A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated Surfaces

Curvature Estimation for Segmentation of Triangulated Surfaces

An important aspect of reverse engineering is the production of digital representations of physical objects for CAD systems. The first stage involves taking 3D coordinate measurements for points on the surface of the object and producing in general an unstructured set of points, called a point cloud. A triangulated surface can be generated from such a point cloud, allowing copies of the origina...

Surfaces of Constant Mean Curvature

On minimax estimation of a sparse normal mean vector

Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a non-negative vector parameter in Gaussian white noise when it is known also that most, i.e. (1 − ǫ), components are zero. We provide a partial asym...

New Constant Mean Curvature Surfaces

We use the DPW construction [5] to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points with a common tangent plane. An appendix, by the t...

Coplanar Constant Mean Curvature Surfaces

We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors [GKS2, GKS1]. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane...