Coding and Compression of Three Dimensional Meshes by Planes

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows not to consider topological aspects of the problem (connectivity information among vertices and edges) since by means of the planes we construct the polyhedron uniquely. Due to the fact that the topological data is ignored this representation provides high degree of compression. Also planes based representation provides a compression of geometrical data because most of the faces of the polyhedron are not triangles but polygons with more than three vertices.Comment: 10 pages, 7 figure

Zonoids with an equatorial characterization

summary:It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid belongs to the class

A representation for convex bodies

In this paper we extend the representation for the support function of centrally symmetric convex bodies to arbitrary convex bodies. We discuss some questions on unique determination of convex bodies and consider some classes of convex bodies in terms of support functions

A representation for convex bodies

In this paper we extend the representation for the support function of centrally symmetric convex bodies to arbitrary convex bodies. We discuss some questions on unique determination of convex bodies and consider some classes of convex bodies in terms of support functions

Waste disposal facilities monitoring based on high-resolution information features of space images

In the article there is represented and solved the problem of space images recognition for the presence of solid household and industrial waste without binarization. The methods of stochastic geometry and mathematical analysis are used. In the work there is proposed an algorithm based on a trace transformation using discrete orthogonal transformations (DOT) to minimize the attribute space and carry out studies on correctness by Tikhonov. For the implementation of the algorithm there are used elements of mathematical analysis, wavelet analysis, functional analysis, theory of discrete orthogonal transformations, methods for deciphering space images in the problem of stochastic scanning of space images based on the formation of a triplet attribute with minimization of attribute space using DOT. The development a trace matrices and the selection of informative features by stochastic geometry to find WDF from high-resolution space images are investigated from the point of view of DOT apparatus application. A study of the sustainability task was also performed. The proposed technique was tested using the example of space photographs with a WDF image. Conclusions are drawn on the use of the method proposed in this article for the task of automatic computer generation and selection of informative features for determining waste disposal facilities from high-resolution space images. It is proposed to use the Tikhonov regularization method to introduce stability in this task