Math for Games Quest, Edition 2

Picks up where Edition 1 ends: rotations and quaternions, transforms, collision tests, splines, noise, steering, balance math and cameras.

What's inside

• 51 quests across 8 worlds, each with step-by-step instructions, a clear "done when" check, and tips for when you get stuck
• A boss project at the end of every world that uses everything you just learned (8 in total)
• XP, levels, badges and streaks, plus target dates for every quest based on the pace you pick
• Comes with a vector lab: drag vectors around and watch the numbers update
• Walkthroughs you can collapse once you don't need the hand-holding

The worlds

• W9 Rotations & Quaternions: Pitch, yaw and roll, Spin in your own frame, Meet gimbal lock, Four numbers, one rotation, Slerp the short way, Aim and turn smoothly. Boss: Security Camera Rig.
• W10 Transforms & Matrices: What a transform holds, Parents and children, Stack two transforms, Undo a transform, A matrix is three arrows. Boss: Snap Point Builder.
• W11 Collision Math: Boxes that overlap, Spheres that touch, Ray meets plane, Ray meets sphere, Closest point on a line. Boss: Hand-Rolled Hit Scan.
• W12 Curves & Splines: Bezier by hand, Curves through points, Lay down a spline, Constant speed on a spline, Nearest point on the path. Boss: Rail Ride.
• W13 Noise & Procedural: Random vs smooth random, Perlin noise, Stack octaves, Same seed, same world, Noise-driven wobble. Boss: Rolling Hills Generator.
• W14 Steering & Motion: Seek, Arrive without overshooting, Flee, Look ahead and avoid, Springs and damping, Smooth at any frame rate. Boss: Drone Swarm.
• W15 Probability & Balance: Expected value, Weighted loot rolls, Pity timers, Shuffle bags, DPS on paper, XP curves. Boss: Balance Simulator.
• W16 Cameras & Screen Space: World to screen, Screen to world, Frame the shot, Trauma-based shake, Look-ahead camera. Boss: Drone Arena.

What you need

Unreal Engine 5 (free), plus vectors, dot products and basic trig, about where Edition 1 leaves you.

How it works

It's one HTML file. Double-click it and it opens in your browser. No account, no install, no subscription, and it works offline. Progress saves in your browser, and a save code in Settings lets you back it up or move it to another computer.

The vector lab is a simplified example for trying ideas. The actual quests happen in Unreal Engine.