---
jupyter:
  description: 'A vent plate as a 2D CAD exercise: a dimensioned drawing to model in planex2d or any CAD system, a
    solution with rounded corners, mounting holes at the corners'' centers and a grid of vent holes from a linear
    pattern in two directions, and the area to check a model against.'
---

# Vent plate

A vent plate covers an opening in a housing and lets air through a grid of holes, and four screws at its rounded corners
hold it. The grid is a pattern, one hole repeated along the plate and across it. Model the plate from the drawing in
planex2d or in any CAD system, then check its area against the value at the end of the page. A solution in planex2d
follows.

![The vent plate exercise: a dimensioned drawing of a rectangular plate with rounded corners, four mounting holes and a grid of 28 vent holes](../_static/gallery/vent-plate.png){.result}

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

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

## The plate

The plate is a rectangle, 120 by 80, drawn with `Rectangle` from the pen at the origin, 120 along $x$ and 80 along $y$.
Its lines are `plate.Line.1` to `plate.Line.4`, counterclockwise from the bottom edge. With
`auto_constraint={"horizontal": True, "vertical": True}`, its edges, drawn level and plumb, stay so, and its corner sits
at the origin. `Fillet` rounds the four corners with a radius of 8, and each fillet makes its radius a dimension,
`corner_1.r` to `corner_4.r` (Figure 1):

```python
plate = px.Sketch(auto_constraint={"horizontal": True, "vertical": True})
plate.Rectangle(120, 80, id="plate")
plate.Constrain("plate.Line.1.start", "origin", px.Coincident)
plate.Constrain("plate.Line.1", px.Distance, 120, id="length")
plate.Constrain("plate.Line.2", px.Distance, 80, id="width")
plate.Fillet(["plate.Line.1.start", "plate.Line.2.start", "plate.Line.3.start", "plate.Line.4.start"], 8,
             id=["corner_1", "corner_2", "corner_3", "corner_4"])
print("status", plate.status, "| degrees of freedom", plate.dof)
```

```python nbsphinx="hide-input"
Row((plate, "The rectangle with its rounded corners, every dimension and tie", {"constraints": True}),
    caption="The plate")
```

## The holes

The mounting holes, 6.6 across for M6 screws, go into the centers of the corner arcs with `concentric=`, so they need no
position of their own. The first vent hole, 8 across, is 24 from the left edge and 22 from the bottom edge.
`LinearPattern` repeats it in a grid, 7 times along $x$ and, in its second direction, 4 times up, 12 apart both ways.
The copies are named by their two steps, `grid.1.0.vent` to `grid.6.3.vent` (Figure 2).

```python
for k in range(1, 5):
    plate.Circle(6.6 / 2, concentric=f"corner_{k}", id=f"mount_{k}")
plate.Constrain("mount_1", px.Diameter, 6.6, id="mount_d")
for k in range(2, 5):
    plate.Constrain(f"mount_{k}", "mount_1", px.Equal)
plate.Circle(8 / 2, center=(25, 20), id="vent")
plate.Constrain("vent", px.Diameter, 8, id="vent_d")
plate.Constrain("vent.center", "plate.Line.4", px.Distance, 24, id="vent_x")
plate.Constrain("vent.center", "plate.Line.1", px.Distance, 22, id="vent_y")
plate.LinearPattern("vent", px.H, 7, 12, dir2=px.V, count2=4, spacing2=12, id="grid")  # 7 along x, 4 up, the first included
print("status", plate.status, "| degrees of freedom", plate.dof)
```

```python nbsphinx="hide-input"
Row((plate, "The mounting holes and the grid of vent holes", {"fill": False}), caption="The holes")
```

## The checks

This is the area, to compare with your own model. It is the rectangle less what the corners round off,
$(4 - \pi) \cdot 8^2$, less the 4 mounting holes and the 28 vent holes. The plate is symmetric about both of its middle
lines, so its centroid lies at its middle (Figure 3):

```python
face = plate.Face()
exact = 120 * 80 - (4 - math.pi) * 8**2 - 4 * math.pi * 3.3**2 - 28 * math.pi * 4**2
c = face.center
print("area", round(face.mass, 2), "mm², exact", round(exact, 2))
print("centroid", tuple(round(v, 6) for v in c[:2]))
```

```python nbsphinx="hide-input"
Row((face, "The vent plate, its centroid marked", {"marks": [c[:2]]}), caption="The vent plate")
```

The plate as DXF in millimeters, for another CAD system or a laser cutter:

```python
plate.WriteDXF("vent_plate.dxf", unit=px.mm, scale=1)  # scale=1: the numbers as they are
```

The plate as DXF: [vent_plate.dxf](vent_plate.dxf)

```python nbsphinx="hidden"
import sys
sys.path.insert(0, "..")
import matplotlib.pyplot as plt
from drawings import SheetFigure, View
from gallery import save_figure

# the grid's pitches as chains of equal spacings, the first hole to the last of a row and of a column
(x0, y0), (x1, _), (_, y1) = (plate.Location(c + ".center") for c in ("vent", "grid.6.0.vent", "grid.0.3.vent"))
mount = plate.Location("mount_2.center")
view = View([(plate, {"length": -16, "width": 140, "corner_3.r": (45, "outside", 4), "vent_d": (150, "leader", 28),
                      "vent_x": -6, "vent_y": -8})],
            axes=[((x0 - 6, y0), (x1 + 6, y0)), ((x0, y0 - 6), (x0, y1 + 6))],
            diameters=[(mount, 6.6 / 2, (315, "leader", 4))],
            measures=[((x0, y1), (x1, y1), 92, "6 × 12 (= 72)"), ((x1, y0), (x1, y1), 128, "3 × 12 (= 36)")])
drawing = SheetFigure([view], margin=28, notes=("planex2d.org", "2D exercise 09"))
print("scale", drawing.planex_scale, "| paper", [round(v * 25.4) for v in drawing.get_size_inches()], "mm")
save_figure(drawing, "vent-plate", dpi=200)
plt.close(drawing)
```