05_prolongation_vector

Intrinsic Tangent Vector Prolongation

This is an example to show how to construct a prolongation operator (a.k.a. interpolation) for tangent vector fields on our intrinsically simplified mesh. Optionally, it can also compute a connection Laplace matrix and mass matrix on the coarsened mesh. To run this example, please compile it using the common cmake/make routine:

cd 05_prolongation_scalar/
mkdir build
cd build
cmake ..
make -j8

Once compiled, one can run the example by typing

./main

and you will see the following example:

This example shows a smooth vector field computed by running Globally-Optimal Direction Fields on the simplified mesh, and using our prolongation operator to transfer this field to the original mesh.

Usage

You can simplify meshes by running the ./main executable. By default, this simplifies the provided dragon_fat.obj mesh down to 500 vertices. You can also specify a mesh and target coarseness as input by running

./main /path/to/mesh.obj nVertices

The input mesh must be a manifold and connected obj file.

The script takes a variety of arguments.

flag	purpose
--area_weight=0	Influence of vertex area on coarsening. 0: none, while 1: pure area weighting. (default=0)
--prolongation_path=prolongation_matrix.spmat	File to save vector prolongation matrix to. If not set, the prolongation matrix is not saved
--laplace_path=laplace_matrix.spmat	File to save simplified connection Laplacian matrix to. If not set, the connection Laplacian is not saved
--mass_path=mass_matrix.spmat	File to save simplified vector mass matrix to. If not set, the mass matrix is not saved
--no_viz	Write requested output files without showing visualization
--help, -h	Display help

File formats

Sparse matrices are is exported as a list of triplets. Explicitly, each line of the output file contains the row index, column index, and value of some entry of the matrix. These indices are 1-indexed to make it easy to load in Matlab.

Complex matrices are written to a pair of files, encoding their real and imaginary parts as separate, real sparse matrices.