time for a snapshot

workshop/steps/02-vectors-length/README.md

@@ -0,0 +1,39 @@
+# Step 02 — Length, Normalize, Dot
+
+## Concept
+
+### Length (magnitude)
+
+An arrow `(x, y)` has a length: how far it reaches. Pythagoras:
+`length = sqrt(x*x + y*y)`. A velocity's length is its **speed**.
+
+### Normalize
+
+Often you want *just the direction* of an arrow, with length exactly 1 (a "unit
+vector"). You get it by dividing the arrow by its own length:
+`(x / len, y / len)`.
+
+This is how your engine turns "the player pressed up+left" into a clean diagonal
+direction before multiplying by a speed — so diagonal movement isn't faster than
+straight movement.
+
+> ⚠️ **The zero-vector trap.** What is the length of `(0, 0)`? Zero. What is
+> `0 / 0`? `NaN`. If you normalize a zero vector naively, you poison it with
+> `NaN`, and `NaN` spreads through every later calculation silently. A correct
+> `normalize` must check for zero length and return `(0, 0)` instead of dividing.
+> Remember this trap — it is exactly the kind of bug that hides in a real engine.
+
+### Dot product
+
+`dot(a, b) = a.x*b.x + a.y*b.y`. One number out of two vectors. For now just
+implement it; in step 09 you'll learn that it answers "how much of arrow A points
+along arrow B?" — the key to sliding along a wall.
+
+## Task
+
+Implement `length`, `normalize` (zero-safe!), and `dot` in `mathv.ts`.
+`vec`/`add`/`sub`/`scale` are already provided in `given.ts`.
+
+```sh
+bun test workshop/steps/02-vectors-length
+```