New algorithm to find isoptic surfaces of polyhedral meshes. (English) Zbl 1476.65025
Summary: The isoptic surface of a three-dimensional shape is recently defined by G. Csima and J. Szirmai [ibid. 47, 55–60 (2016; Zbl 1418.51011)] 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 [loc. cit.], Wolfram Mathematica, Version 10.3 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 \(\mathbb{E}^3\), 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.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
Citations:
Zbl 1418.51011Software:
MathematicaReferences:
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