Game math for developers: vectors, angles and smooth motion

Most of the maths in games is not advanced. It is a small set of tools used again and again: vectors for positions and directions, the dot product for "is it in front of me", trigonometry for angles and circles, interpolation and easing for smooth motion, and a little bit of randomness used well. The trouble is that these tools are usually taught in abstract form, far away from the games where you need them.

This course teaches them through game problems. How do I make an enemy face the player? How do I check if the player is inside a vision cone? Why does my camera jitter? How do I make a projectile arc? Each lesson starts with a problem, explains the idea visually and then implements it.

What you will learn

• Vectors: adding, scaling, normalising, length and distance
• Dot and cross products and what they tell you
• Angles, radians, sine and cosine for rotation and orbits
• Interpolation, easing curves and frame rate independent smoothing
• Projectile motion and simple physics integration
• Random numbers, noise and weighted choices
• An introduction to transforms, local versus world space and quaternions

Engine agnostic

Examples are shown in GDScript and C# for Unity, but the ideas apply to any engine or framework. Each lesson includes a small interactive demo you can play with to build intuition.

You should be able to program in at least one language and have tried a game engine before. School level algebra is enough; we rebuild everything else.