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Snap rounding of Bézier curves

Eigenwillig, Arno and Kettner, Lutz and Wolpert, Nicola

December 2006, 39 pages.

Status: available - back from printing

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},