  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 Thurston
geometries. Based on the procedure first described in [10], we are able to give
the isoptic surface of any segment implicitly. We rely heavily on the
calculations published in [41, 42]. As a special case, we examine the Thales
sphere in both geometries, which are called Thaloid. In our work we will use
the projective model of $S^2\times R$ and $H^2\times R$ described by E.
Moln\'ar in [20].

Metric Geometry