FORMATION OF BASIS TRIANGLES WHEN SIMULATING A CIRCUIT ACCORDING TO THE GIVEN CONDITIONS

Abstract

The formation of complex functional surfaces based on an array of points is an urgent task of geometric modeling. Creating a geometric model of such a surface involves the formation of a discrete ruled framework. The linear elements of the frame are one-dimensional contours. The paper solves the problem of modeling flat one-dimensional contours with a monotonic change in curvature. The source data for modeling the contour is an ordered point series that represents a discretely presented curve (DPC).

The contour is formed by thickening the initial point series of an arbitrary configuration in areas where it is possible to provide a monotonic change in the values of characteristics.

After assigning the positions of the tangents in the initial points, we get a chain of basic triangles (BT) bounded by the tangents passing through two consecutive points and the chord that connects these points. After that, the ranges of radiuses of curvature are determined, which can be obtained on the basis of the formed BT chain. Within the obtained ranges, the radiuses of curvature in the initial points are assigned. Assigned characteristics are provided as a result of local thickening of the curve section.

Inside the BT, the position of the tangent condensation and the condensation point on it are assigned. As a result, we get two new BT. The positions of the point and the tangent of the condensation are assigned within the ranges providing a second order of smoothness and a monotonic change of radiuses of curvature along the contour.

The formed sections of monotonous DPC are joined with the second order of smoothness at the points of change of increase and decrease of the radius of curvature and inflection points. The developed algorithm will allow the formation of contours with a regular change in the curvature of various fixation orders.

Keywords: discretely presented curve (DPC), radius of curvature, monotonicity of change of characteristics, method of condensation, barycentric coordinates, basic triangle.