Can you elaborate on how the cotan laplacian becomes the one on the grid?

What about meshes with more than 4 edges? How can we approximate Laplacian? Do we triangulate them first?

Why donâ€™t we use the definition of the Laplacian (i.e. sum of second derivatives) to approximate it?

How would the triangle mesh operation be broken down into convolutions like in the grid case?

What do values at the vertices u and i represent? What are the underlying functions?

What do the convolutions on the triangle mesh look like?

Can you elaborate on how the cotan laplacian becomes the one on the grid?

What about meshes with more than 4 edges? How can we approximate Laplacian? Do we triangulate them first?

Why donâ€™t we use the definition of the Laplacian (i.e. sum of second derivatives) to approximate it?

How would the triangle mesh operation be broken down into convolutions like in the grid case?

What do values at the vertices u and i represent? What are the underlying functions?

What do the convolutions on the triangle mesh look like?