In this post AI quickly explains the majority of the math nessicary for basic game development. It begins with the foundational idea of space—1D lines, 2D planes, and 3D volumes defined by axes labeled x, y, and z, while also acknowledging higher dimensions like w in 4D. Building on this, it explores vectors as quantities with direction and magnitude, and introduces operations like the cross product to find perpendicular vectors, which are essential for understanding surfaces and reflections. Next, it discusses the dot product, a way to measure how aligned two vectors are, and how it helps with projections and reflections in physics and graphics. Moving into angles, it explains how vectors relate to directions on a unit circle, introduces degrees and radians as measures of rotation, and shows how sine and cosine functions describe these rotations. Matrices then come into play as tools to perform transformations like scaling, rotating, and translating vectors in space, including how matrix multiplication combines these operations. Finally, it touches on basic physics modeling, showing how position updates over time by applying velocity and acceleration with respect to frame rate, introducing the concept of delta time to keep motion consistent regardless of hardware speed.
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