Dual Bézier curves and convexity preserving interpolation
type: Item
instance of: scholarly article
title: Dual Bézier curves and convexity preserving interpolation
zbMATH Open document ID: 0769.65002
DOI: 10.1016/0167-8396(92)90042-N
author: J. M. Carnicer
published in: Computer Aided Geometric Design
publication date: 1993-01-18T00:00:00Z
review text: Convexity preserving interpolation has been considered by several points of view. The problem reduces to the problem of finding a strictly convex function on an interval with prescribed function values and derivatives at the end points \(f(x_ 0) = y_ 0\), \(f(x_ 1) = y_ 1\), \(f'(x_ 0) = m_ 0\), \(f'(x_ 1) = m_ 1\). In the present paper the author studies this approach by a geometrical point of view. He considers the equivalent problem of finding an arc of a curve \(\Gamma\) passing through the points \(P_{00}(x_ 0,y_ 0)\), \(P_{11}(x_ 1,y_ 1)\) with non-vertical tangents \(y = t_{00}(x)\), \(y = t_{11}(x)\) at these two points.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 85947
zbMATH Keywords: Bézier curves
zbMATH Keywords: convexity preserving interpolation
reviewed by: A. Laforgia
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 85947