Simple Parametrization

This repo containes implementations related to parametrization algorithms.

Algorthims

• SLIM (with and without fixed boundary)
• Tutte

Utils

• Mesh cut
• Seam path definition

Requirements

All the algorithms rely on CGAL or libigl. Other dependencies:

• boost
• Eigen3
• gmp
• cmake

Compile

mkdir build
cd build
cmake .. && make -j4

If an error regarding "COMP0048 version" appears then please edit build/_deps/libigl-src/CMakeLists.txt commenting out ligigl version.

SLIM

SLIM parametrization can be compute with:

./build/slim your_obj_file.obj

this will generate a new file your_obj_file_slim.obj containing the parametrize mesh to the unit disk. Note this algorithm requires a surface homeomorphic to a disk. If has a higher genus, then it is possible to cut it.

Free SLIM

SLIM parametrization without a fixed boundary can be compute with:

./build/slim your_obj_file.obj

this will generate a new file your_obj_file_freeslim.obj containing the parametrize mesh. Note this algorithm requires a surface homeomorphic to a disk. If has a higher genus, then it is possible to cut it.

Tutte

SLIM parametrization can be compute with:

./build/tutte your_obj_file.obj

this will generate a new file your_obj_file_tutte.obj containing the parametrize mesh to a disk. Note this algorithm requires a surface homeomorphic to a disk. If has a higher genus, then it is possible to cut it.

Seam path definition

A seam path is computed based on an ordered set of points it cut through. These points can be defined in pairs. For example:

4199 3041
3041 410

the seam will list all vertex starting from vertex #4199 to vertex #3041. Then from vertex #3041 to vertex #410. The seam path is defined based on Dijkstra algorithm.

Running:

./build/dijkstra_seam your_obj_file.off your_vertex_list.txt

produces a txt file your_obj_file.off.selection.txt containing the seam path.

Seam cut

Once the seam path is defined, it is possible to cut the mesh:

./build/cut your_obj_file.off your_obj_file.off.selection.txt

this produces a new obj file your_obj_file_cut.obj.