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In this work, we examine the isoptic surface of line segments in the$S^2\times R$ and $H^2\times R$ geometries, which are from the 8 Thurstongeometries. Based on the procedure first described in [10], we are able to givethe isoptic surface of any segment implicitly. We rely heavily on thecalculations published in [41, 42]. As a special case, we examine the Thalessphere in both geometries, which are called Thaloid. In our work we will usethe projective model of $S^2\times R$ and $H^2\times R$ described by E.Moln\'ar in [20].

Isoptic surfaces of segments in $S^2\times R$ and $H^2\times R$ geometries