Planar shape manipulation using approximate geometric primitives

Abstract

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is $\bigo(n\log n+k)$ for an input of size $n$ with $k=\bigo(n^2)$ consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms in floating point using sequences of six set operations and Euclidean transforms on shapes bounded by curves of algebraic degree~1 to~6. We test generic and degenerate inputs. Keywords: robust computational geometry, plane subdivisions, set operations.