume that this surface does not admit contracting deformations (a particular case of such surfaces is formed by area minimizing surfaces). Then this surface inherits the upper curvature bound, that is, this surface has also curvature bounded above by k, with respect to the intrinsic metric induced from ...

In this paper we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a Kähler-Einstein surface. We prove that the blow-up flow Σ∞ s at a singular point (X0, T0) of a symplectic mean curvature flow Σt or of a Lagrangian mean curvature flow Σt is a non trivial minimal surface in R, if Σ∞ −∞ is connected.

The effect of surface tension on the Rayleigh-Taylor (RT) instability and Richtmyer – Meshkov (RM) instability induced development of nonlinear structures like spike and bubble at two fluid interface have been investigated .In case of RT instability, the surface tension reduces the velocity of the tip of both the bubble and the spike by the factor (1-k /3 kc ) where, kc =(h-l)g/T .For k > 3 k...

We propose a framework for 3D geometry processing that provides direct access to surface curvature to facilitate advanced shape editing, filtering, and synthesis algorithms. The central idea is to map a given surface to the curvature domain by evaluating its principle curvatures, apply filtering and editing operations to the curvature distribution, and reconstruct the resulting surface using an...

Constant mean curvature surfaces (abbriviated as CMC surfaces) in the space forms are typical examples of isothermic surfaces. Bonnet showed that every constant mean curvature surface admits a one-parameter family of isometric deformations preserving the mean curvature. A surface which admits such a family of deformations is called a Bonnet surface. Both the isothermic surfaces and Bonnet surfa...

In recent years it has become clear that electronic Berry curvature (BC) is a key concept to understand and predict physical properties of crystalline materials. A wealth interesting Hall-type responses in charge, spin heat transport are caused by the BC associated bands inside solid: anomalous Hall effects magnetic materials, various nonlinear Nernst non-magnetic systems lack inversion symmetr...

we study the equilibrium states for an energy functional with a parametric force field on a region of a surface. consideration of free equilibrium states is based on lyusternik - schnirelman's and skrypnik's variational methods. consideration of equilibrium states under a constraint of geometrical character is based on an analog of skrypnik's method, described in cite{vyr3}. in local coordinate...