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Closed cap
condition under the cap construction algorithm
Mercedes Sandu, Shuyi Weng and Jade Zhang |
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Vol. 17 (2024), No. 5, 723–736
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Abstract |
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Every polygon can be companioned by a cap polygon such that and serve as two parts of the boundary surface of a polyhedron . Pairs of vertices on and are identified successively to become vertices of . We study the cap construction that asserts equal angular defects at these pairings. We exhibit a linear relation that arises from the cap construction algorithm, which in turn demonstrates an abundance of polygons that satisfy the closed cap condition, that is, those that can successfully undergo the cap construction process. |
Keywords
polygon, algorithm, cap construction, closed cap condition,
computational geometry
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Mathematical Subject Classification
Primary: 52-08, 52B55, 52C30, 68U05
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Milestones
Received: 30 September 2022
Revised: 10 June 2023
Accepted: 10 June 2023
Published: 21 November 2024
Communicated by Kenneth S. Berenhaut
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Authors |
| Mercedes Sandu | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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| Shuyi Weng | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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| Jade Zhang | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
