Laplacian-Smoothing-and-Spectral-reconstruction

An implementation of the Laplace Beltrami computation, with different applications.

Implementation of Laplacian Mesh Processing. Implementation of Laplacien Mesh Spectral Reconstruction. Implementation of Implicit Laplacian Smoothing.

Coded in C++, with the LibIGL library.

Usage

Dependencies

Libraries needed :

• LibIGL . Put the libigl source code folder two levels above this repository.
• Spectra (for large scale eigen value computations). Put the Spectra source code folder one level above this repository, or change the include_directories and in the CMake to the corresponding paths.

Building and running the code

Build using CMake and the CMakeLists.txt provided. Run the Laplacian_processing_viewer target. Change the line string mesh_file_name with the right filenames of your point clouds, in main.cpp.

Using the interface

The libigl GUI menu I built has several options you can manipulate :

• Play with the "Curvature - Spectral reconstruction - Smoothing" slider to change the visualization mode : 0 : visualize the different curvatures - 1 : visualize spectral reconstruction - 2 : visualize mesh smoothing
• If in "Spectral reconstruction" mode, change the values of "Number of eigen vectors" to set the number of eigen vectors used for reconstruction
• If in "Smoothing" mode, choose between "Explicit mode" and "Implicit mode", to perform explicit or implicit smoothing iterations.
• If in "Smoothing" mode : change the value of "Lambda explicit/implicit smoothing" to change the value of the smoothing parameter. Change the "Number of smoothing iterations" using the +/- buttons.
• If in "Smoothing" mode : click "Smoothing iteration" to perform an iteration of the smoothing algorithm. Press "Reset" to go back to the initial state.
• You can add Gaussian noise to the vertex positions before smoothing, by changing the value of "Amount of noise", and setting the "Add noise" slider to 1.