An inexpensive bounding representation for offsets of quadratic curves

  • Authors:
  • Erik Ruf

  • Affiliations:
  • Microsoft Research

  • Venue:
  • Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
  • Year:
  • 2011

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Abstract

We describe a simple mechanism for bounding the portion of the plane lying between a quadratic Beizer curve segment and its offset curve at distance d. Instead of comprising one or more partial bounding polygons, our representation consists of only a single approximate offset curve segment, also in quadratic Bezier form. Evaluated on a corpus of real-world curves, this technique avoids 68--99% of antialias-distance queries and 41--96% of brush-parameter queries. A proof of correctness is provided.