G 2 Hermite Interpolation by Segmented Spirals

Yuxuan Zhou, Yajuan Li () and Chongyang Deng
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Yuxuan Zhou: School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
Yajuan Li: School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
Chongyang Deng: School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

Mathematics, 2022, vol. 10, issue 24, 1-20

Abstract: A curve with single-signed, monotonically increasing or decreasing curvatures is referred to as a planar spiral. G 2 Hermite data are spiral G 2 Hermite data for which only interpolation by a spiral is possible. In this study, we design segmented spirals to geometrically interpolate arbitrary C-shaped G 2 Hermite data. To separate the data into two or three spiral data sets, we add one or two new points, related tangent vectors and curvatures. We provide different approaches in accordance with the various locations of the external homothetic centers of two end-curvature circles. We then match new data by constructing two or three segmented spirals. We generate at most three piecewise spirals for arbitrary C-shaped data. Furthermore, we illustrate the suggested techniques with several examples.

Keywords: piecewise spiral; monotone curvature; spiral G 2 Hermite data; G 2 Hermite interpolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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