New algorithm to find isoptic surfaces of polyhedral meshes

The isoptic surface of a three-dimensional shape is recently defined by Csima and Szirmai (2016) as the generalization of the well-known notion of isoptics of curves. In that paper, an algorithm has also been presented to determine isoptic surfaces of convex polyhedra. However, the computation of isoptic surfaces by that algorithm requires extending computational time and CAS resources (in Csima and Szirmai, 2016Wolfram MathematicaInc, 2015 was used), even for simple regular polyhedra. Moreover, the method cannot be extended to concave shapes. In this paper, we present a new searching algorithm to find points of the isoptic surface of a triangulated model in E3, which works for convex and concave polyhedral meshes as well. Alternative definition of the isoptic surface of a shape is also presented, and isoptic surfaces are computed based on this new approach as well.