time for a snapshot

workshop/steps/03-integration/README.md

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+# Step 03 — Integration (moving over time)
+
+## Concept
+
+"Integration" sounds like calculus, but the version we need is one line. An
+object has a **position** and a **velocity**. Each frame we advance the position
+by the velocity, scaled by how much time passed:
+
+```
+newPosition = position + velocity * delta
+```
+
+That's `add(pos, scale(vel, delta))`. This single step is the beating heart of
+every game's update loop.
+
+### Why `delta`?
+
+`delta` is the number of **milliseconds since the last frame**. Frames are not
+evenly spaced — a busy frame takes longer. If you moved a fixed amount *per
+frame* instead of *per millisecond*, your game would run faster on a fast
+computer and slower on a slow one.
+
+By storing velocity as **units-per-millisecond** and multiplying by `delta`, the
+distance travelled over a given stretch of real time is the same no matter how
+the frames are chopped up. That property is called **framerate independence**,
+and one of the tests below proves it: moving once with `delta = 16` lands in the
+same place as moving sixteen times with `delta = 1`.
+
+## Task
+
+Implement `integrate(pos, vel, delta)` in `motion.ts`.
+
+```sh
+bun test workshop/steps/03-integration
+```