Phasefields

This repository contains the numerical code for my master thesis. It provides a GUI application for the hierarchical optimization of phasefields. Some of the highlights are :

• A phasefield parameterization of the Yamabe energy, which can be used to compute surface segmentations which can be conformally mapped to the plane with low area distortion.

• A topological penalty term which enforces connectedness of the segments.

• A hierarchical segmentation scheme, which combines multiple phasefields, to compute segmentations with more than two segments.

The GUI also support some other niceties like editing phasefields using a brush-like tool, mesh IO via Assimp, making and exporting videos using ffmpeg, color optimization for segmentations etc.

You can try it out in your browser, but be aware the webassembly build might have one or two bugs ;). There are four compiled in resources which can be loaded by choosing the corresponding resource at 'IO/Experiment' and then pressing the 'Load Experiment' button. Then just need to press the '/Optimization Options/Optimize' button and the phasefield should start moving.

Here is a teaser image of the optimization of the Yamabe energy for varying interface length penalties

Building

You will need a C++20 conformant compiler and CMake for project file generation.

Before building make sure that git submodules are downloaded. You can download them via:

git submodules update --init --recursive

Build files are generated using cmake. If you want to build the project on a unix like platform you can use the following command

mkdir build && cd build && cmake .. -DCMAKE_BUILD_TYPE=Release && make -j

There are some more dependencies which you can enable using the following cmake options:

• Loading meshes using Assimp (PHASEFIELD_WITH_IO).
• Exporting videos via ffmpeg (PHASEFIELD_WITH_IO)
• Solving constrained optimization problems using Ipopt (PHASEFIELD_WITH_IPOPT).
• Checking derivatives via AD using ADOL-C (PHASEFIELD_WITH_ADOLC).
• Solving the Yamabe equation faster using Suite Sparse (PHASEFIELD_WITH_SUITESPARSE).
• A different lBFGS implementation provided by ceres-solver (PHASEFIELD_WITH_CERES).
• Threading using TBB (PHASEFIELD_WITH_TBB).

Related Work

The diffuse Yamabe energy draws inspiration from the paper 'Variational Surface Cutting' for which there is also code available here