Abstract
We present a rational Bézier solution to the geometric Hermite interpolation problem. Given two points and respective unit tangent vectors, we provide an interpolant that can reproduce a circle if possible. When the tangents permit an ellipse, we produce one that deviates least from a circle. We cast the problem as a theorem and provide its proof, and a method for determining the weights of the control points of a rational curve. Our approach targets ellipses, but we also present a cubic interpolant that can find curves with inflection points and space curves when an ellipse cannot satisfy the tangent constraints.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 141-149 |
| Number of pages | 9 |
| Journal | Computer Aided Geometric Design |
| Volume | 29 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2012 |
Keywords
- Bézier curves
- Conics
- Ellipses
- Hermite interpolation
ASJC Scopus subject areas
- Modeling and Simulation
- Automotive Engineering
- Aerospace Engineering
- Computer Graphics and Computer-Aided Design
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Cite this
Femiani, J. C., Chuang, C. Y., & Razdan, A. (2012). Least eccentric ellipses for geometric Hermite interpolation. Computer Aided Geometric Design, 29(2), 141-149. https://doi.org/10.1016/j.cagd.2011.10.006