Game Development Math: Vectors & Movement, Frame-Rate Independence, Easing Curves, Collision Checks, Damage Formulas & Difficulty Curves
Work through the maths behind moving, colliding and balancing objects in a game: normalised movement vectors, the same speed at any frame rate, easing curves, circle and box collisions, aiming at targets, damage formulas and difficulty curves in tables you can chart, with every cell checked as you go.
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About this course
This course works through the maths of a small fictional 2D game prototype in a spreadsheet. You normalise movement vectors so diagonals are not faster, use delta time to keep speed the same at 30, 60 and 144 fps and clamp a lag spike. You model acceleration, a top-speed cap and friction, build ease-in, ease-out, smoothstep and sine easing curves and chart them. You test circle and box collisions and count hits with SUMPRODUCT, aim a turret with ATAN and a quadrant correction, rotate points with SIN and COS, compare damage models with crits and DPS, and grow enemy stats and spawn rates into a difficulty curve.
Lessons
- 2D Vectors: Position, Velocity & Normalised Diagonal Movement Pro
- Frame-Rate Independence: Speed × Delta Time at 30, 60 and 144 fps Pro
- Acceleration, Friction & Top Speed Frame by Frame Pro
- Easing Curves: Linear, Ease-In, Ease-Out, Smoothstep & Sine Pro
- Collision Checks: Circles, Boxes & Hit Counts Pro
- Aiming & Rotation: Angle to Target, Rotating Points & Turn Speed Pro
- Damage Formulas: Attack vs Armour, Crits, DPS & Time to Defeat Pro
- Difficulty Curves: Enemy Stats per Level, Spawn Rates & Time to Defeat Pro