Planar shape manipulation using approximate geometric primitives

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

Robust Complete Path Planning in the Plane

We present a complete path planning algorithm for a plane robot with three degrees of freedom and a static obstacle. The part boundaries consist of n linear and circular edges. The algorithm constructs and searches a combinatorial representation of the robot free space. Its computational complexity is O((n4 + c3) log n) with c3ε O(n6) the number of configurations with three simultaneous contacts between robot and obstacle edges. The algorithm is implemented robustly using our adaptive-precision controlled perturbation library. The program is fast and memory efficient, is provably accurate, and handles degenerate input