Geometric Hermite interpolation with Tschirnhausen cubics

✍ Scribed by D.S. Meek; D.J. Walton

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 673 KB
• Volume: 81
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(97)00066-6

✦ Synopsis

Explicit formulae are found that give the unique Tschirnhausen cubic that solves a geometric Hermite interpolation problem. That solution is used to create a planar G1 spline by joining segments of Tschirnhausen cubits. If the geometric Hermite data is from a smooth function, the Tschirnhausen cubic approximates the smooth function. The error in the approximation of a short segment of length h can be expressed as a power series in h. The error is O(h4) and the coefficient of the leading term is found.