Abstract
The problem of finding all intersections between two space curves is one of the fundamental problems in computer-aided geometric design and computational geometry. This article proposes a new iterative/subdivision hybrid algorithm for this problem. We use a test based on Kantorovich’s theorem to detect the starting point from which Newton’s method converges quadratically and a subdivision scheme to exclude certain regions that do not contain any intersections. Our algorithm is guaranteed to detect all intersections in the domain for nondegenerate and non-ill-posed cases.
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Srijuntongsiri, G. An iterative/subdivision hybrid algorithm for curve/curve intersection. Vis Comput 27, 365–371 (2011). https://doi.org/10.1007/s00371-010-0543-x
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DOI: https://doi.org/10.1007/s00371-010-0543-x