---
jupyter:
  description: 'A stencil from font outlines: the islands inside letters are found
    and each gets a bridge through its middle so nothing falls out; the cut path as
    DXF.'
---

# Stencil lettering with bridges

Lettering cut out of a sheet makes a stencil, but the inside of a p, an a or an e would fall out, which is why a
stencil font leaves bridges. The example is a stencil of the word "planex", 40 high: the letters come from a font as
outlines, the islands are found, and each gets a bridge through its middle. Lengths are in mm.

![A stencil of the word planex2d with bridges holding the letters' islands](../_static/gallery/stencil-lettering.png){.result}

```python
import math
import matplotlib.pyplot as plt
from matplotlib.font_manager import FontProperties
from matplotlib.textpath import TextPath
import planex as px
```

```python nbsphinx="hidden"
from docs_figures import RED, Row
```

## The letters

Matplotlib turns text into outlines, and their polygons, drawn into one sketch, give the letters as faces, including
the holes inside them. The outlines consist of short straight pieces, and `FitArcs` turns them back into arcs and
lines, which a laser or a plotter follows more smoothly.

```python
outline = TextPath((0, 0), "planex", size=40.0, prop=FontProperties(family="DejaVu Sans", weight="bold"))
sketch = px.QuickSketch()
for polygon in outline.to_polygons():
    points = [tuple(p) for n, p in enumerate(polygon[:-1]) if n == 0 or math.dist(p, polygon[n - 1]) > 1e-9]
    sketch.Move(points[0])
    for p in points[1:]:
        sketch.Line(p)
    sketch.Close()
letters = sketch.Shape()
smooth = px.Unify([face.Copy().FitArcs(tol=0.02, max_edge_length=3) for face in letters.faces])
print(len(letters.faces), "letters with", sum(len(f.inner) for f in letters.faces), "holes")
print(len(letters.edges), "edges from the font,", len(smooth.edges), "after fitting arcs")
print("area", round(letters.mass, 3), "fitted", round(smooth.mass, 3))
```

## Islands

The sheet reaches 10 beyond the letters. In the sheet minus the letters, every hole of a letter becomes a loose island:

```python
(x0, y0), (x1, y1) = smooth.bounding_box
sheet = px.QuickSketch((x0 - 10, y0 - 10)).Rectangle(x1 - x0 + 20, y1 - y0 + 20).Face()
plain = sheet - smooth
print("the cut sheet falls apart into", len(plain.faces), "pieces")
```

## Bridges

Through the middle of each hole runs a vertical bridge, 2 mm wide, across the whole letter. The letter loses that
strip, and the island stays joined to the sheet above and below it (Figure 1).

```python
bridges = []
for face in smooth.faces:
    (lx0, ly0), (lx1, ly1) = face.bounding_box
    for hole in face.inner:
        cx = hole.Face().center[0]
        bridges.append(px.QuickSketch((cx - 1, ly0 - 1)).Rectangle(2, ly1 - ly0 + 2).Face())
stencil = sheet - (smooth - px.Unify(bridges))
print(len(bridges), "bridges, the stencil is", len(stencil.faces), "piece")
px.WriteDXF(stencil, "stencil.dxf")
```

```python nbsphinx="hide-input"
islands = [f for f in plain.faces if f.mass < 0.5 * sheet.mass]
Row((plain, "Without bridges: the islands fall out", {"fills": [(f, RED) for f in islands]}),
    (stencil, "With bridges: one piece"), caption="The stencil without and with bridges")
```

The stencil's cut path: [stencil.dxf](stencil.dxf)

```python nbsphinx="hidden"
fig, (top, bottom) = plt.subplots(2, 1, figsize=(10, 6))
plain.Plot(ax=top, face_col="steelblue", legend=False)
for f in islands:
    f.Plot(ax=top, face_col="tab:red", legend=False)
top.set_title("Without bridges: the islands in red fall out")
stencil.Plot(ax=bottom, face_col="steelblue", legend=False)
bottom.set_title("With bridges: one piece")
for ax in (top, bottom):
    ax.set_aspect("equal")
    ax.axis("off")
import sys
sys.path.insert(0, "..")
from gallery import save_scene, save_figure, save_animation, HIDDEN
save_figure(fig, "stencil-lettering")
plt.close(fig)
```