Journal for Geometry and Graphics 30 (2026), No. 1, 061--074
Copyright by the authors licensed under CC BY SA 4.0
Blending of Parametric Curves via Smoothing Functions with Global Cn-Continuity
Volodymyr V. Gotsulenko
Institute of Engineering Thermophysics, National Academy of Sciences, Kyiv, Ukraine
e-mail_gosul@ukr.net
This paper proposes a geometric modeling approach for blending parametric curves based on a class of smoothing functions ensuring global Cn-continuity. The method constructs a composite curve that smoothly connects two given spatial curves by introducing a transition segment defined as a convex combination of their coordinate functions. The smoothing functions are formulated on the unit interval and extended to arbitrary parameter domains through affine transformations while satisfying prescribed boundary and differentiability conditions of arbitrary order. The resulting framework is independent of the specific parameterizations of the input curves and provides explicit analytical representations of the blended geometry. Several illustrative examples demonstrate the flexibility and robustness of the proposed approach, highlighting its potential for applications in geometric modeling, surface generation, and shape morphing.
Keywords: Geometric modeling, curve blending, smoothing function, parametric curve, C-n-continuity.
MSC: 51M04
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