Taking on the mathematics of a 3D graphics engine is the ultimate test of applied linear algebra and trigonometry. Whether you are pushing vertices on the CPU or writing custom shader mechanics to execute on the GPU, you are essentially building a massive matrix calculator. Furthermore, if you are architecting a native prefab editor directly within a game binary, mastering this spatial math is what allows you to translate a user's 2D mouse click into a 3D coordinate in your world.
Here is your condensed master course on the mathematics of 3D graphics.
Phase 1: The Primitives (Vector Math)
Before we can move a 3D object, we must define it. A 3D model is just a massive array of points in space, called Vertices . To calculate how these vertices interact with light and cameras, we use vectors.
| Concept | Explanation | Mathematical Formula |
| | | |
| Vectors | A direction and magnitude in 3D space. | $\mathbf{v} = \langle x, y, z \rangle$ |
| Vector Length | The physical length of the vector (Pythagorean theorem in 3D). | $\Vert{}\mathbf{v}\Vert{} = \sqrt{x^2 + y^2 + z^2}$ |