Reshaping Convex Polyhedra
This monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrov’s Gluing Theorem, shortest paths and cut loci, Cauchy’s Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer Nature Switzerland
2024, 2024
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| Edition: | 1st ed. 2024 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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