  This article proposes a technique for the geometrically stable modeling of
high-degree B-spline curves based on S-polygon in a float format, which will
allow the accurate positioning of the end points of curves and the direction of
the tangent vectors. The method of shape approximation is described with the
purpose of providing geometrical proximity between the original and
approximating curve. The content of the notion of a harmonious, regular form of
B-spline curve's S-polygon in a float format is revealed as a factor in
achieving a high-quality of fit for the generated curve. The expediency of the
shape modeling method based on S-polygon in a float format at the end portions
of the curve for quality control of curve modeling and editing is
substantiated. The results of a comparative test are presented, demonstrating
the superlative efficacy of using the Mineur-Farin configuration for
constructing constant and monotone curvature curves based on an S-polygon in a
float format. The findings presented in this article confirm that it is
preferable to employ the principle of "constructing a control polygon of a
harmonious form (or the Mineur-Farin configuration) of a parametric polynomial"
to a B-spline curve's S-polygon in a float format, and not to a B-polygon of
the Bezier curve. Recommendations are given for prospective studies in the
field of applying the technique of constructing a high-quality B-spline curves
to the approximation of log-aesthetic curves, Ziatdinov's superspirals, etc.
The authors of the article developed a technique for constructing smooth
connections of B-spline curves with ensuring a high order of smoothness of the
composite curve. The proposed techniques are implemented in the
FairCurveModeler program as a plug-in to engineering CAD systems.
