Least Squares Approximation By G1 Piecewise Parametric Cubes

Abstract

Parametric piecewise cubic polynomials are used throughout the computer graphics industry to represent geometric curved shapes. The exploration of the use of parametric curves and surfaces can be viewed as the birth of Computer Aided Geometric Design (CAGD). In this thesis, least squares approximation is used for fitting a geometrically continuous (G1) piecewise parametric cubic polynomial to a sequence of ordered points in the plane. Cubic Bezier curves are used as a basis. The parameterization, the control points, the number of knots, and their locations are determined as part of the approximation process. A development of the algorithm is given, along with some results for a variety of sets of ordered data.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1993
Accession Number
ADA277978

Entities

People

  • Marion R. Holmes

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computer Graphics
  • Computer Science
  • Computer-Aided Design
  • Computers
  • Continuity
  • Coordinate Systems
  • Curve Fitting
  • Differential Equations
  • Equations
  • Graphics
  • Interpolation
  • Mathematics
  • Numerical Analysis
  • Polynomials
  • Probability
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.