Shape Packer

Shape packing

This application searches for the best way to arrange a number of shapes (circles and polygons) within another shape. It does this by maximising the radius of the inner shapes with respect to the radius of the outer shape. For polygons the radius is the distance from the centre to one of the verteces.

- Picture goes here.

Best:

Settings

Circles:			Temperature:
Triangles:			Move step:
Squares:			Angle step:
Pentagons:			Per second:
Hexagons:			Outer Shape:
Heptagons:
Octogons:
Nonogons:

Instructions

Start	Will start a new simulation using the shape counts and attributes specified in the table above.
Pause	Pauses the current simulation.
Resume	Resumes a paused simulation.
Update	Updates the attributes of the current simulation but leaves the shapes unchanged.
Best	Shows the best fit achieved since the simulation started. The simulation will also pause, but can be resumed.
Reset Best	Clears the best so far value and saved state.
T-Cycle	Starts a temperature cycling mode to help find solutions. This will keep decreasing the temperature until a minimum is reached, at which point it resets to a high temperature and starts again. This mode can be cancelled using "Start" or "Update".
Shapes	Determines how many of each shape type are used in the simulation.
Temperature	Determines how much freedom of movement the shapes have. Low temperatures tend to freeze in a configuration, larger temperatures allow the shapes to explore a larger range of sizes. If your simulation seems to be trapped in a sub-optimal configuration you can raise the temperature for a bit to try to shake it out.
Move step	The size of the random moves that will be generated.
Angle step	The size of the random rotations that will be generated (radians).
Per second	The number of iterations that will be attempted in one second. The actual number may be smaller if your computer isn't up to it.

Java Version

The original Java applet that this javascript application is based on can be found here. It no longer workds with the latest versions of Java.

Strategy

To find good packing solutions:

Choose a set of shapes and the outer border
Run the simulation for a while to see what configuration the system settles into.
Once it has settled into a stable configuration reduce the temperature to freeze it in and measure the packing value. This is the value shown by "Scale". The lager this value is the better the shapes are packed. After changing the temperature use "Update" to apply the change. This will retain the current shape positions and remember the best configuration found so far.
If you think there may be a better packing arrangement increase the temperature to shake it up a bit, then cool it down a bit to freeze a configuration in.
Alternatively you could use the "T-Cycle" mode which attempts to automate this process.

Best Text

Cut and past this text to preserve your best packings. That's how I've encoded the images on the results page. One day I might implement a viewer. Or you could create your own results page by copying and editing mine.