# Computing the Geometric Intersection Number of Curves

Symposium on Computational Geometry, pp. 1-49, 2019.

EI

Keywords:

Computational topologycombinatorial geodesiccurves on surfacesintersection number

Abstract:

The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e., of any curve obtained by continuous deformation. Given a curve c represented by a closed walk of length at most ℓ on a combinatorial surface of complexity n, we describe simple algorithms to (1) compute the g...More

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