Building a Ray Tracer from Scratch in C++ Part 1: Mathematical Foundations

Graphics APIs and game engines make rendering look easy, but they hide most of the interesting details. I wanted to understand what actually happens under the hood, so I decided to build a small 3D renderer from scratch using C++. By the end of this article, you’ll understand the core ideas behind ray tracing and be able to build a simple renderer yourself. We’ll finish by rendering the image shown below, without using any graphics libraries or engines but with C++ and Maths. Why Ray tracing In computer graphics, there are two main rendering techniques: rasterization and ray tracing. You might ask, what exactly is rendering? In simple terms, rendering is the process of generating a 2D image or video from a 3D model or scene. It’s considered the final stage of a 3D engine. While rasterization is fast and used in real-time applications like games, ray tracing simulates how light behaves in the real world to produce highly realistic images, shadows, and reflections. It traces the path of