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 2012 |
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Keywords
- Bézier curves
- Conics
- Ellipses
- Hermite interpolation
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Aerospace Engineering
- Automotive Engineering
- Modeling and Simulation
Cite this
Least eccentric ellipses for geometric Hermite interpolation. / Femiani, John C.; Chuang, Chia Yuan; Razdan, Anshuman.
In: Computer Aided Geometric Design, Vol. 29, No. 2, 02.2012, p. 141-149.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Least eccentric ellipses for geometric Hermite interpolation
AU - Femiani, John C.
AU - Chuang, Chia Yuan
AU - Razdan, Anshuman
PY - 2012/2
Y1 - 2012/2
N2 - 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.
AB - 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.
KW - Bézier curves
KW - Conics
KW - Ellipses
KW - Hermite interpolation
UR - http://www.scopus.com/inward/record.url?scp=84055200797&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84055200797&partnerID=8YFLogxK
U2 - 10.1016/j.cagd.2011.10.006
DO - 10.1016/j.cagd.2011.10.006
M3 - Article
VL - 29
SP - 141
EP - 149
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
SN - 0167-8396
IS - 2
ER -