Merging split edges

The task is the union of a grid of 20 × 20 unit squares. The planex2d union merges the pieces of each side into one edge by itself. OpenCASCADE’s Fuse leaves them split until UnifySameDomain runs, and after that, both have the four edges of the outline. The squares have no arcs, so the polygon libraries get them exactly. Figure 1 shows the squares and the unions from planex2d and from OpenCASCADE, with their vertices marked, and Figure 2 shows the times.

import netgen.occ as occ
import shapely
import planex as px
from comparison_libraries import best, chart, union

n = 20
cells = [(i, j) for i in range(n) for j in range(n)]
px_squares = [px.QuickSketch((i, j)).Rectangle(1, 1).Face() for i, j in cells]
occ_squares = [occ.WorkPlane().MoveTo(i, j).Rectangle(1, 1).Face() for i, j in cells]
polygons = [shapely.box(i, j, i + 1, j + 1) for i, j in cells]

t_px, a = best(lambda: px.Unify(px_squares))
t_occ, b = best(lambda: occ.Fuse(occ_squares).UnifySameDomain(), repeats=1)
others = union(polygons)

print(f"planex2d   {t_px:.4f} s, {len(a.edges)} edges")
print(f"OCC        {t_occ:.4f} s, {len(b.edges)} edges")
for name, (t, area) in others.items():
    print(f"{name:10} {t:.4f} s, area {area:.6f}")

planex2d   0.0010 s, 4 edges
OCC        1.7253 s, 4 edges
shapely    0.0057 s, area 400.000000
pyclipper  0.0006 s, area 400.000000
gdstk      0.0006 s, area 400.000000
manifold3d 0.0004 s, area 400.000000

(a) 400 unit squares

(b) planex2d: 4 edges

(c) OpenCASCADE: 4 edges

Figure 1: The union of a grid of unit squares

* polygon based: only straight lines, curves are approximated by them

Figure 2: Uniting 400 unit squares