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This article proposes a technique for the geometrically stable modeling ofhigh-degree B-spline curves based on S-polygon in a float format, which willallow the accurate positioning of the end points of curves and the direction ofthe tangent vectors. The method of shape approximation is described with thepurpose of providing geometrical proximity between the original andapproximating curve. The content of the notion of a harmonious, regular form ofB-spline curve's S-polygon in a float format is revealed as a factor inachieving a high-quality of fit for the generated curve. The expediency of theshape modeling method based on S-polygon in a float format at the end portionsof the curve for quality control of curve modeling and editing issubstantiated. The results of a comparative test are presented, demonstratingthe superlative efficacy of using the Mineur-Farin configuration forconstructing constant and monotone curvature curves based on an S-polygon in afloat format. The findings presented in this article confirm that it ispreferable to employ the principle of "constructing a control polygon of aharmonious 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 ofthe Bezier curve. Recommendations are given for prospective studies in thefield of applying the technique of constructing a high-quality B-spline curvesto the approximation of log-aesthetic curves, Ziatdinov's superspirals, etc.The authors of the article developed a technique for constructing smoothconnections of B-spline curves with ensuring a high order of smoothness of thecomposite curve. The proposed techniques are implemented in theFairCurveModeler program as a plug-in to engineering CAD systems.

Techniques for modeling a high-quality B-spline curves by S-polygons in a float format