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

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

Mar 28, 2024 282 likes •697 views

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

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SLIDE 1

Visualizing Geometric Proofs

3D surface diagrams

Lukas Heidemann

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SLIDE 2

Diagrams

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SLIDE 3

0-diagrams

1

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SLIDE 4

1-diagrams: bead diagrams

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SLIDE 5

1-diagrams: bead diagrams

2

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SLIDE 6

2-diagrams: string diagrams

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SLIDE 7

2-diagrams: string diagrams

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SLIDE 8

2-diagrams: string diagrams

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SLIDE 9

3-diagrams: surface diagrams

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SLIDE 10

3-diagrams: reassociate

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SLIDE 11

3-diagrams: snake elimination

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SLIDE 12

3-diagrams: double snake elimination

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SLIDE 13

3-diagrams: stacked cups

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Scaffolds

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SLIDE 15

2-diagram

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SLIDE 16

2-scaffold

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2-scaffold: slices

regular regular regular singular singular singular singular

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2-scaffold: edges

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SLIDE 19

2-scaffold: edges

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SLIDE 20

2-scaffold: edges

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SLIDE 21

2-scaffold: edges

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2-scaffold with layout

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SLIDE 23

2-scaffold without layout

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Layout via Linear Program

  • 1. Distance constraints
  • 2. Average constraints
  • 3. Height constraints

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3-diagram

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SLIDE 26

3-scaffold points

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SLIDE 27

3-scaffold edges

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SLIDE 28

3-scaffold contraction

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SLIDE 29

3-scaffold contraction

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3-scaffold contraction

?

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3-scaffold contraction

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Geometry

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SLIDE 33

Surface

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SLIDE 34

Surface

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Surface

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SLIDE 36

Surface

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SLIDE 37

Surface

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SLIDE 38

Conclusion

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SLIDE 39

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.

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SLIDE 40

Thank you!

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