Many surfaces can be modeled by interpolating data points digitized from existing products. But the digitized data points could have measuring errors. To adjust the points, fairing is performed. We present an automatic local fairing algorithm using nonlinear programming. For the objective function of the algorithm, we derive discrete fairness metrics. The metrics are consisted of discrete princ...

We measure the velocities of the mean flows that are driven by curved rolls in a pattern formation system. Curved rolls in Faraday waves are generated in experimental cells consisting of channels with varying widths. The mean flow magnitudes are found to scale linearly with roll curvatures and squares of wave amplitudes, agreeing with the prediction from the analysis of phase dynamics expansion...

introduction: the aim of this study was to compare centering ability and dentin removal of three rotary systems in curved root canals of extracted teeth. materials and methods: sixty root canals of mandibular first molars with curvatures ranging between 25-35 o were divided into three groups of 20 teeth each. based on pre-instrumentation radiographs that assessed the angle and the radius of can...

We examine the smoothness properties of the principal curvatures of subdivision surfaces near irregular points. In particular we give an estimate of their Lp class based on the eigenstructure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures enabling their use as shape functions in F...

The treatment of stream lines path lines and streak lines is a powerful method for visualizing the behavior of unsteady i e time dependent ow elds Although a closed parametric form of these lines does not exist we show how to compute their curvatures The visualiza tion of the curvatures of these curves shows several aspects of the ow such as location and movement of turbulent areas The techniqu...

In this paper we study properties of linear Weingarten immersions and graphs related to non-existence problems and behaviour of its curvatures. The main results are obtained giving a harmonic representation of linear Weingarten surfaces and by proving optimal estimates of the height and curvatures that the immersion must satisfy, characterizing the spherical caps as the only ones achieving thes...

Abstract. We prove integral formulas for closed hypersurfaces in C, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then we follow the Reilly approach to prove an isoperimetric inequality. As an application, we obtain the “Soap Bubble Theorem” for starshaped dom...

In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by extending the work of Dimakis et al and discuss linear connections and curvatures on graphs. Especially, we calculate connections and curvatures explicitly for t...

Let Sg be a closed surface of genus g and Mg be the moduli space of Sg endowed with the Weil-Petersson metric. In this paper we investigate the Weil-Petersson curvatures of Mg for large genus g. First, we study the asymptotic behavior of the extremal Weil-Petersson holomorphic sectional curvatures at certain thick surfaces in Mg as g → ∞. Then we prove two curvature properties on the whole spac...

We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspaces are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvat...