---
jupyter:
  description: 'Moving, rotating, mirroring and scaling planex2d objects: in place or as a copy, exact symmetry,
    patterns of copies, and motions in 3D that move the plane. A T-slot nut and a perforated brake disc.'
---

# Moving, rotating, mirroring, scaling

Motions work on wires, faces, shapes, compounds and sketches. There are four, each in the plane with 2D arguments:

- `Translate((dh, dv))` moves by an offset;
- `Rotate(center, angle)` turns about a point by an angle in degrees, counterclockwise for a positive angle;
- `Mirror(point, dir)` mirrors about the axis through a point along a direction;
- `Scale(center, factor)` scales about a point.

`Rotate` changes the object and returns it, while `Rotated` returns a copy, and the other motions follow the same
rule. With 3D arguments, a motion moves the object's plane instead (see [In 3D](#In-3D)). Symmetric parts can be drawn
as one half and mirrored, and patterns are built from copies.

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

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

## Symmetry: a T-slot nut

The example is a T-slot nut with a flange 18 wide and 4 high and a neck 10 wide and 6 high. Its right half
(Figure 1a) is mirrored about the y axis, shown dashed, and united with its copy (Figure 1b). Mirroring about an axis
through the origin is exact, so the two halves share the edge on the axis bit for bit. The union has no seam, and its
top and bottom are one line each.

```python
half = px.QuickSketch().Line((9, 0)).Line((9, 4)).Line((5, 4)).Line((5, 10)).Line((0, 10)).Close().Face()
nut = half + half.Mirrored((0, 0), (0, 1))
```

```python nbsphinx="hide-input"
axis = px.Line((0, -1), (0, 11))
Row((half, "The right half", {"dashed": [axis], "view": ((-10, 10), (-1.5, 11.5))}),
    (nut, "Mirrored and united", {"view": ((-10, 10), (-1.5, 11.5))}),
    caption="A T-slot nut from its right half")
```

```python
print("area", nut.mass, "exact", 2 * (9 * 4 + 5 * 6))
print(len(nut.edges), "edges")
```

## Patterns: a perforated brake disc

The example is a brake disc with a radius of 100 and a center bore of radius 30. One hole of radius 6 at a radius
of 70 is rotated into a ring of twelve, 30° apart. The same hole, moved out to 85, is rotated into a second ring,
offset by half a step (Figure 2a). Subtracting the bore and all 24 holes from the disc gives the brake disc
(Figure 2b).

```python
hole = px.Circle((70, 0), 6).Face()
inner_ring = [hole.Rotated((0, 0), 30 * k) for k in range(12)]
outer_ring = [hole.Translated((15, 0)).Rotated((0, 0), 30 * k + 15) for k in range(12)]
disc = px.Subtract([px.Circle((0, 0), 100).Face(), px.Circle((0, 0), 30).Face(), *inner_ring, *outer_ring])
```

Inside a sketch, `CircularPattern` and `LinearPattern` repeat the sketch's own elements in the same way. See
[Several loops](../sketch/several-loops.md) for an example.

```python nbsphinx="hide-input"
outlines = [px.Circle((0, 0), 100), px.Circle((0, 0), 30)]
Row((px.Compound(inner_ring + outer_ring), "One hole, 24 copies", {"dashed": outlines}), (disc, "The brake disc"),
    caption="A perforated brake disc from one hole")
```

```python
print("area", disc.mass, "exact", math.pi * (100**2 - 30**2) - 24 * math.pi * 6**2)
```

## Scaling

`Scaled((0, 0), 0.5)` scales the disc by one half about its center. It keeps its shape at a quarter of the area
(Figure 3). The mesh sizes `maxh` and `minh` stay as they are unless `scale_maxh=True` or `scale_minh=True` is
given.

```python
small = disc.Scaled((0, 0), 0.5)
print("area ratio", small.mass / disc.mass)
```

```python nbsphinx="hide-input"
Row((small, "Scaled by 0.5", {"dashed": [outlines[0]], "view": ((-105, 105), (-105, 105))}))
```

## In place

`Rotate` and `Translate` change the nut itself and return it, so the calls can be chained. The example turns the
nut by 90° about the origin and then moves it 20 along x (Figure 4).

```python
nut.Rotate((0, 0), 90).Translate((20, 0))
print(nut.bounding_box)
```

```python nbsphinx="hide-input"
origin = [px.Line((-2, 0), (2, 0)), px.Line((0, -2), (0, 2))]
Row((nut, "The nut turned by 90° and moved 20 along x, the origin dashed", {"dashed": origin}))
```

## In 3D

With 3D arguments, a motion moves the object's plane: `Rotated(point, dir, angle)` turns about an axis in space, and
`Mirrored(point, normal)` mirrors about a plane. Turned about the x axis, the nut's plane faces −y, up to the rounding
of cos 90°. Mirrored about the xy plane, it faces −z (Figure 5). See [The plane in 3D](plane.md) for planes in
general.

```python
turned = nut.Rotated((0, 0, 0), (1, 0, 0), 90)
mirrored = nut.Mirrored((0, 0, 0), (0, 0, 1))
print("turned: normal", turned.Normal())
print("mirrored: normal", mirrored.Normal())
```

```python nbsphinx="hide-input"
parts = [(s.ToOCCShape(), style) for s in (nut, turned) for style in ("shade", "ink")]
Views(("The nut in the xy plane and turned by 90° about the x axis", parts), angles=(-60, 0, 30))
```