Calculating the Self-Intersections of Bezier Curves.

Abstract

A user-friendly divide-and-conquer algorithm is presented for finding all the self intersection points of a parametric curve in the Bernstein-Bezier representation. The underlying idea of the algorithm is to deal with the Bexier polygon instead of the curve description itself. By alternately subdividing the Bezier polygon and estimating the self intersection regions the self intersection points are finally approximated by straight line intersections of the refined Bezier polygons. The algorithm also calculates the parameter values of the self intersection points. In addition to the convex hull and the approximation property of the Bezier polygon the working of the algorithm is based on a very intuitive angle criterion. Keywords: Bezier curves; Spline curves; Intersection.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1988
Accession Number
ADA192371

Entities

People

  • Dieter Lasser

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Civil Engineering
  • Computations
  • Computer Graphics
  • Computer Science
  • Computer-Aided Design
  • Computers
  • Equations
  • Graphics
  • Interactive Graphics
  • Mathematics
  • Polynomials
  • Rotation
  • Schools
  • User Friendly

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.