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Intersection points of planar curves can be computed

Article type: Research Article

Authors: Weihrauch, Klaus; *

Affiliations: Faculty of Mathematics and Computer Science, FernUniversität in Hagen, Germany

Correspondence: [*] Corresponding author. klaus.weihrauch@fernuni-hagen.de.

Abstract: Consider two paths ϕ,ψ:[0;1]→[0;1]2 in the unit square such that ϕ(0)=(0,0), ϕ(1)=(1,1), ψ(0)=(0,1) and ψ(1)=(1,0). By continuity of ϕ and ψ there is a point of intersection. We prove that from ϕ and ψ we can compute closed intervals Sϕ,Sψ⊆[0;1] such that ϕ(Sϕ)=ψ(Sψ).

Keywords: Computable analysis, planar curves

DOI: 10.3233/COM-210311

Journal: Computability, vol. 11, no. 2, pp. 113-133, 2022

Published: 13 May 2022
Price: EUR 27.50
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