prepro_cpptools

4. Generating shapes and packings with generator

Goal

3375 small cubes, placed on a grid with random orientations, fall into a box of 25 cm. Nothing is written by hand: the shapes, the walls, the cubes and the whole input file are produced by the application generator, from short command files.

Notions

• The application generator and its commands generateShape:..., generatePacking:... (generator).
• Its commands open, print, close and Particles:placeHolder, which write a complete input file.
• Several shape files, or several pieces of an input file, put together.

Files

File	Content
genCube.txt	Command of generator that writes the shape of a cube
genBox.txt	Command that writes the shapes of the walls of a box
genPacking.txt	Commands that place the 6 walls and the 3375 cubes
input_head.txt	The beginning of the input file, without the particles
genAll.txt	All of the above in a single command file

Run it

Either step by step:

generator genCube.txt > shapes.txt
generator genBox.txt >> shapes.txt
generator genPacking.txt > sample.txt
sed 's/^Particles XXXX/Particles 3381/' input_head.txt > input.txt
cat sample.txt >> input.txt
rockable input.txt -j 4          # about 15 minutes on one thread, less with -j 4
see

or all at once:

generator genAll.txt             # writes shapes.txt and input.txt
rockable input.txt -j 4

What happens

The cube. genCube.txt holds a single command:

generateShape:cube Cube 0.0005 0.01

a cube named Cube, of side 1 cm (the outer size, the rounding included), with a Minkowski radius of 0.5 mm. generator writes the shape on its standard output, with its volume and inertia (preCompDone y).

The walls. genBox.txt,

generateShape:xyz_walls   0.25 0.25 0.25   0.0005

writes three wall shapes, x-wall, y-wall and z-wall, normal to x, y and z, for a box of 25 cm, with a radius (half-thickness) of 0.5 mm. >> appends them to shapes.txt.

The packing. genPacking.txt holds two commands, whose arguments are given on the following lines:

generatePacking:wallBox
1                  group of the walls
0.25 0.25 0.25     inner size of the box
0.0005             half-thickness (the radius of the wall shapes)

generatePacking:grid
Cube               shape
0 0 0              corner of the grid
0.25 0.25 0.25     size of the grid
15 15 15           number of particles along x, y, z
0                  group
0                  cluster
1.0                homothety
1                  1: random orientations, 0: all aligned

The six walls come first: with nDriven 6, they are the driven bodies, and since nothing drives them, they stay fixed. The cubes, on a grid of 15 × 15 × 15, are 1.67 cm apart. generator tells how many bodies each command added (on the error output, so that it does not end up in the file):

@generatePacking:wallBox, Number of added bodies: 6
@generatePacking:grid, Number of added bodies: 3375

The input file. input_head.txt holds the parameters of the computation and ends with Particles XXXX: sed puts the number of particles, 3381, in its place, and the lines of sample.txt are appended.

All at once. genAll.txt does the same in a single file. open shapes.txt sends what follows into shapes.txt until close; print writes a line as it is; Particles:placeHolder writes Particles and leaves room for the number, which generator fills in at close with the count of the particles added in between.

The computation. There is no gravity line: the default gravity, (0, -9.81, 0), applies. The cubes fall, pile up at the bottom of the box, and are at rest from about t = 0.5 s. With 3375 particles, the computation takes about 15 minutes on one thread; -j 4 runs it on 4 threads.

What to look at

• In see, the key d hides the walls.

• The kinetic energy, kineticEnergy.txt, which drops once the cubes are piled up:

  gnuplot -p -e "set logscale y; plot 'kineticEnergy.txt' using 1:2 with lines title 'translation'"

• shapes.txt: the shapes written by generator.

Exercises

1. Replace the cube by an elongated cuboid: generateShape:cuboid Cube 0.0005 0.015 0.005 0.005 (the name is kept, so that nothing else has to change).
2. Put fewer cubes, aligned (5 5 5 and a last 0 in generatePacking:grid). The number of particles is then 131: change it in the command sed, or use genAll.txt, which counts them.
3. Make the box twice as high: 0.25 0.5 0.25 in genBox.txt, and for the size of the box and of the grid in genPacking.txt.
4. Look at the other commands of generator (spheres, polyhedra, random close packings, transformations) on the page generator.

Going further

• DominoFun: a whole system written by generator, with clusters of glued particles.
• The C++ functions behind generator, in prepro/genesis/cpptools, can be used directly in a program.