spectral mesh processing

refer to paper :Spectral Geometry Processing with Manifold Harmonics and Spectral Mesh Processing(SIGGRAPH Asia 2009 Course).
I implement manifold harmonics transform by matlab

(note:great software Graphite also already implement MHT with some alternate methods, mine is cotant method)

(I didn't use ARPACK before,and for saving time,matlab already packaged ARPACK for important step:eigen-problem in MHT,so I use matlab)

(in future,I will learn ARPACK and implement MHT by c/c++)
(note:Graphite's MHT has some problems, as Bruno levy(a big fish)says,FEM not use 'function' dot-product as his paper in Graphite,so FEM has problem in shape reconstruction,i.e inverted MHT(I already fix it,but there exsit other problems ...) ,

also like cotant method has problem on some models in inverted MHT, but mine is ok, I guess it may be eigen-problem with ARPACK in Graphite or SuperLU...).

I show shape reconstruction with rator model,two smoothed model(100 and 300 MHB).

after, I will also implement MHT based on FEM.

NOTE: HERE, my says has wrong expression, i.e my cotant method named manifold harmonics transform: not correct, please refer above two paper. In course paper: there are two laplacian operators:1.Graph Laplacians(e.g:mine) 2.laplace beltrami(e.g: FEM), Bruno levy (in other paper) call manifold harmonics in laplace beltrami operator,i.e the continuous settings , not the discrete settings(mine).

also google some resources: like Spectral Graph Theory.

I already implement FElumpedmass method , seeing sreenshot from my photos.

conception clear!!!!!!!!!!!!!!!!!!!!!!!!!

Laplace operator Laplace–Beltrami operator Laplace–de Rham operator

from wikipedia:

http://en.wikipedia.org/wiki/Laplace_operator

http://en.wikipedia.org/wiki/Laplace%E2%80%93Beltrami_operator

In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds. This more general operator goes by the name Laplace–Beltrami operator, after Laplace and Eugenio Beltrami. Like the Laplacian, the Laplace–Beltrami operator is defined as the divergence of the gradient, and is a linear operator taking functions into functions. The operator can be extended to operate on tensors as the divergence of the covariant derivative. Alternatively, the operator can be generalized to operate on differential forms using the divergence and exterior derivative. The resulting operator is called the Laplace–de Rham operator.