UDC 004.925.86
ABOUT THE REDUCED INTERPOLATION ERRORS OF NON-ANALYTICAL CURVES
Yu. N. Kosnikov, Dr. in technical sciences, full professor, full professor, PSU, Penza, Russia;
orcid.org/0000-0003-4717-7682, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
D. R. Abubekerov, postgraduate student, PSU, Penza, Russia;
orcid.org/0009-0005-5364-3258, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Many applied problems of digitizing and visualizing flat contours require the use of interpolation meth ods. Known interpolation methods often have limitations that hinder their use in visualization systems. Mathematical expressions to estimate the error in interpolating planar contours based on a set of control points using a new type of geometric primitive are proposed. The geometric primitive is a section of a com posite curve connecting several control points. Mathematically, it is described by two parametrically related equations consisting of several terms. Their number corresponds to the number of control points connected by a primitive. The terms are weighted values of mixing functions. The sets of control points of adjacent sec tions intersect at several points to achieve smooth transition between the sections. To estimate the interpola tion error using the primitive proposed a measure of divergence between interpolant curve and test curve is used. The divergence is determined by the Cartesian distances between primitive currents and test curve points. Normalized root-mean-square deviation and normalized discrete Hausdorff distance reduced to the diagonal of test curve domain are used. The experiment conducted on several different mixing functions and different lengths of interpolant sections confirmed the correctness of the estimates proposed.
Key words: : interpolation, mixing function, composite curve, curve compartment, reduced normalized standard deviation, reduced discrete Hausdorff distance.