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Conference Paper

Snap Rounding of Bézier Curves

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Eigenwillig,  Arno
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Kettner,  Lutz
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Wolpert,  Nicola
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Eigenwillig, A., Kettner, L., & Wolpert, N. (2007). Snap Rounding of Bézier Curves. In Proceedings of the Twenty-Third Annual Symposium on Computational Geometry (SCG'07) (pp. 158-167). New York, NY: ACM.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-20B6-5
Abstract
We present an extension of snap roundingfrom straight-line segments (see Guibas and Marimont, 1998)to Bézier curves of arbitrary degree, and thus the first method for geometric roundingof curvilinear arrangements.Our algorithm takes a set of intersecting Bézier curvesand 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 arrangementthat has all Bézier control points at integer pointsand comes with the same geometric guarantees as instraight-line snap rounding: during rounding, objects do not movefurther than the radius of a pixel, and features of thearrangement may collapse but do not invert.