06_delaunay_refinement

Intrinsic simplification & intrinsic Delaunay refinement

This is an example to show how to combine our intrinsic simplification with intrinsic Delaunay refinement to produce guaranteed quality intrinsic triangulations. This example can be compiled using the common cmake/make routine:

cd 06_delaunay_refinement/
mkdir build
cd build
cmake ..
make -j8

Once compiled, one can run the example by typing

./main

and you will see the following example:

Simple Remeshing by Refinement & Simplification

In Section 6.3 of the paper, we show that by doing intrinsic refinement followed by simplification, we can perform preliminary intrinsic remeshing. This can be achieved by adding a few arguments:

1. switching the option to --refinement_time=BEFORE to perform refinement before simplification.
2. adding non-zero area weight in the simplification --area_weight=0.1 so that the newly added vertices from the refinement will not be removed immediately (because they have zero Gaussian curvature).

For instance, one can run

/main ../../meshes/boxpart.obj 200 --area_weight=0.1 --refinement_time=BEFORE

to intrinsically remesh the boxpart model to 200 vertices

Usage

You can simplify meshes by running the ./main executable. By default, this simplifies the provided dragon_fat.obj mesh down to 500 vertices, and then performs intrinsic Delaunay refinement, adding another 200 vertices to guarantee a high quality triangulation. 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 with UV coordinates.

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)
--refinement_time=AFTER	Whether to perform intrinsic Delaunay refinement before or after simplification. (Options: BEFORE, AFTER, BOTH, NEITHER; default=AFTER)
--texture_width=2048	Texture width in pixels. Generated textures are always square (default=2048)
--texture_path=texture.png	File to save the texture to. The texture will be saved as a png. If not set, the texture is not saved
--prolongation_path=prolongation_matrix.spmat	File to save prolongation matrix to. If not set, the prolongation matrix is not saved
--laplace_path=laplace_matrix.spmat	File to save simplified Laplace matrix to. If not set, the laplace matrix is not computed
--mass_path=mass_matrix.spmat	File to save simplified mass matrix to. If not set, the mass matrix is not computed
--vector_prolongation_path=vector_prolongation_matrix.spmat	File to save vector prolongation matrix to. If not set, the prolongation matrix is not saved
--connection_laplace_path=laplace_matrix.spmat	File to save simplified connection Laplacian matrix to. If not set, the connection Laplacian is not computed
--vector_mass_path=mass_matrix.spmat	File to save simplified vector mass matrix to. If not set, the mass matrix is not computed
--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.

Textures are saved as png images.