Define tangencies. Get precise circle packings.
A robust Java library that computes Euclidean circle packings from triangulations. Inspired by Gerald Orick’s GOPack.
Supply a Triangulation that defines which circles are tangent to which. CircuPack handles all the geometry: it calculates exact radii and center positions so every specified tangency is visually perfect.
- Simple Input: Implement the
Triangulationinterface to define your graph of tangencies — pure combinatorics, no geometry needed. - Automatic Geometry: No need to guess positions or sizes. The engine computes everything.
- Multiple Layouts: Pack into a disc (max packing), a rectangle, or a polygon with prescribed corner angles.
- Production-Ready: Stable, reliable and fast (10k circles in ~1s).
// 1. Define your triangulation (e.g., from Tinfour)
IIncrementalTin tin = new IncrementalTin();
// ... add vertices ...
Triangulation tri = new TinfourTriangulation(tin);
// 2. Create the packer (defaults to max packing in the unit disc)
CircuPacker packer = new CircuPacker(tri);
// 3. Compute the packing
double maxError = 0.01; // max visual error (overlap, as a fraction of circle radius)
packer.riffle(maxError); // Iterate until max error is below threshold
// 4. Retrieve results
double[] radii = packer.getRadii();
double[] centersX = packer.getCentersX();
double[] centersY = packer.getCentersY();Instead of a disc, the boundary can be packed into an n-gon: pick boundary vertices as corners and (optionally) prescribe the interior angle at each. Side lengths emerge from the packing itself.
CircuPacker packer = new CircuPacker(tri);
// rectangle: 4 corners with right angles, chosen evenly along the boundary...
packer.setRectanglePack();
// ...or supply your own corner vertices
// packer.setRectanglePack(new int[] { c0, c1, c2, c3 });
// general polygon: n evenly spaced corners with equal angles...
// packer.setPolygonPack(5);
// ...or explicit corners and angles (angles sum to (n-2)*pi)
// packer.setPolygonPack(corners, angles);
packer.riffle(0.01);
int[] corners = packer.getCorners(); // CCW corner vertices actually used
double aspect = packer.getAspect(); // rectangle aspect ratio (4-corner packings)