We examine the smoothness properties of the principal curvatures of subdivision surfaces near extraordinary points. In particular we give an estimate of their Lp class based on the eigen structure 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 justifying their use as shape functio...

Abstract. In this paper, we consider an equivalence problem of second order partially differential equations (PDE) and a duality of the flat differential equation. For the equivalence problem, explicit form of invariants (curvatures) are given. In particular, if all of the curvatures vanish, then PDE are equivalent to the flat equation. We also investigate a duality associated with the flat equ...

Three methods for the damage localization of impact damage in laminated composite plates, based on their vibrational characteristics, are presented in this paper. These methods use double pulse TV holography with acoustic excitation for mode shapes acquisition and the differences in translations, rotations and curvatures. The rotations and curvatures are obtained by numerical differentiation of...

We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We prove that the ratio of circumradius to inradius is bounded by a function of the circumradius with limit 1 at zero. We apply this result to the motion of hypersurfaces by arbitrary speeds which are smooth homogeneous ...

The concept of a differential Shack-Hartmann (DSH) curvature sensor was recently proposed, which yields wavefront curvatures by measuring wavefront slope differentials. As an important feature of the DSH curvature sensor, the wavefront twist curvature terms can be efficiently obtained from slope differential measurements, thus providing a means to measure the Monge-equivalent patch. Specificall...

Quantum chemistry calculations were performed to investigate the effect of the surface curvature of a Boron Nitride (BN) nanotube/nanosheet on gas adsorption. Curved boron nitride layers with different curvatures interacting with a number of different gases including noble gases, oxygen, and water on both their convex and concave sides of the surface were studied using density functional theory...

To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the differential of the Gauss map of the underlying surface. The Gauss map assigns to each point in the surface the unit normal vector of the tangent plane to the surface...

In this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the about spacelike axis according to Gaussian and mean curvatures $E_{1}^{4}$ give some results with aid of curvatures. After that, deal Gauss map hypersurface by obtaining obtain second third Laplace-Beltrami operators on $E_{1}^{4}$. Also, these characterizations for timelike lightlike axes, too.

Root canal curvatures are often the main reason for a poor root canal treatment. The clinical x-ray images often do not give a precise view of the degree of the root curvature from the axial axis. The aim of the present study was to measure the severe curvatures > 25o separately for upper and lower jaw in representative number of extracted human molars. The length of each root was measured from...

Curvatures on the surface are important geometric invariants and are widely used in different area of research. Examples include feature recognition, segmentation, or shape analysis. Therefore, it is of interest to develop an effective algorithm to approximate the curvatures accurately. The classical methods to compute these quantities involve the estimation of the normal and some involve the c...