This is the source code for the examples in the following paper:

• Yue Peng, Bailin Deng, Juyong Zhang, Fanyu Geng, Wenjie Qin, and Ligang Liu. 2018. Anderson acceleration for geometry optimization and physics simulation. ACM Trans. Graph. 37, 4, Article 42 (July 2018).

The code has been tested with the following systems and compilers:

• Ubuntu 18.04 using GCC 7.3;
• macOS High Sierra 10.13.6, using Apple Clang 9.1 (without OpenMP support) and GCC 8.2 (with/without OpenMP support).

Compile the code using the following steps:

1. Before compiling the code, make sure Eigen (version 3.3+) is installed, using either of the following methods:

   • Download the package from the Eigen homepage, unzip it into a folder eigen within the folder AndersonOpt/external. Make sure the file external/eigen/Eigen/Dense can be found.
   • Alternatively, use a package manager of your operating system to install Eigen, e.g.:
     • on Ubuntu, use the command apt-get install libeigen3-dev;
     • on macOS, install homebrew and run brew install eigen.

2. GLUT is required to compile the simulation code.

3. Create a folder build within the folder AndersonOpt.

4. From within the build folder, run the following commands:

   $ cmake -DCMAKE_BUILD_TYPE=Release ..
   $ make
   

   • On mac, the default Apple clang compiler does not support OpenMP. To enable OpenMP, first install the homebrew GCC using command brew install gcc. This should install the latest gcc with associated commands gcc-X and g++-X where X is the version number, e.g. gcc-8 and g++-8. Then use the following commands to compile the code with homebrew GCC:

   $ cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_C_COMPILER=gcc-8 -DCMAKE_CXX_COMPILER=g++-8 ..
   $ make
   

5. Afterwards, there should be five executables in the build folder: PlanarityOpt, WireMeshOpt, ARAP2D, ARAP3D and TetMeshSimulation.

6. Test models are provided in folder Test_files.

• Use the following commands for planar quad mesh and wire mesh optimization respectively:

   $ PlanarityOpt INPUT_POLY_MESH REF_TRI_MESH OPTION_FILE OUPUT_MESH
  

   $ WireMeshOpt INPUT_POLY_MESH REF_TRI_MESH OPTION_FILE OUTPUT_MESH
  

  • INPUT_POLY_MESH is the input mesh to be optimized.
  • REF_TRI_MESH is the triangle mesh for the reference shape.
  • OPTION_FILE is a text file storing the algortihm parameters. An example file is provided as Options.txt.
  • OUTPUT_MESH is the output mesh file name.

• To perform 2D as-rigid-as-possible optimization:

   $ ARAP2D PROBLEM_DEF_MESH INIT_MESH HANDLE_IDX_FILE HANDLE_COORDS_FILE OPTION_FILE OUTPUT_MESH
  

  • PROBLEM_DEF_MESH is a mesh that defines the rest shape.
  • INIT_MESH is the initial shape of the mesh to be optimized.
  • HANDLE_IDX_FILE is a text file storing the handle vertex indices.
  • HANDLE_COORDS_FILE is a file that stores the 2D coordinates of handle vertices.

• To perform 3D as-rigid-as-possible optimization:

   $ ARAP3D PROBLEM_DEF_MODEL_NAME INIT_COORD_MODEL_NAME HANDLE_IDX_FILE HANDLE_COORDS_FILE OPTION_FILE OUTPUT_MESH
  

  • PROBLEM_DEF_MODEL_NAME is the name (without suffix) for the ele and node files that describe the tet mesh of the rest shape.
  • INIT_COORD_MODEL_NAME is the name (without suffix) for the ele and node files that describe the initial shape of the tet mesh to be optimized.
  • HANDLE_IDX_FILE is a text file storing the handle vertex indices.
  • HANDLE_COORDS_FILE is a file that stores the 3D coordinates of handle vertices.
  • OUTPUT_MESH is a mesh that stores the boundary surface of the optimized tet mesh.

• To perform physics simulation for elastic tet mesh:

   $ TetMeshSimulation MODEL_NAME HANDLE_IDX_FILE OPTION_FILE
  

  • INIT_COORD_MODEL_NAME is the name (without suffix) for the ele and node files that describe the initial shape of the tet mesh.
  • HANDLE_IDX_FILE is a text file storing the handle vertex indices. The handle vertices are fixed during simulation.

  The simulation is controlled using the following keys:

  • Press s to simulate one frame.
  • Press 1 to start the demo.
  • Press e to suspend demo.
  • Press Esc to exit the program.

• Below are example commands using the data provided in Test_files.

  • $ ARAP2D bar.obj bar_Init.obj bar_Handle.txt xy_bar.txt Options.txt output.obj
  • $ ARAP3D boy boy_Init boy_handle.txt xyz_boy.txt Options.txt output.obj
  • $ PlanarityOpt bunny_poly.obj bunny_ref.obj Options.txt output.obj
  • $ WireMeshOpt MaleTorso.obj MaleTorso_target.obj Options.txt output.obj
  • $ TetMeshSimulation armadillo armadilloH.txt Options.txt

The code is released under BSD 3-Clause License.

Please contact Bailin Deng <bldeng@gmail.com> or Yue Peng <echoyue@mail.ustc.edu.cn> if you have any comments or questions.