Uncertain lines and circles with dependencies

Classical computational geometry algorithms handle geometric constructs whose shapes and locations are exact. However, many real-world applications require the modeling of objects with geometric uncertainties. Existing geometric uncertainty models cannot handle dependencies among objects. This results in the overestimation of errors. We have developed the Linear Parametric Geometric Uncertainty Model, a general, computationally efficient, worst-case, linear approximation of geometric uncertainty that supports dependencies among uncertainties. In this paper, we present the properties of the uncertainty zones of a line and circle, defined using this model, and describe efficient algorithms to compute them. We show that the line's envelope has linear space complexity and is computed in low polynomial time. The circle's envelope has quadratic complexity and is also computed in low polynomial time.