New algorithm to find isoptic surfaces of polyhedral meshes

作者：Nagy Ferenc^*; Kunkli Roland; Hoffmann Miklos

来源：Computer Aided Geometric Design, 2018, 64: 90-99.

DOI：10.1016/j.cagd.2018.04.001

• Isoptic surface
• Spherical geometry
• Triangulated meshes
• Subdivision 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, 2016 Wolfram Mathematica Inc, 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 E-3, 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.

• 出版日期2018-8