# Step 05 — Sweeping in 1D (entry & exit time)

This is the seed of the whole engine. Get this one _in your bones_ and the scary
2D `sweptAABB` becomes "do this twice and combine."

## Concept

Forget 2D. Forget boxes. We have:

- a **point** sitting at position `p` on a number line,
- moving with velocity `v` — meaning over this one frame it travels a total of
  `v` units (so at fraction `t` of the frame, it's at `p + v*t`, for `t` from 0
  to 1),
- and a static **interval** `[min, max]` on that same line.

Question: **during this frame, for which `t` is the point inside `[min, max]`?**

### The slab math

The point reaches `min` when `p + v*t = min`, i.e. `t = (min - p) / v`. Likewise
it reaches `max` at `t = (max - p) / v`.

```
t1 = (min - p) / v
t2 = (max - p) / v
```

If `v` is **negative** (moving left), the point hits `max` _before_ `min`, so
`t1 > t2`. We always want `entry` to be the smaller and `exit` the larger, so
**swap them if they're out of order**. Then:

- `entry` = the time the point _enters_ the interval,
- `exit` = the time it _leaves_.

> These can be negative or greater than 1 — that just means the crossing happens
> before this frame started or after it ends. Don't clamp here; the caller (step
> 06/08) decides whether `entry` falls within `[0, 1]`. Keeping the raw numbers
> is what lets us combine axes later.

### The `v == 0` edge case

If the point isn't moving (`v == 0`), it never _crosses_ an edge — dividing by
zero is meaningless. Instead: it's either already inside the interval for the
whole frame, or never. So:

- if `min <= p <= max`: it's inside the entire time → `entry = -Infinity`,
  `exit = +Infinity`.
- otherwise: it never overlaps → return `null`.

(Those infinities are deliberate: in 2D they let a non-moving axis say "I'm not
the axis that limits the collision," without breaking the `max`/`min` combine
step. You'll see why in step 06.)

## Task

Implement `sweepInterval(p, v, min, max)` in `sweep1d.ts`. Return
`{ entry, exit }`, or `null` only in the not-moving-and-outside case.

```sh
bun test workshop/steps/05-sweep-1d
```