---
jupyter:
  description: 'Dimensions in a planex2d sketch: Measure(id) and Measure(id, to=) give lengths, radii, angles and
    distances of elements by their ids, to check a drawing against its intent.'
---

# Dimensions in a sketch

`sketch.Measure(id)` measures the element or the point with that id, drawn or construction, and with `to=` it
measures between two of them: lengths, radii, angles and distances. A drawing built from references, rather than from
numbers, can be checked this way against its design intent.

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

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

## The bracket and the link

The example checks two sketches. The first is the bracket from [Parallel, perpendicular,
angle](../sketch/parallel-perpendicular-angle.md): its ramp was drawn at β = 35° to the ground and ends on the wall, a
= 10 away, so the back is a · tan β high (Figure 1a, with the ramp and the back highlighted). The second is the link
from [Tangents](../sketch/tangent.md), two bosses of radius r1 = 1.5 and r2 = 1 with their centers d = 6 apart. With
sin α = (r1 − r2) / d, the end arc of the large boss spans 180° + 2α, and the tangent lines meet at 2α and come
closest at the small boss, 2 r2 cos α apart (Figure 1b).

```python
a, beta, t = 10.0, 35.0, 0.8
b = px.QuickSketch()
b.Move((-1, 0)).Line((a + 2, 0), id="ground", construction=True)
b.Move((a, -1)).Line((a, 8), id="wall", construction=True)

b.Move((0, 0)).Line("wall", angle=beta, id="ramp")
b.Line("ground", congruent="wall", id="back")
b.Close(id="base")

b.Move((0, 0), dir=(1, 0)).Line(14, parallel="ramp", distance=-t, id="ramp in", construction=True)
b.Move((0, 0), dir=(1, 0)).Line(a + 2, parallel="ground", distance=t, id="ground in", construction=True)
b.Move((0, 0), dir=(0, 1)).Line(9, parallel="wall", distance=t, id="wall in", construction=True)
b.Line("ground in", "wall in", congruent="ramp in")
b.Line("ground in", congruent="wall in")
b.Close()

link = px.QuickSketch()
link.Circle(0, 0, 1.5, id="boss1", construction=True)
link.Circle(6, 0, 1.0, id="boss2", construction=True)
link.Line(tangent=("boss1", "boss2"), id="upper")
link.Line(tangent=("boss1", "boss2"), reverse=True, id="lower")
link.Arc("lower", "upper", congruent="boss2", id="end2")
link.Arc("upper", "lower", congruent="boss1", id="end1")
link.Circle(0, 0, 0.6, id="hole1").Circle(6, 0, 0.4, id="hole2")
r1, r2, d = 1.5, 1.0, 6.0
alpha = math.degrees(math.asin((r1 - r2) / d))
```

```python nbsphinx="hide-input"
Row((b, "The ramp and the back", {"fill": False, "highlight": [e for n in ("ramp", "back") for e in b.Edge(n).edges]}),
    (link, "The end arc and the tangents", {"fill": False, "highlight": [e for n in ("end1", "upper", "lower") for e in link.Edge(n).edges]}),
    caption="A bracket and a link, measured by their ids")
```

```python
print("ramp to ground", b.Measure("ramp", to="ground")["angle"], "exact", beta)
print("back", b.Measure("back")["length"], "exact", a * math.tan(math.radians(beta)))

end1 = link.Measure("end1")
print(end1["type"], end1["radius"], end1["angle"], "exact", 180 + 2 * alpha)
between = link.Measure("upper", to="lower")
print("tangents meet at", between["angle"], "exact", 2 * alpha)
print("closest", between["distance"], "exact", 2 * r2 * math.cos(math.radians(alpha)))
```

The distance between the holes is the center distance minus both radii:

```python
print(link.Measure("hole1", to="hole2")["distance"], "exact", d - 0.6 - 0.4)
```