Chan's algorithm

In computational geometry, Chan's algorithm, named after Timothy M. Chan, is an optimal output-sensitive algorithm to compute the convex hull of a set ${\displaystyle P}$ of ${\displaystyle n}$ points, in 2- or 3-dimensional space. The algorithm takes ${\displaystyle O(n\log h)}$ time, where ${\displaystyle h}$ is the number of vertices of the output (the convex hull). In the planar case, the algorithm combines an ${\displaystyle O(n\log n)}$ algorithm (Graham scan, for example) with Jarvis march (${\displaystyle O(nh)}$), in order to obtain an optimal ${\displaystyle O(n\log h)}$ time. Chan's algorithm is notable because it is much simpler than the Kirkpatrick–Seidel algorithm, and it naturally extends to 3-dimensional space. This paradigm has been independently developed by Frank Nielsen in his Ph. D. thesis.

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