Least eccentric ellipses for geometric Hermite interpolation

John C. Femiani, Chia Yuan Chuang, Anshuman Razdan

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)141-149
Number of pages9
JournalComputer Aided Geometric Design
Volume29
Issue number2
DOIs
StatePublished - Feb 2012

Fingerprint

Hermite Interpolation
Ellipse
Interpolants
Tangent line
Interpolation
Circle
Unit tangent vector
Point of inflection
Rational Solutions
Space Curve
Rational Curves
Interpolation Problem
Control Points
Curve
Target
Theorem

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 journalArticle

Femiani, John C. ; Chuang, Chia Yuan ; Razdan, Anshuman. / Least eccentric ellipses for geometric Hermite interpolation. In: Computer Aided Geometric Design. 2012 ; Vol. 29, No. 2. pp. 141-149.
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