1. Lectures on Discrete Differential Geometry – Weeks 5 & 7 Etienne Vouga March 5, 2014 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A AAAAAA

2. Properties of Laplace-Beltrami 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle

3. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix)

4. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix)

5. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix) func. of lengths & angles

6. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix) func. of lengths & angles is negative semidefinite

7. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix) func. of lengths & angles is negative semidefinite

8. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix) func. of lengths & angles is negative semidefinite

9. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix) func. of lengths & angles is negative semidefinite ( for planar meshes) “linear precision”

10. Discrete Dictionary 1.Linear 2. 3.Intrinsic 4. 5. 6.Local 7. 8.Maximum Principle Linear ( is a matrix) func. of lengths & angles is negative semidefinite ( for planar meshes)

11. Standard Form Linear ( is a matrix) func. of lengths & angles is negative semidefinite ( for planar meshes)

12. Standard Form Linear ( is a matrix) func. of lengths & angles is negative semidefinite ( for planar meshes)

13. Standard Form Linear ( is a matrix) func. of lengths & angles func. of lengths & angles is negative semidefinite ( for planar meshes)

14. Standard Form Linear ( is a matrix) func. of lengths & angles func. of lengths & angles is negative semidefinite ( for planar meshes)

15. Standard Form Linear ( is a matrix) func. of lengths & angles func. of lengths & angles is negative semidefinite ( for planar meshes)

16. Standard Form Linear ( is a matrix) func. of lengths & angles func. of lengths & angles is negative semidefinite ( for planar meshes)

17. Is there a “perfect” Laplacian? Weight Formula Intrinsic? Weights Positive? Rank n-1? Linear Precision?

18. Schönhardt Polytope

19. Lifting

20. Lifting and Reciprocal Diagrams

22. dual edge

23. Lifting and Reciprocal Diagrams dual edge