The shape of a liquid surface bounded by an acute or obtuse wedge is considered by using classical analysis methods. For acute wedges the two principal curvatures are of the order of the (fixed) mean curvature. But for obtuse wedges, the principal curvatures both diverge as the vertex is approached. The power-law divergence becomes stronger with increasing opening angle. Possible implications o...

The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But for obtuse sectors, the principal curvatures both diverge as the vertex is approached. The powerlaw divergence becomes stronger with increasing opening angle...

ÐWe improve the basic tensor voting formalism to infer the sign and direction of principal curvatures at each input site from noisy 3D data. Unlike most previous approaches, no local surface fitting, partial derivative computation, nor oriented normal vector recovery is performed in our method. These approaches are known to be noise-sensitive since accurate partial derivative information is oft...

We present a geometry processing framework that allows direct manipulation or preservation of positional, metric, and curvature constraints anywhere on the surface of a geometric model. Target values for these properties can be specified point-wise or as integrated quantities over curves and surface patches embedded in the shape. For example, the user can draw several curves on the surface and ...

Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly computing accurate metric principal curvature values from noisy point clouds which was implemented on GPU. In contrast to existing readily available solutions which...

The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature ßow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive...

We consider embedded hypersurfaces evolving by fully nonlinear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a noncollapsing estimate: Precisely, the function which gives the curvature of the largest interior sphere touching the hypersurface at each point is a subsolution of the linearized flow equation i...

Interactive visualization is a very convenient tool to explore complex scientific data or to try different parameter settings for a given processing algorithm. In this article, we present a tool to efficiently analyze the curvature tensor on the boundary of potentially large and dynamic digital objects (mean and Gaussian curvatures, principal curvatures, principal directions and normal vector f...

This paper explores the representation of the human face by features based on shape and curvature of the face surface Curvature captures many features necessary to accurately describe the face such as the shape of the forehead jaw line and cheeks which are not easily detected from standard intensity images Moreover the value of curvature at a point on the surface is also viewpoint invariant Unt...

This thesis presents a new class of surface patches for the creation of sculptured surfaces in mechanical engineering applications of computer aided design. Ideas from differential geometry are used to create principal patches whose edges are lines of curvature. This is done by ensuring that the sides obey two equations called the frame matching and position matching conditions. It is shown tha...