Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer

Characterizing the finiteness of the Hausdorff distance between two algebraic curves

“…The results obtained in this paper do not provide an alternative method to this question, but a way of applying important and effective existing methods to the case in which some assumptions on the input curves are not satisfied, as for instance the boundedness (see e.g. [2,3,9,10], etc.) or the finiteness of the Hausdorff distance between them (see [7,8]).…”

“…Many authors have addressed some problems in this frame (see e.g. [2,3,[7][8][9][10], etc.) but all of them assume that the given curves are bounded or that the Hausdorff distance between them is finite.…”

“…Once one has ensured that the Hausdorff distance between the two curves is finite, some additional existing methods can be applied to estimate the Hausdorff distance between two not bounded curves (see [8]), or for a chosen bounded frame of the input curves (see e.g. [2,3,9,10], etc. ).…”

“…This approach assumes that the two curves are fairly close to each other. In [2], a real-time algorithm for computing the precise Hausdorff distance between two planar freeform curves is presented. The algorithm is based on an effective technique that approximates each curve with a sequence of G 1 biarcs within an arbitrary error bound.…”

Comparison of three bounding regions with cubic convergence to planar freeform curves

“…This is even a longer history than some of the early developments of bounding volume hierarchies (mostly in the mid 90s) such as sphere tree [9,22,23], BOXTREE [5], AABB (Axis-Aligned Bounding Box) tree [26], OBB (Oriented Bounding Box) tree [8], k-DOP (k-Discrete Oriented Polytope) [16] and SSV (Swept Sphere Volume) tree [18]. Nevertheless, it is a relatively recent trend that fat arcs are extensively used in the acceleration of geometric algorithms for freeform planar curves [2,3,10,13].…”