Abstract
In this note we prove that the corner cutting procedure preserves continuity properties, i.e., a sequence of polygons obtained in this way belongs to the Lipschitz class of the same constant and exponent. As a consequence this also holds for all functions or curves obtained as the limit of this procedure, such as the Bernstein polynomials, Bézier and spline parametric curves, etc.
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Supported by NSF and SF of National Education Committee of China.
Supported by the Research Council of Slovenija.
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Yuyu, F., Kozak, J. Cutting corners preserves Lipschitz continuity. Appl. Math. 9, 31–34 (1994). https://doi.org/10.1007/BF02662023
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DOI: https://doi.org/10.1007/BF02662023