---
jupyter:
  description: 'Construction elements and points in a planex2d sketch: they place what comes next and never reach
    wires, faces or exports. A pillow block from a construction circle and a flange from points with ids.'
---

# Construction elements and points

Construction elements and points are the helper geometry of a drawing: center lines, reference circles, the
positions of holes. They place what comes next but never become part of the part, so they never appear in `Wires()`,
faces or exports. Any element becomes construction with `construction=True`, and `Vertex(id, point)` adds a point
with an id. A construction element also leaves the pen where it is, so the outline continues as if it were not
there.

The points of every element can be referred to by id: `"id.start"`, `"id.end"`, `"id.mid"` and, for arcs and
circles, `"id.center"`.

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

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

## A pillow block from a construction circle

The example is a pillow block with a base of 80 × 12, an axis 45 high, a boss of radius 22 around the axis and a
bore of 25 (Figure 1). The boss is a construction circle around the point `axis`. Its outline is drawn in three
steps.

First the construction: the axis, the boss, and the left flank's tangent from the top of the left foot to the boss.
The point given with the boss, (0, 45), picks the touch point on the left side.

```python
s = px.QuickSketch()
s.Vertex("axis", (40, 45))
s.Circle(40, 45, 22, id="boss", construction=True)
s.Move((0, 12))
s.Line(tangent=("boss", (0, 45)), id="left tangent", construction=True);
```

Then the outline. The pen is still at (0, 12), so the outline runs down the left foot, along the base and up the
right foot, then tangent to the boss on the right. The crown follows the boss until it meets the left tangent, and
`Close` draws the left flank along it. Last, the bore goes around the axis, and a construction line from the middle of
the base up to the crown measures the overall height.

```python
s.Line((0, 0), id="left foot").Line((80, 0), id="base")
s.Line((80, 12), id="right foot")
s.Line(tangent=("boss", (80, 45)), id="right flank")
s.Arc("left tangent", congruent="boss", id="crown")
s.Close(id="left flank")
s.Move("axis").Circle(12.5, id="bore")
s.Move("base.mid", dir=(0, 1))
s.Line(until="crown", id="height", construction=True)
block = s.Face()
```

```python nbsphinx="hide-input"
Row((s, "The sketch, the boss and the height line dashed", {"fill": False}), (block, "The pillow block"),
    caption="A pillow block from a construction circle")
```

The flanks touch the boss, so their distance from the axis is the boss radius of 22. The center of the crown is the
axis, and the height line is 45 + 22 long:

```python
for ref in ("left flank", "right flank"):
    print(ref, "distance from the axis", s.Edge(ref).Distance((40, 45)))
print("crown center", s.Location("crown.center"), "axis", s.points["axis"])
print("height", s.Edge("height").mass, "exact", 45 + 22)
```

## A bolt circle from points

The example is a round flange with an outer diameter of 100, a bore of 40 and six holes of 9 on a bolt circle of 75
(Figure 2). The hole positions are construction points with the ids `bolt0` to `bolt5` (a). `sk.points` lists every
point of the sketch, and a loop draws a hole around each (b).

```python
f = px.QuickSketch().Circle(50).Circle(20)
for k in range(6):
    a = math.radians(60 * k)
    f.Vertex(f"bolt{k}", (37.5 * math.cos(a), 37.5 * math.sin(a)))
points = f.Copy()
for ref in f.points:
    f.Move(ref).Circle(4.5)
flange = f.Face()
```

```python nbsphinx="hide-input"
Row((points, "The points bolt0 to bolt5", {"fill": False}), (flange, "The flange"),
    caption="A bolt circle from points with ids")
```

```python
print("area", flange.mass, "exact", math.pi / 4 * (100**2 - 40**2 - 6 * 9**2))
```

The same bolt circle can also be drawn as one hole and a `CircularPattern` of it. See
[Several loops](several-loops.md) for an example.