
Reshaping Convex Polyhedra
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Reviews / Votes
"A nice feature of the text is the abundance of carefully worked illustrative examples, as well as the care and attention paid to when and where algorithms are available for performing various tasks suggested by the theoretical developments. . I believe that numerous individuals who are keen on exploring convex polyhedra, the rigidity of polyhedra, combinatorial operations involving polyhedra, and similar topics will discover a wealth of intriguing content within this text." (Gordon Ian Williams, Mathematical Reviews, October, 2025)
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Persons
Joseph O'Rourke is Professor at Smith College. Prior to joining Smith in 1988 to found and chair the computer science department, Joseph O'Rourke was an assistant and then associate professor at Johns Hopkins University. His research is in the field of computational geometry. In 2001, he was awarded the NSF Director's Award for Distinguished Teaching Scholars. He is also a professor of mathematics.
Costin Vîlcu
is affiliated with the Simion Stoilow Institute of Mathematics of the Romanian Academy. His research interests include geometry of Alexandrov surfaces and intrinsic geometry of convex surfaces, including polyhedral convex surfaces.
Content
I. Tailoring for Every Body.- 1. Introduction to Part I.- 2. Preliminaries.- 3. Domes and Pyramids.- 4. Tailoring via Sculpting.- 5. Pyramid Seal Graph.- 6. Algorithms for Tailoring via Sculpting.- 7. Crests.- 8. Tailoring via Flattening.- 9. Applications of Tailoring.- II. Vertex-Merging and Convexity.- 10. Introduction to Part II.- 11. Vertex-Merging Reductions and Slit Graphs.- 12. Planar Spiral Slit Tree.- 13. Convexity on Convex Polyhedra.- 14. Minimal-length Enclosing Polygon.- 15. Spiral Tree on Polyhedron.- 16. Unfolding via Slit Trees.- 17. Vertices on Quasigeodesics.- 18. Conclusions.- Bibliography.- References.- Index.
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