Least eccentric ellipses for geometric Hermite interpolation

John C. Femiani; Chia Yuan Chuang; Anshuman Razdan

doi:10.1016/j.cagd.2011.10.006

Least eccentric ellipses for geometric Hermite interpolation

John C. Femiani, Chia Yuan Chuang, Anshuman Razdan

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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	https://doi.org/10.1016/j.cagd.2011.10.006
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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abstract = "We present a rational B{\'e}zier 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.",

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T1 - Least eccentric ellipses for geometric Hermite interpolation

AU - Femiani, John C.

AU - Chuang, Chia Yuan

AU - Razdan, Anshuman

PY - 2012/2/1

Y1 - 2012/2/1

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

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DO - 10.1016/j.cagd.2011.10.006

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EP - 149

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

SN - 0167-8396

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ER -

Least eccentric ellipses for geometric Hermite interpolation

Abstract

Keywords

ASJC Scopus subject areas

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