---
jupyter:
  description: 'Several loops in one planex2d sketch: Move lifts the pen, and Face() turns nested loops into holes,
    while overlapping parts are united instead. A flange gasket and a dog bone, checked against their areas.'
---

# Several loops

`Move` lifts the pen, so one sketch can hold many loops. `Face()` takes all drawn edges together and decides what is
material by nesting: a loop inside another loop is a hole, and a loop inside a hole is material again. The same rule
applies where separately drawn loops overlap: a region inside two loops counts as a hole. Parts that overlap and
should become one region are therefore drawn as separate faces and united.

```python
import math
import planex as px
```

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

## A pipe flange gasket

The example is a gasket with an outer diameter of 150, an inner diameter of 90 and eight holes of 14 on a bolt circle
of 120 (Figure 1). The first hole is drawn at 22.5°, and `CircularPattern` repeats it eight times around the origin.
These are ten circles in one sketch, and the nesting makes nine of them holes.

```python
s = px.QuickSketch().Circle(75).Circle(45)
a = math.radians(22.5)
s.Circle(60 * math.cos(a), 60 * math.sin(a), 7, id="hole")
s.CircularPattern("hole", "origin", 8)
gasket = s.Face()
```

```python nbsphinx="hide-input"
Row((gasket, "A pipe flange gasket: ten circles, one face"))
```

```python
print("area", gasket.mass, "exact", math.pi / 4 * (150**2 - 90**2 - 8 * 14**2))
```

## A dog bone

The example is a dog bone: two discs of radius 10, 40 apart, and a bar 8 wide between their centers (Figure 2a).
Drawn into one sketch, the parts of the bar inside the discs lie inside two loops and become holes. The outline then
falls apart into three regions, so `Face()` raises an error, and `Shape()` keeps all three (Figure 2b). As separate
faces, `px.Unify` joins the three parts into one dog bone (Figure 2c).

```python
one_sketch = px.QuickSketch().Circle(10).Circle(40, 0, 10).Move((0, -4)).Rectangle(40, 8)
try:
    one_sketch.Face()
except ValueError as err:
    print(err)

discs = [px.Circle((0, 0), 10).Face(), px.Circle((40, 0), 10).Face()]
bar = px.QuickSketch((0, -4)).Rectangle(40, 8).Face()
bone = px.Unify([*discs, bar])
```

```python nbsphinx="hide-input"
Row((px.Compound([*discs, bar]), "Two discs and a bar"), (one_sketch.Shape(), "In one sketch: the overlaps are holes"),
    (bone, "United"), caption="A dog bone from overlapping parts")
```

The united area is the two discs and the bar, less the two pieces of the bar inside the discs:

```python
inside = 4 * math.sqrt(10**2 - 4**2) + 10**2 * math.asin(8 / 20)
print("area", bone.mass, "exact", 2 * math.pi * 10**2 + 40 * 8 - 2 * inside)
```

See [Faces, shapes and compounds](../basics/faces-shapes-compounds.md) for faces of several regions, and
[Boolean operations](../booleans/index.md) for unions and differences.