Fast Detection of the Geometric Form of Two-Dimensional Cubic Bézier Curves

This paper appears in issue Volume 7, Number 3.
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Abstract

This paper presents and algorithm that determines, from the control points of a cubic two-dimensional Bézier durve, the geometric form of the curve (arch, single inflection, two inflections, cusp, loop, or the degenerate forms staight line or point). The algorithm is based on a case analysis of the signs fo the determinants of the control-point triples. Source code is avaialble online.

Author Information

Stephen Vincent, Adobe Systems, 1551800 Stokes Street, San Jose, CA 95126 svincent@ca.inter.net

Source Code

Source code for a C implementation of this algorithm is available here: BezType.c (6K HTML text). The code was empirically tested against a large sample of randomly generated curves whose geometric characteristics were determined by subdividing the curve into a large number of small linear sections and exhaustively testing for curve types.

BibTeX Entry

@article{Vincent02,
  author = "Stephen Vincent",
  title = "Fast Detection of the Geometric Form of Two-Dimensional Cubic Bézier Curves",
  journal = "journal of graphics, gpu, and game tools",
  volume = "7",
  number = "3",
  pages = "43-51",
  year = "2002",
}