nage/workshop/steps/09-slide/README.md

Step 09 — Slide (this is what dot was for)

Back in step 02 you implemented dot and I said "you'll see later." This is later. Sliding is the difference between a game that feels good and one where you stick to every wall like glue.

The problem

You're moving with velocity v and you hit a wall whose outward normal is n. If you just stop (velocity → 0), the player jams against the wall — press into a wall diagonally and all motion dies, even the part that was parallel to the wall and perfectly fine. What we actually want: cancel only the part of v that pushes into the wall, and keep the part that runs along it. That's a slide.

The math (projection)

Any velocity v can be split into two pieces relative to the wall:

• the part along the normal (into/out of the wall) — this is what the wall forbids,
• the part along the wall surface (perpendicular to the normal) — this is fine.

Because n is a unit vector, the amount of v pointing along n is exactly dot(v, n). That single number is "how much of v goes straight into the wall." The vector piece pointing into the wall is n * dot(v, n). Subtract it off:

vSlide = v - n * dot(v, n)

What's left has zero component along the normal — it lies flat against the wall. (That's the geometric meaning of dot: it measures how much two vectors share a direction. Subtract the shared-with-the-normal part, and nothing pointing into the wall survives.)

Feel it with numbers

Move v = (10, 5) into a wall whose normal is n = (-1, 0) (a vertical wall on your right, pushing you left):

• dot(v, n) = 10*(-1) + 5*0 = -10
• n * dot = (-1,0) * -10 = (10, 0)
• vSlide = (10,5) - (10,0) = (0, 5)

The rightward motion (10) is gone — that was driving you into the wall — but the downward motion (5) survives untouched. You slide down the wall. Exactly right.

This is the very last line of your engine's moveAndSlide: velocity -= normal * (velocity · normal).

Task

Implement slide(v, normal) in slide.ts using dot, scale, and sub (all in given.ts). Return the velocity with its into-the-wall component removed.

bun test workshop/steps/09-slide