DESIGNING DISCRETE NETWORKS AND THE SURFACE ON THE BASIS OF ISOTROPIC B-SPLINE

Abstract

Modeling geometric objects in isotropic space allows us to simplify a number of calculations related to the calculation of differential characteristics. To create the ability to control the curved contours of objects, it is advisable to apply parametric curves based on characteristic polygons. For each type of such curves, there are limitations to the calculation of coordinates and lengths in isotropic space. Studies on modeling isotropic B-splines and based on them grids and surfaces are local in nature and require more detailed consideration.

The paper proposes to model isotropic B-splines based on the recursive Cox de Boer formulas. The coordinates of the points for the spline are calculated based on the equal to zero side lengths of the characteristic polygons. Examples of constructed splines for different types of nodal vectors are given. It is shown that some types of nodal vectors do not allow the curve to pass through the start and end points of polygons. In this case, it is necessary to carry out adjustments to the nodal vector.

The authors of the work developed an algorithm for modeling discrete grids and surfaces based on B-splines. All calculations are made in a complex space. When displaying geometric objects, the selection of the real part and the transition to the real space are carried out. As an example, visualization of the grid and surface based on an open uniform nodal vector is given.

To research isotropic discrete curves, grids and surfaces based on B-splines, C # software was created for the .Net Core platform.

Further research is related to the study of the influence of nodal vectors on the basis of an isotropic B-spline and surfaces.

Keywords: isotropic curve, B-spline, discrete grids, discrete surfaces based on isotropic splines.