Modelling of Segments of One-Dimensional Contours According to the Specified Conditions

Abstract

The formation of one-dimensional contours on the basis on the given conditions is one of the most popular geometric modeling problems. The problem is solved by variative discrete geometric modeling, which assumes the formation of intermediate points for the initial set of condensation points. The discrete model of the curve consists of a point sets, given geometric characteristics and a condensation algorithm.
 A discretely presented curve (DPC) is formed by a condensation of the initial point set of an arbitrary configuration in areas on which it is possible to ensure a monotonic change in the values of its characteristics. Monotone plots are joined at special points. Every three consecutive points of the duodenum define an adjacent plane. Four adjacent planes passing through two consecutive points limit the tetrahedron. The chain of consecutive tetrahedrons defined on all segments is the region of the location of the smooth curve of the constant stroke line interpolating the initial point sets. The torsion on the sections of the DPC is estimated by the value of the ratio of the angle between adjacent adjacent planes to the length of the corresponding chord of the accompanying broken line. The point of thickening is assigned inside the tetrahedron of the DPC. As a result of successive condensations, we obtain a continuous bypass of a constant stroke, at each point of which there is a single position of the main trihedron. The point of condensation is assigned in such a way that the values of the torsion in the duodenum points change monotonically. This ensures that the torsion values are regular at the points of the bypass.
 The imposition of additional conditions on the DPC formed requires the definition of the corresponding region of a possible solution within the DPC arrangement tetrahedron.