MPI-I-2006-1-005

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.