Reshaping Convex Polyhedra 9783031475115, 9783031475108
The focus of this monograph is converting―reshaping―one 3D convex polyhedron to another via an operation the authors cal
119 51
English Pages 526 Year 2024
Table of contents :
Cover
Front Matter
Part 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. Algorithm for Tailoring via Sculpting
7. Crests
8. Tailoring via Flattening
9. Applications of Tailoring
Part 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. Unfoldings via Slit Trees
17. Vertices on Quasigeodesics
18. Conclusions and Open Problems
Back Matter
Cover
Front Matter
Part 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. Algorithm for Tailoring via Sculpting
7. Crests
8. Tailoring via Flattening
9. Applications of Tailoring
Part 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. Unfoldings via Slit Trees
17. Vertices on Quasigeodesics
18. Conclusions and Open Problems
Back Matter
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