WIP

workshop/steps/09-slide/README.md

@@ -1,28 +1,31 @@
 # 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.
+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
+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.
+- 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:
+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)
@@ -30,8 +33,8 @@ 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.)
+share a direction. Subtract the shared-with-the-normal part, and nothing
+pointing into the wall survives.)
 
 ### Feel it with numbers