The Curve of Least Energy.

Abstract

Here we search for the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computer-aided design, curves have been sought which maximize 'smoothness'. The curve discussed here is the one arising in this way from a commonly used measure of smoothness. The human visual system may use such a curve when it constructs a subjective contour. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1981
Accession Number
ADA098054

Entities

People

  • B. K. P. Horn

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Calculus Of Variations
  • Cartesian Coordinates
  • Computer-Aided Design
  • Curvature
  • Differential Equations
  • Eccentricity
  • Equations
  • Fresnel Integrals
  • Integrals
  • New Jersey
  • Orientation (Direction)
  • Quadrants
  • Rational Functions
  • Shape
  • Square Roots
  • Symmetry
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computer Vision.
  • Instructional Design and Training Evaluation.