---
jupyter:
  description: 'Lines that end on other edges in a planex2d sketch: an end given by a target, lines between two
    targets, and until=px.first and px.last. A gusset plate, a rib and rays in a link.'
---

# To, from and until

A line often has to end where it meets another edge. Instead of computing that intersection, you give the edge as the
line's end, and planex2d finds the point. The end can be a named target, as in `Line("web", angle=...)`, or the first
or last edge ahead of the pen, with `until=px.first` or `until=px.last`.

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

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

## To an edge

The example is a gusset plate welded between a flange and a web. It runs 60 along the flange, its free edge rises at
35° until it meets the web, and its inner corner is sniped by 8 to clear the weld (Figure 1). The web is a
construction line. `Line("web", angle=180 - 35)` draws the free edge: the angle sets its direction, and the web sets
its end.

```python
s = px.QuickSketch()
s.Move((0, -5)).Line((0, 60), id="web", construction=True)
s.Move((8, 0), dir=(1, 0)).Line(52, id="flange side")
s.Line("web", angle=180 - 35, id="free edge")
s.Line((0, 8), id="web side").Close(id="snipe")
gusset = s.Face()
```

```python nbsphinx="hide-input"
Row((s, "The sketch, the web dashed", {"fill": False}), (gusset, "The gusset plate"),
    caption="A gusset plate whose free edge ends on the web")
```

The area is the triangle between the flange and the free edge, less the snipe:

```python
print("area", gusset.mass, "exact", 60**2 * math.tan(math.radians(35)) / 2 - 8**2 / 2)
```

## From one edge to another

With two targets, a line runs from the first to the second, and a helper such as `parallel=` sets the line it runs
on. The example is a rib between a hub and a wall, parallel to the pen's direction (Figure 2a).

```python
rib = px.QuickSketch().Circle(0, 0, 1, id="hub")
rib.Move((4, -2)).Line((4, 2), id="wall")
rib.Move((0, 0.3), dir=(1, 0))
rib.Line("hub", "wall", parallel=rib.pen, id="rib");
```

## Until the first or last edge

`until=px.first` stops a line at the first edge it meets ahead of the pen, and `until=px.last` at the last one,
construction edges included. The example is the link from [Tangents](tangent.md), with rays every 15° from a point
inside it, each ending on the first edge it meets (Figure 2b).

```python
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")
rays = link.Copy()
for angle in range(0, 360, 15):
    rays.Move((3, 0.3)).Line(angle=angle, until=px.first, col=(0.85, 0.35, 0))
```

```python nbsphinx="hide-input"
Row((rib, "A rib from the hub to the wall", {"fill": False}),
    (rays, "Rays until the first edge", {"colors": True, "fill": False}),
    caption="Lines between two targets, and until the first edge")
```

The difference between the two shows on a line that crosses a circle twice. A line along x from the origin meets a
construction circle of radius 1 around (3, 0) at x = 2 and at x = 4, and the pen ends at the first or the second
point:

```python
s = px.QuickSketch().Circle(3, 0, 1, construction=True).Move((0, 0), dir=(1, 0))
print("until=px.first:", s.Copy().Line(until=px.first).pen.position)
print("until=px.last:", s.Copy().Line(until=px.last).pen.position)
```

## To other objects

A target does not have to be part of the sketch. Faces, wires and single edges work as well. The example draws a line
from (−3, 0.5) along x until it meets a plate of 4 × 2 centered on the origin, at (−2, 0.5):

```python
plate = px.QuickSketch().RectangleC(4, 2).Face()
end = px.QuickSketch((-3, 0.5), dir=(1, 0)).Line(until=plate).pen.position
print("the line ends at", end)
```