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