Modeling Geometric Objects by Expanding the Dimensionality of Space

Abstract:

We consider the method of determining the exit points from the plane in the point calculus, which is analogous to the vector product of vectors in the vector calculus. It is generalized both in the direction of reducing the dimensionality of space, and in the direction of increasing it. The mathematical apparatus for determining the exit points from the space of different dimensionality is presented. The approach to modeling geometric objects with the help of points that expand the dimensionality of space has been proposed and implemented. As a result, by using the exit segment length function of different dimensionality the set of flat curves in one-dimensional simplex and spatial curves in two-dimensional ones are defined. Examples of definition of an elliptic cylinder and a spatial line on an elliptic cylinder in a planar simplex are given.

Keywords:

Geometric modeling, point calculus, point out of plane, extension of space dimensionality, projections, reconstruction of geometric objects