The top image shows three squares of the grid, which have been split into triangular cells. The red curve traces an isosurface through this field based on the sign of grid vertices. Each triangular cell is processed individually, and subdivided as necessary so that the green layer can be filled with triangular elements, as shown in the middle image.

I extended this basic scheme to implement the precedence operator, as illustrated in the bottom image. To avoid T-junctions in the final model, the green triangles require extra subdivision to match the blue and orange layers.