Hole-Measures

Software for computing the hole measures (thickness and breadth-balls) of topological holes from a 3D volumetric object represented by polygonal mesh of its surface. The theoretical work linked with this repository has been published in a special issue of Computer Aided Design: Computing Geometrical Measures of Topological Holes.

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Requirement

This project requires the CGAL library with Boost and QT5 (on Linux distributions, sudo apt-get install libcgal-dev libcgal-qt5-dev should do the job). The library PHAT is already in the repository (include/phat/). The project also requires Cmake with version above 2.8.10.

Usage

This software can read a polygonal surface mesh in OFF format and computes the hole-balls. Two different approaches are developed:

• on one hand, the link approach pretends to compute every thickness and breadth-balls of an object as well as their homological link (i.e. the pairing between thickness and breadth-balls that corresponds to the same hole).
• On the other hand, the medial axes approach is a faster method that computes thickness and breadth-balls without their homological link.

To compile, create a build directory in the git initial folder and run cmake .. ; make in it. It will compile and create two executable programs: main_link and main_medial.

Link approach

The main_link executable corresponds to the link approach. More precisely, it computes the hole-balls and the TB-pairs using the Voronoi filtration.

Usage: main_link object.off [-E] [-o output_file] [-h] Compute hole measures of the 3D object object.off using the Voronoi filtration. By default, store only the present hole measures in the object.link.tb file using the tb format (see Output section).

Some parameters can be used:

• -E, --exhaustive : store every hole measures (not only the present hole measures).
• -o output_file : write the hole measures in output_file.
• -h, --help : display the usage message.

Medial axes approach

The main_medial executable corresponds to the medial axes approach. More precisely, it computes the hole-balls the inner and outer medial axis filtration. Note that it produces arbitrary TB-pairs that do not corresponds to the real ones.

Usage: main_medial object.off [-I] [-O] [-E] [-c] [-o output_file] [-h] Compute hole-balls of the 3D object object.off using the medial axes filtration. By default, store only the present hole measures in the object.medial.tb file using the .tb format (see Output section).

Some parameters can be used:

• -I, --in : compute only holes measures of the inner medial axis filtration.
• -O, --out : compute only holes measures of the outer medial axis filtration.
• -E, --exhaustive : store every hole measures (not only the present hole measures).
• -c, --critical : take into account Delaunay critical points to correct wrong hole-balls.
• -o output_file : write the hole measures in output_file.
• -h, --help : display the usage message.

Output

A hole measure is a pair of two hole-balls (the T-ball and the B-ball) that can be associated to a topological hole of an volumetric object. The software computes hole measures and store them in a .tb file. In the .tb file, every pair of hole-balls is outputted in a line as

dim t t_x t_y t_z b b_x b_y b_z

Where:

• dim is the dimension of the considered hole (0, 1 or 2 for 3D objects);
• the thickness-ball is a ball of radius t centered at point (t_x t_y t_z);
• the breadth-ball is a ball of radius b centered at point (b_x b_y b_z);

Note that there is always a thickness-ball of dimension 0 that has no corresponding breadth-ball. It appears as

0 t t_x t_y t_z inf inf inf inf

Visualization

To visualize the result, the user can open the .tb file and its associated .off file in the GUI tools/gui/hole-measures-gui.pro. tools/gui/hole-measures-gui.pro can compiled using qtcreator.