---
jupyter:
  description: 'Fillets and chamfers in planex2d: rounded and cut corners on wires, faces and shapes, in a quick sketch
    by point ids, and in a constraint sketch with the radius and the lengths as dimensions that can change later.'
---

# Fillets and chamfers

A fillet replaces a corner with an arc of a given radius, tangent to both edges, and a chamfer replaces it with a
straight cut. Both work in two places: on finished geometry, where `Fillet` and `Chamfer` take a corner of a wire,
face or shape, and in a sketch, where the corner is given by the id of its point. In a constraint sketch, the radius
and the lengths become dimensions that can be changed later.

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

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

## On faces

The example is the profile of an angle bracket, with legs 60 and 40 long and 8 thick (Figure 1). Its inner corner
gets a fillet of radius 6, which adds material, and the outer corner at the end of the long leg gets a chamfer of 3.
A corner is given as a vertex, as a point on a vertex, or as a vertex name, and a list gives several corners at once.
`Filleted` and `Chamfered` return a copy, while `Fillet` and `Chamfer` change the object in place.

```python
bracket = px.FromPolyline([(0, 0), (60, 0), (60, 8), (8, 8), (8, 40), (0, 40)], closed=True).Face()
rounded = bracket.Filleted((8, 8), 6)
cut = rounded.Chamfered((60, 8), 3)
```

```python nbsphinx="hide-input"
Row((bracket, "(a) The bracket"), (cut, "(b) Filleted and chamfered"),
    caption="An angle bracket with a fillet in its inner corner and a chamfer on its long leg")
```

A fillet in a right-angled corner adds or removes r²(1 − π/4), and a chamfer of 3 on both edges removes 3²/2:

```python
print("fillet", rounded.mass - bracket.mass, "exact", 6**2 * (1 - math.pi / 4))
print("chamfer", rounded.mass - cut.mass, "exact", 3**2 / 2)
```

A chamfer can also have two different lengths, with `d2=`, or a length and an angle, with `angle=` in degrees from
the first edge. A chamfer of 3 at 30° removes a triangle with the legs 3 and 3 tan 30°:

```python
steep = bracket.Chamfered((60, 8), 3, angle=30)
print("chamfer at 30°", bracket.mass - steep.mass, "exact", 3 * 3 * math.tan(math.radians(30)) / 2)
```

## In a sketch

In a sketch, `Fillet` and `Chamfer` take the corner as a point id, such as `"bottom.end"`, as a point, or as a list
of them. The new arc gets the id `Fillet.1` and the new line `Chamfer.1`. The two edges at the corner keep their ids.
The pieces they lose stay in the sketch as construction lines that meet at the sharp corner, so a dimension can still
refer to that corner. The example is a cover plate of 50 × 30 with two corners rounded to 5 and one chamfered by 4
(Figure 2).

```python
sk = px.QuickSketch()
sk.Line(50, id="bottom").Turn(90).Line(30, id="right")
sk.Turn(90).Line(50, id="top").Close(id="left")
sk.Fillet(["bottom.end", "right.end"], 5)
sk.Chamfer("top.end", 4);
```

```python nbsphinx="hide-input"
Row((sk, "A cover plate, the cut-off corners dashed"), caption="Fillets and a chamfer in a quick sketch")
```

```python
plate = sk.Face()
print("area", plate.mass, "exact", 50 * 30 - 2 * 5**2 * (1 - math.pi / 4) - 4**2 / 2)
```

The new arc or line takes the properties of the drawing calls, `name=`, `maxh=`, `hpref=` and `col=`, as one value
for all corners or as a list with one value per corner, for example
`sk.Fillet(["a.end", "b.end"], 1, name=["r1", "r2"])`.

In a constraint sketch, the radius of a fillet and the lengths of a chamfer are dimensions that can change later.
See [Offsets and profiles revisited](../constraints/offsets-profiles.md) for details.

See [Trimming and splitting](trimming.md) for corners cut by hand.