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Spherical occlusion diagrams (SOD) were introduced by Viglietta as an axiomatic framework to analyze the visibility maps of points in the interior of a nonconvex polyhedron from which no vertex is visible; and conjectured that every SOD is realizable as a visibility map of a point in some polyhedron. In this paper, we disprove this conjecture, and construct an SOD that is not realizable as a visibility map.

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Nonrealizable Planar and Spherical Occlusion Diagrams

  • 会议论文

  • 发表日期：

    2026年

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  • Kimberly Kokado,
  • Csaba D. Tóth

摘要

Spherical occlusion diagrams (SOD) were introduced by Viglietta as an axiomatic framework to analyze the visibility maps of points in the interior of a nonconvex polyhedron from which no vertex is visible; and conjectured that every SOD is realizable as a visibility map of a point in some polyhedron. In this paper, we disprove this conjecture, and construct an SOD that is not realizable as a visibility map.