# Lectures on Discrete Differential Geometry Weeks 5 & Lectures on Discrete Differential Geometry Weeks 5 & 7 Etienne Vouga March 5, 2014 Properties of LaplaceBeltrami 1. Linear 1. 2. 2. Local

3. Intrinsic 3. 4. 4. Maximum Principle Discrete Dictionary 1. Linear 1. Local

2. 2. 3. Intrinsic 3. Maximum Principle 4. Linear ( is a matrix) 5.

Discrete Dictionary 1. Linear 1. Local 2. 2. 3. Intrinsic 3. Maximum Principle 4.

Linear ( is a matrix) 5. Discrete Dictionary 1. Linear 1. Maximum Principle 2. Linear ( is a matrix)

3. Intrinsic 4. 5. 6. Local 7. func. of lengths & angles Discrete Dictionary 1. Linear 1. Maximum Principle 2.

Linear ( is a matrix) 3. Intrinsic 4. func. of lengths & angles 5. is negative semidefinite 6. Local 7.

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

5. is negative semidefinite 6. Local 7. Discrete Dictionary 1. Linear 1. Maximum Principle 2.

Linear ( is a matrix) 3. Intrinsic 4. func. of lengths & angles 5. is negative semidefinite 6. Local 7.

Discrete Dictionary 1. Linear Linear ( is a matrix) 2. 3. Intrinsic func. of lengths & angles 4. is negative semidefinite

5. 6. Local 7. 8. Maximum Principle ( for planar meshes) ion is c e r

p r a line Discrete Dictionary 1. Linear Linear ( is a matrix) 2. 3. Intrinsic func. of lengths & angles

4. is negative semidefinite 5. 6. Local 7. 8. Maximum Principle ( for planar meshes)

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

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

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

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

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

func. of lengths & angles Is there a perfect Laplacian? Weight Formula Intrinsic? Weights Positive? Rank n-1?

Linear Precision? Schnhardt Polytope Lifting Lifting and Reciprocal Diagrams Lifting and Reciprocal Diagrams Lifting and Reciprocal

Diagrams dual edge Lifting and Reciprocal Diagrams dual edge