We study the properties of single boundary spike solutions for the following singularly perturbed problem 2 u ? u + u p = 0 in ; u > 0 in and @u @ = 0 on @ It is known that at a nondegenerate critical point of the mean curvature function H (P), there exists a single boundary spike solution. In this paper, we show that the single boundary spike solution is unique and moreover it has exactly (N ?...

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects' sensitivity to the curvature of a curve lying on a surface and chan...

In the previous lecture we developed the notion of the curvature of a surface, showing a bunch of nice theoretical properties. But aside from theoretical elegance, what’s so great about curvature? Well, remember from the plane curve setting that the curvature function uniquely defines a curve parameterized by arc length up to a rigid motion. A similar result holds for surfaces, though the proof...

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...

The parasitoid wasps of the genus Trichogramma use the surface curvature of their insect egg hosts to set an upper limit to the number of progeny allocated to the host, as well as the duration of their host examination. In addition, host recognition and host acceptance are in part mediated by surface curvature. In this paper, the relationships between the positions of body parts of the wasp and...

Surface fairing, generating free-form surfaces satisfying aesthetic requirements, is important for many computer graphics and geometric modeling applications. A common approach for fair surface design consists of minimization of fairness measures penalizing large curvature values and curvature oscillations. The paper develops a numerical approach for fair surface modeling via curvature-driven e...