Algebraic Representations for Volumetric Frame Fields
This code includes algorithms for computing volumetric (octahedral and odeco) frame fields, described in detail in our preprint:
Palmer, D., Bommes, D., & Solomon, J. (2019). Algebraic Representations for Volumetric Frame Fields. arXiv preprint arXiv:1908.05411.
First, remember to build and install the Mosek Fusion API as described here.
The following commands will compile all MEX files and add the code to the MATLAB path.
cd src/batchop mexbuild /path/to/tbb/include cd ../sdp mexbuild /path/to/tbb/include /path/to/mosek/9.0 cd ../.. install
The main commands for computing fields are
Some tetrahedral meshes in
Medit format are included in the
meshes directory for convenience. To load a mesh, use
mesh = ImportMesh('meshes/rockerarm_91k.mesh'); % Medit format
We also support meshes in
mesh = ImportMesh('path/to/file.node'); % Tetgen .node/.ele format
Computing Frame Fields
The following commands compute octahedral and odeco fields by MBO with random initialization:
qOcta = MBO(mesh, OctaMBO, , 1, 0); qOdeco = MBO(mesh, OdecoMBO, , 1, 0);
For modified MBO as described in our paper, set the diffusion time multiplier and exponent as follows:
qOcta = MBO(mesh, OctaMBO, , 50, 3); qOdeco = MBO(mesh, OdecoMBO, , 50, 3);
The following lines compute octahedral and odeco fields by RTR with specified initial fields. Drop the second argument for random initialization.
qOcta = OctaManopt(mesh, qOcta); qOdeco = OdecoManopt(mesh, qOdeco);
To visualize an octahedral or odeco field, use
VisualizeResult, which plots the integral curves and singular structure, e.g.,
PlotInterpolatedFrames plots field-oriented cubes at specified sample points:
PlotInterpolatedFrames(q, mesh.tetra, samples)
samples is a $k \times 3$ matrix of sample positions.
We have included scripts for generating (MATLAB versions of) figures that appear in the paper in the
EnergyTestcompares energy divergence behavior of octahedral and odeco fields, as in Figure 8 in the paper.
PrismFiguresgenerates a figure similar to Figure 1 in the paper, showing scaling behavior of an odeco field.
To verify the exactness of SDP projection into the octahedral and odeco varieties, respectively, execute
for a sufficiently large value of
The following three scripts display comparisons to previous work. These require a patched version of the code released with [Ray et al. 2016]. To avoid any possible copyright issues, we are not including this code in this public release. Please contact the authors if you need it.
ProjectionComparisongenerates figures like Figure 4 in the paper.
ConvergenceComparisonsgenerates figures like Figures 5 and 6 in the paper:
GenerateComparisonsgenerates a table like that in our supplemental document: