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Snap rounding of Bézier curves

Eigenwillig, Arno and Kettner, Lutz and Wolpert, Nicola

MPI-I-2006-1-005. December 2006, 39 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We present an extension of snap rounding
from straight-line segments (see Guibas and Marimont, 1998)
to Bézier curves of arbitrary degree,
and thus the first method for geometric rounding
of curvilinear arrangements.
Our algorithm takes a set of intersecting Bézier curves
and directly computes a geometric rounding of their true arrangement,
without the need of representing the true arrangement exactly.
The algorithm's output is a deformation of the true arrangement
that has all Bézier control points at integer points
and comes with the same geometric guarantees as in
straight-line snap rounding: during rounding, objects do not move
further than the radius of a pixel, and features of the
arrangement may collapse but do not invert.
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  AUTHOR = {Eigenwillig, Arno and Kettner, Lutz and Wolpert, Nicola},
  TITLE = {Snap rounding of {B}{\'e}zier curves},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2006-1-005},
  MONTH = {December},
  YEAR = {2006},
  ISSN = {0946-011X},