Chapter 13 · The Arcade

Three tiny games.
Three kinds of math.

The RTS showed everything at once — the arcade splits it by genre. A racer that IS a Bézier curve, a platformer that IS a parabola, and a turret game that IS a vector equation. Each one playable, each one showing its formula while you play.

insert coin ↓
Game 1 · racing — chapters 02 · 09 · 11

🏎 Bézier GP

The racing line is a loop of cubic Bézier curves — the kart's position is literally P(t). Hold ⬆ throttle: your speed lerps toward the pedal (ch 09), and the camera's FOV widens with speed — a Projection-matrix edit (ch 11) that makes fast feel fast.

hold ⬆ / W to floor it

Pedals

pos = P(t) · speed += (pedal − speed)·k
t = 0.00 · 0 km/h · FOV 55°
ch 02 bézierch 09 lerpch 11 projection
Game 2 · platformer — chapters 08 · 09 · 07

🐸 Parabola Run

Every jump in every platformer is the same two lines: vy += g·dt; y += vy·dt (ch 08). The ground rolls on a sine wave (ch 07), the camera chases you with a spring (ch 09). Time your jumps over the gaps — fall and you restart.

SPACE or the button to jump

Controls

vy += −22·dt · y += vy·dt
dist 0 m · best 0 m
ch 08 integrationch 09 spring camch 07 sine ground
Game 3 · shooter — chapters 01 · 08

🎯 Lead the Target

Your shells are slow — aim where the drone will be, not where it is. That's one vector equation: aim = pos + vel · (dist / shellSpeed) (ch 01). Each drone carries a faint ghost showing its predicted position — click the ghost, not the drone. Impacts burst into particles (ch 08).

click to fire · drag to orbit

Range officer

aim = pos + vel · (dist / 26)
hits 0 / shots 0
ch 01 vectorsch 08 particles