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

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

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

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

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

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

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

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

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

Discrete Dictionary 1.Linear 2. 3.Intrinsic Local 7. 8.Maximum Principle 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)

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

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

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

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

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

Schönhardt Polytope

Lifting

Lifting and Reciprocal Diagrams

dual edge

Lifting and Reciprocal Diagrams dual edge