ISOMETRIC DEFORMATION OF THE SURFACE OF MINIMAL AREA OF A CYLINDER INCREASING ITS VOLUME

ISOMETRIC DEFORMATION OF THE SURFACE OF MINIMAL AREA OF A CYLINDER INCREASING ITS VOLUME Lizandro Baldomero, Reyna Zegarra y Heron Juan Morales Marchena Departamento de Matemáticas, Universidad Nacional del Santa, Chimbote, Perú DOI: https://doi.org/10.33017/RevECIPeru2010.0001/ ABSTRACT A method for increasing the volume of a cylinder with minimal area preserving the isometry is expounded. To do this, it was necessary to use numerical methods and a computer program. Such method let us set down a theorem which is analogy to that given for the case of a cube instead of a cylinder, being an immediate application of this theorem to the case of optimization in designing commercial bottles. To get an analytical proof of this new theorem is demanded. Keywords: surface of minimal area; optimization in designing commercial bottles; increasing the volume without stretching.

Isometric Deformation of (m,n)-Type Helicoidal Surface in the Three Dimensional Euclidean Space

We consider a new kind of helicoidal surface for natural numbers ( m , n ) in the three-dimensional Euclidean space. We study a helicoidal surface of value ( m , n ) , which is locally isometric to a rotational surface of value ( m , n ) . In addition, we calculate the Laplace–Beltrami operator of the rotational surface of value ( 0 , 1 ) .

3D Face Recognition Under Isometric Expression Deformations

In this paper, 3D face recognition under isometric deformation (induced by facial expressions) is considered. The main objective is to employ the shape descriptors that are invariant to (isometric) deformations to provide an efficient face recognition algorithm. Two methods of the correspondence are utilized for automatic landmark assignment to the query face. One is based on the conventional iterative closest point (ICP) method and another is based upon the geometrical/topological features of the human face. The shape descriptor is chosen to be the well-known geodesic distance (GD) measure. The recognition task is performed on SHREC08 database for both correspondence methods and the effect of feature (GD) vector size as well as landmark positions on the recognition accuracy were argued.