Least eccentric ellipses for geometric Hermite interpolation

John C. Femiani, Chia Yuan Chuang, Anshuman Razdan

Research output: Contribution to journalArticle

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