Steklov Spectral Geometry for Extrinsic Shape Analysis

This repo contains an implementation of the paper

• Steklov Spectral Geometry for Extrinsic Shape Analysis.

  Yu Wang, Mirela Ben-Chen, Iosif Polterovich and Justin Solomon.

  ACM Transactions on Graphics 38(1). (Presented at) ACM SIGGRAPH 2019.

  OpenAccessPaper.\ arXiv:1707.07070. Paper.

We provide a docker container for ease of setting up dependencies. Alternatively you can install all depenciencies manually following the Dockerfile.

To build the docker image, run:

sudo docker build -t steklov-py2 .

And start the container as:

sudo docker run -it steklov-py2

As a starting example, in the docker container, the following code

cd steklov-core/include
python example_eigen.py

will solve the Steklov eigenvalue problem on a test mesh (unit sphere).

If the code runs correctly, you should expect output eigenvalues like

[0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5...]

(Not exactly the numerics since the input is an polygon mesh approximating the sphere. In my case, I got:

[0.01004436 0.98603902 0.98855039 0.99042844 1.99039739 1.99604268
 1.99926872 2.00135786 2.00480661 3.00011596 3.00434902 3.00624768
 3.00751291 3.00917211 3.01196417 3.0124851  4.00351974 4.00446321
 4.00626848 4.00839618 4.00995248 4.01127969 4.01239172 4.01256993
 4.01452445 5.00554734 5.00791356 5.00822096 5.00949137 5.0104079
 5.01165094 5.01183372 5.01255543 5.01390004 5.01497264 5.01618703
 6.00388227 6.0089286  6.00975284 6.01054685 6.01299514 6.01395933
 6.01752202 6.01898825 6.01980104 6.02056086 6.02172131 6.02300891
 6.02432555]

Email wangyu9@mit.edu for any question with the code.