Game Development Math: Vectors & Movement, Frame-Rate Independence, Easing Curves, Collision Checks, Damage Formulas & Difficulty Curves

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn key inputs into movement vectors, measure their length with SQRT, normalise them so diagonals are not faster, and move a player frame by frame.
• Compare per-frame movement with delta-time movement at 30, 60 and 144 fps and clamp a lag spike, so the dash covers the same distance on every machine.
• Update the velocity frame by frame with acceleration, a top-speed cap and friction, then work out how many frames the run-up and the coast take and how far the player slides.
• Build five easing curves over normalised time, turn one into a panel position and chart the curves to see how each one starts and stops.
• Test circle pairs by distance against the sum of the radii, test axis-aligned boxes with four overlap conditions in AND, and count the hits straight from the data with SUMPRODUCT.
• Find the angle from a turret to each target with ATAN plus a quadrant correction, rotate the barrel tip with SIN and COS, and limit how fast the turret may turn.
• Apply a ratio armour model, add the expected value of critical hits, turn it into damage per second and time to defeat, and see why a subtractive model needs a minimum damage.
• Grow enemy hit points exponentially and damage linearly, speed up spawning down to a floor, compare enemy toughness with the player's planned DPS and chart the curve.