75 lines
2.9 KiB
Markdown
75 lines
2.9 KiB
Markdown
# Step 06 — Ray vs AABB (two sweeps become one hit)
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This is where step 04 ("collision = the AND of two 1D tests") and step 05 ("the
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entry/exit time of one sweep") finally fuse. A **moving point vs a static box**.
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## Concept
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A point at `p` moves by `v` over the frame. A static box has a left/right edge
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(its x-interval) and a top/bottom edge (its y-interval). The point is inside the
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**box** only while it's inside the x-interval **and** the y-interval _at the
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same time_.
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So run `sweepInterval` twice:
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```
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spanX = sweepInterval(p.x, v.x, box.x, box.x + box.w) // the x-edges
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spanY = sweepInterval(p.y, v.y, box.y, box.y + box.h) // the y-edges
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```
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Each gives you a time-window `[entry, exit]` during which the point is inside
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_that one axis's_ strip. You're inside the box during the **overlap of the two
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windows**:
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```
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entry = max(spanX.entry, spanY.entry) // inside the box once you're inside the LAST axis
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exit = min(spanX.exit, spanY.exit) // out of the box once you leave the FIRST axis
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```
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Read those two lines until they feel obvious — they're the whole algorithm:
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- You're only truly _inside the box_ once you've entered **both** strips, so the
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real entry is the **later** of the two entries → `max`.
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- You **leave** the box the instant you exit **either** strip → the **earlier**
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exit → `min`.
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### When is there NO hit?
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1. **A span is `null`** — on some axis the point isn't moving and is already
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outside that strip. It can never be inside the box. Return `null`
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immediately.
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2. **`entry > exit`** — the two windows never overlap. The point is inside one
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strip, then the other, but never both at once. That's the classic "flies past
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the corner" miss.
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3. **`entry >= 1` or `exit <= 0`** — the windows overlap, but not _during this
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frame_ (it's entirely in the future, or entirely in the past). Not our
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problem this frame.
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### The normal (which wall did we hit?)
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When you do collide, you also want to know **which face** you hit, so the
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response later can push you back the right way. That's the `normal` — a unit
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vector pointing out of the surface you struck.
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The trick: **the axis you entered _last_ is the axis you actually hit.** Compare
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the two entry times — whichever is larger is the blocking axis:
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- if `spanX.entry > spanY.entry` → you hit a **vertical** wall (left/right
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face). The normal is horizontal, pointing back against your x-motion:
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`normal = { x: v.x > 0 ? -1 : 1, y: 0 }`.
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- otherwise → you hit a **horizontal** wall (top/bottom). The normal is
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vertical: `normal = { x: 0, y: v.y > 0 ? -1 : 1 }`.
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(Moving right and hitting something → the surface pushes you left → normal `-1`.
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That sign rule is all there is to it.)
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## Task
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Implement `rayVsAABB(p, v, box)` in `ray.ts`. Return `{ time, normal }` for the
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entry, or `null` for any of the three no-hit cases. `sweepInterval` is provided
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in `given.ts` — **reuse it**, don't re-derive it.
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```sh
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bun test workshop/steps/06-ray-vs-aabb
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```
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