Construction of interpolating space curves with arbitrary degree of geometric continuity

This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in , applicable to any given set of ordered points in . The construction involves four essential components: local functions, blending functions, redistributing functions, and gluing functions. The resultin...

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Bibliographic Details
Published inSampling theory, signal processing, and data analysis Vol. 23; no. 2
Main Authors Hu, Tsung-Wei, Lai, Ming-Jun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Subjects
Abstract Harmonic Analysis
Machine Learning
Mathematics
Mathematics and Statistics
Original Article
Signal,Image and Speech Processing
Interpolation
CAGD
Spline
Smooth curve
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Summary:This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in , applicable to any given set of ordered points in . The construction involves four essential components: local functions, blending functions, redistributing functions, and gluing functions. The resulting curve possesses favorable attributes, including geometric smoothness, locality, the absence of cusps, and no self-intersections. Numerical examples show that the curve interpolates the given points without overshooting or undershooting. Moreover, the algorithm is adaptable to various scenarios, such as preserving convexity, interpolating sharp corners, and ensuring sphere preservation. This paper substantiates the efficacy of the proposed method through the presentation of numerous examples, offering a practical demonstration of its capabilities.
ISSN:2730-5716
2730-5724
DOI:10.1007/s43670-025-00108-1