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Geometric Hermite interpolation

✍ Scribed by K. Höllig; J. Koch

Book ID
107919482
Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
791 KB
Volume
12
Category
Article
ISSN
0167-8396

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We present several Hermite-type interpolation methods for rational cubics. In case the input data come from a circular arc, the rational cubic will reproduce it.

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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

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✍ Lianghong Xu; Jianhong Shi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 128 KB

This paper considers the geometric Hermite interpolation for spacial curves by parametric quartic Bézier curve. In additon to position and tangent direction, the curvature vector is prescribed at each knot. We prove that under appropriate assumptions the interpolant exists locally with one degree of