where |B| is the length of second fundamental form. |B|2 = 4|H|2 − 2K, where H is the mean curvature and K is the Gauss curvature. The curvature of minimal surfaces is nonpositive. Then we exam what is still hold for some minimal surface theorems if extending the minimal condition H ≡ 0 to the surfaces with K ≤ 0 and (1). In 2001, F. Xavier [18] has the following theorem: Theorem [Xavier]. Let ...

A first-order phase transition is found in two types of intrinsic curvature models defined on dynamically triangulated surfaces of disk topology. The intrinsic curvature energy is included in the Hamiltonian. The smooth phase is separated from a non-smooth phase by the transition. The crumpled phase, which is different from the non-smooth phase, also appears at sufficiently small curvature coef...

Our main contributions in this paper are twofold. In the first instance, we demonstrate how H K surface labelling can be realised using dictionary-based probabilistic relaxation. To facilitate this implementation we have developed a dictionary of feasible surface-label configurations. These configurations observe certain constraints on the contiguity of elliptic and hyperbolic regions, and, on ...

Curvature based surface optimization is an important constituent of various geometric modeling and scientific computing tasks. Smooth surfaces are often modelled in a variational setting, where the objective function is used to express the beauty of the shape. Optimization is also used for fitting a smooth, virtual surface to samples of a real, scanned object. Energy minimizing surfaces are als...

Geometers have been interested in constructing minimal surfaces for long time. One possible way to produce such surfaces is to deform a given surface by its mean curvature vector. More precisely, the surface evolves in the gradient flow of the area functional, and such a flow is the so-called mean curvature flow. A mean curvature flow, however, develops singularity after finite time in general ...

Structure from motion often refers to the computation of 3D structure from a matched sequence of images. However, a (relative) depth map of a surface may not be a good representation for storage and recognition; a more concise representation seems necessary. The sign of the Gaussian curvature of a surface is one candidate to be a part of a useful representation of the surface. I will show that ...

to investigate the changes in yield and yield components of dry land wheat (triticum aestivum l. cv agosta), under the influence of residue and nitrogen levels and different tillage practices, a field experiment was conducted during the 2006-2007 growing season, in the agricultural research station of the college of agriculture, shiraz university, iran. the experiment was designed as a split-sp...

In general, the noise that is present in real-world 3D surface scan data prevents accurate curvature calculation. In this paper we show how curvature can be extracted from noisy data by applying filtering after a noisy curvature calculation. To this end, we extend the standard Gaussian filter (as used in 2D image processing) by taking adjacent point distances along the scanned surface into acco...

Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. ...

Estimating principal curvatures and principal directions of a smooth surface represented by a triangular mesh is an important step in many CAD or graphics related tasks. This paper presents a new method for curvature tensor estimation on a triangular mesh by replacing flat triangles with triangular parametric patches. An improved local interpolation scheme of cubic triangular Bézier patches to ...