Given a set of 2D irregular shapes (polygons), we would like to enclose the collection in the smallest possible container such that no two shapes overlap. The problem is interesting from a purely mathematical view point, but also sees various applications ranging from CNC cutting, to circuit design, to 3D art creation, and more.

The method here is based on no-fit-polygon generation and heuristic techniques for finding optimal polygon orientation and orderings. In this sense, the method trades off optimality for efficiency.

We define our polygon collection using traditional vertex and index buffers as described here. Also, define the target container: a 500 x 400 unit box.

Vector64[] verts = data.verts;
int[] tris = data.tris;
Rect64 container = new Rect64(0, 400, 500, 0);

Create a Nester class object and pass our data, with an optional padding parameter.

Nester nester = new Nester();
int[] handles = nester.AddUVPolygons(verts, tris, 0.0);

Queue commands for determining optimal rotation, nesting and refitting the polygons into a container.

nester.CMD_OptimalRotation(null);
nester.CMD_Nest(null, NFPQUALITY.Full);
nester.CMD_Refit(container, false, null);

Execute command buffer with async callbacks for progress updates and completion of commands.

nester.ExecuteCommandBuffer(NesterProgress, NesterComplete);

Various quality settings trade off speed for quality of solutions.

public enum NFPQUALITY
{
    Simple,         // simplify shapes to bounding boxes
    Convex,         // use convex hull of shapes
    Concave,        // use shape boundary (ignore holes)
    Full            // use full shape boundary and holes
}

We can compare the results under these settings on a model with 1622 irregular shapes with an Intel Core i7-6700.