Curvature-based blending of closed planar curves

• Published in: Graphical models Vol. 76; no. 5; pp. 263 - 272
• Main Authors: Saba, Marianna, Schneider, Teseo, Hormann, Kai, Scateni, Riccardo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-09-2014; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Blending; Computer science; control theory; systems; Curvature; Curves; Discretization; Exact sciences and technology; Interpolation; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Pattern recognition. Digital image processing. Computational geometry; Sciences and techniques of general use; Strategy; Interpolation; Blending; Curvature; Curves; Discretization; Problem solving; Metric; Curve fitting; Computer animation
• ISSN: 1524-0703; 1524-0711
• DOI: 10.1016/j.gmod.2014.04.005

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A common way of blending between two planar curves is to linearly interpolate their signed curvature functions and to reconstruct the intermediate curve from the interpolated curvature values. But if both input curves are closed, this strategy can lead to open intermediate curves. We present a new algorithm for solving this problem, which finds the closed curve whose curvature is closest to the interpolated values. Our method relies on the definition of a suitable metric for measuring the distance between two planar curves and an appropriate discretization of the signed curvature functions.