Visualizing Geometric Proofs 3D surface diagrams Lukas Heidemann - PowerPoint PPT Presentation

Visualizing Geometric Proofs 3D surface diagrams Lukas Heidemann

Diagrams

0-diagrams 1

1-diagrams: bead diagrams 2

1-diagrams: bead diagrams 2

2-diagrams: string diagrams 3

2-diagrams: string diagrams 4

2-diagrams: string diagrams 5

3-diagrams: surface diagrams 6

3-diagrams: reassociate 7

3-diagrams: snake elimination 8

3-diagrams: double snake elimination 9

3-diagrams: stacked cups 10

Scaffolds

2-diagram 11

2-scaffold 12

2-scaffold: slices singular regular singular regular singular regular singular 13

2-scaffold: edges 14

2-scaffold: edges 15

2-scaffold: edges 16

2-scaffold: edges 17

2-scaffold with layout 18

2-scaffold without layout 19

Layout via Linear Program 1. Distance constraints 2. Average constraints 3. Height constraints 20

3-diagram 21

3-scaffold points 22

3-scaffold edges 23

3-scaffold contraction 24

3-scaffold contraction 25

3-scaffold contraction ? 26

3-scaffold contraction 27

Geometry

Surface 28

Surface 29

Surface 30

Surface 31

Surface 32

Conclusion

Long way to go 1. Transparency, silhouettes, etc. 2. Exportable illustrations for inclusion in papers. 3. Interactivity. 4. Bugs and performance. 5. Building software that is useful to you. 33

Thank you! 34