Quadratic-cycloidal curves
For a given \(\alpha\), such that \(0<\alpha< 2\pi\), normalized B-basis for the space \(Q ([0,\alpha]) \equiv \) span \(\{1, t, t^2, \)cos \( t , \)sin \(t \}, t \in [0,\alpha]\) is known [see \textit{E. Mainar, J. M. Peña}, and \textit{J. Sánchez-Reyes}, Comput. Aided Geom. Des. 18, No. 1, 37--60 (2001; Zbl 0972.68157)]. Assuming \(0<\alpha<\pi\) and using the elements of the foregoing B-basis, a quadratic-cycloidal (QC)-spline segment is defined in terms of a new basis which is shown to be normalized total positive.This enables the authors to derive some shape preserving properties of QC-splines. It is also shown that as \(\alpha\) tends to zero, the limit of a QC-B-spline curve approaches a B-spline curve of degree 4.
scientific article; zbMATH DE number 2057588