Simultaneous containment of several polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Computational Geometry: Theory and Applications
MPFR: A multiple-precision binary floating-point library with correct rounding
ACM Transactions on Mathematical Software (TOMS)
Snap rounding of Bézier curves
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Controlled perturbation for certified geometric computing with fixed-precision arithmetic
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.