Separate (trim) overlapping convex shapes into disjoint convex shapes with minimal volume loss.

Disjoint convex shell (DC-shell) is a set of disjoint convex objects approximating non-convex overlapping object sets. The DC-shell method we proposed provides better approximation than those created by other methods. In addition, DC-shell enables faster collision response and realistic fracturing simulation by preventing convex objects from overlapping themselves.

DC-shell implements the algorithms described in the following paper: "Disjoint Convex Shell and its Applications in Mesh Unfolding", SPM 2017, by Yun-hyeong Kim, Zhonghua Xi, and Jyh-Ming Lien. (Project Web Site / Video)

The provided code constructs disjoint convex objects from overlapping or segmented parts as inputs. The code can produce DC-shells created by LSF (least-squares fit) heuristic method, SVM, and exact volume optimization methods. Moreover, before creating DC-shells, we can simplify and remesh the convex parts to decrease the complexity and increase their regularity.

To demonstrate the power of DC-shell, we studied how DC-shell can be used in mesh unfolding. The nets of polyhedra we used were created by software tools developed by the MASC group at George Mason University.

The provided code has been tested and can be run on Mac OSX. It was currently tested on a MacBook Air, with Mac OSX 10.9.5 and 10.11.6. It is likely that the following instructions may compile the code on Linux and Windows via cmake.

The required program and library are listed.

• Mac OS X 10.9.5 or newer

• CMake 2.6 or newer

  To install CMake program via MacPorts, please type this in the terminal: $ sudo port install cmake or brew install cmake

• CGAL

  The provided code requires only CGAL to install. Additional libraries are included in the "dcshell/lib" directory. To install CGAL via MacPorts, please type this in the terminal: $ sudo port install cgal +qt5 or brew install cgal

• To compile the provided code, please type the commands below in the "dcshell" directory:

    $ chmod +x gen.sh
    $ ./gen.sh
  

  The provided code can be compiled using the script file, "gen.sh" and create a "dcshell" file linked to the execution file.

• To run the provided code, please type the command below in the "dcshell" directory, the root dirctory:

    $ ./dcshell <model_1.obj> <model_2.obj> ... <model_n.obj>
  

  This program takes one or more OBJ files. You can try to run this program following several steps in the Usage Section. The program also works with a single OBJ file that contains multiple connected components. (NOTE: if you want to get disjoint convex objects from a given model, the model should be composed of multiple parts or you will need to segment it before using the model.)

• To create figures or tables or plots our paper contains, please type this in the "dcshell/models/*" directory:

    $ sh run
  

  Once you type the script file, "run", it creates a "dcshell" file linked to the execution file and it runs with the segmented objects in the directory.

This section is focused on and illustrates how to produce DC-shell step by step.

1. Go to the "dcshell/models" directory in the repository and then go to one of the models' directories. For example, select the "Yoshi" directory.

   • In the directory, there is "yoshi-sep.obj". It will be used as an input model.

2. Run the DC-shell program by typing this:

   $ sh run(this command will be used in the other model directory) or $ ./dcshell yoshi-sep.obj

   • Once you run the program, it would open both a window (left) and a control panel (right). You might see like this:

2. (Very important) Press the 'h' key to show the convex hulls.

3. Press the 'Simplify Hulls' button to simplify the convex hulls.

   • Before pressing the button, set the 'iteration' and 'maximum volume increase' parameters.
     • We usually use 10 iterations and leave the maximum volume increase as it is
   • You can also press the 'Simplify Hulls' button multiple times until you are satisified with the result
   • Press Rebuild Hulls' to reset if something goes wrong

4. Press the 'Remsh Hulls' button to remesh the convex hulls.

   • Before pressing the button, set the 'iteration' and 'maximum volume increase'parameters.
     • We usually use 10 iterations and leave the maximum volume increase as it is
   • Once the remeshing process is started, the weighted average fatness for every iteration at different percentages of maximum volume increase will be recorded in the "*_fatness_all.txt" file.
   • To check the current weighted average fatness of the triangles, press the 'Print Fatness' button.
   • You can also press the 'Remsh Hulls' button multiple times until you are satisified with the result
   • Press Rebuild Hulls' to reset if something goes wrong

5. Press one of the three buttons such as'Use Heuristic', 'Use Exact Volume', and 'Use SVM' to make the hulls disjoint.

   • Before pressing the button, set 'collapse vertex dist', 'volume sample size', and 'c-svm C' parameters.

     • In all of the examples in the paper, we use the default values
     • So, you can leave the values as they are in most cases

   • The cost parameter, 'c-svm C', affects both running time and output quality.

     • The value of C is more for SVM method. For Heuristic and Exact Volume methods, 'C' does not have much effect.
     • If 'c-svm C' is larger, both the computation time and the output quality should increase.

   • These buttons use the methods

     • The 'Use Heuristic' button: trimming the given objects using the least-squares fit (LSF) method
     • The 'Use SVM' button: trimming the given objects using the support vector machine (SVM) method
     • The 'Use Exact Volume' button trimming the given objects using SVM & exact volume computation method

6. Press the 'Save Hulls' button to save the resulting DC shells to files. Those resulting files, "*_hull_*.obj", are in the same directory where the Yoshi model exists.

7. If anything goes wrong, please reset all of the processes, press 'Rebuild Hulls'.

In the "dcshell/models" directory, there are models either composed of multiple parts or manually segmented into parts. Most of the original models used in this paper are obtained from Thingiverse and all Pokemon models are from ROEStudios.