Finding compact coordinate representations for polygons and polyhedra
IBM Journal of Research and Development
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Practical segment intersection with finite precision output
Computational Geometry: Theory and Applications
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Computational Geometry: Theory and Applications
Inner and outer rounding of set operations on lattice polygonal regions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Complete subdivision algorithms, I: intersection of Bezier curves
Proceedings of the twenty-second annual symposium on Computational geometry
An approximate arrangement algorithm for semi-algebraic curves
Proceedings of the twenty-second annual symposium on Computational geometry
Improved output-sensitive snap rounding
Proceedings of the twenty-second annual symposium on Computational geometry
Iterated snap rounding with bounded drift
Proceedings of the twenty-second annual symposium on Computational geometry
An intersection-sensitive algorithm for snap rounding
Computational Geometry: Theory and Applications
Reliable and efficient computational geometry via controlled perturbation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Iterated snap rounding with bounded drift
Computational Geometry: Theory and Applications
Technical note: Robust cascading of operations on polyhedra
Computer-Aided Design
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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.