blum medial axis
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2016 ◽  
Vol 60 (2) ◽  
pp. 461-480 ◽  
Author(s):  
Graham Mark Reeve ◽  
Farid Tari

AbstractWe study the Minkowski symmetry set of a closed smooth curveγin the Minkowski plane. We answer the following question, which is analogous to one concerning curves in the Euclidean plane that was treated by Giblin and O’Shea (1990): given a pointponγ, does there exist a bi-tangent pseudo-circle that is tangent toγboth atpand at some other pointqonγ? The answer is yes, but as pseudo-circles with non-zero radii have two branches (connected components) it is possible to refine the above question to the following one: given a pointponγ, does there exist a branch of a pseudo-circle that is tangent toγboth atpand at some other pointqonγ? This question is motivated by the earlier quest of Reeve and Tari (2014) to define the Minkowski Blum medial axis, a counterpart of the Blum medial axis of curves in the Euclidean plane.


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