Ray marching, is a technique used in computer graphics to render 3D scenes using distance functions. In traditional rendering techniques, objects in a scene are represented by meshes, which consist of many triangles that define the surface of the object. However, with ray marching, the geometry of the scene is represented by a distance function, which is a mathematical function that returns the distance between any point in space and the nearest surface of the scene.

The ray marching algorithm works by casting a ray from the camera into the scene, and then stepping along the ray, testing at each step whether the ray intersects with the distance function. If the ray intersects with the function, the distance to the nearest surface is calculated. This distance is then used to determine the next position along the ray to test for intersection. The process is repeated until the ray reaches the surface of the object, or until a maximum number of steps have been taken.

The key advantage of ray marching is that it allows for the rendering of complex shapes and scenes with much greater efficiency than traditional rendering techniques. With ray marching, the distance function can be used to represent complex geometry such as fractals, organic shapes, and procedural textures, which can be difficult or impossible to represent using traditional mesh-based techniques. Additionally, because the distance function is a mathematical function, it can be evaluated very quickly on a GPU, making ray marching a very efficient technique for real-time graphics applications.

One challenge of ray marching is that it requires a large amount of computation to accurately render scenes with complex geometry. To address this, various optimizations have been developed, such as adaptive step sizes, early termination, and multi-resolution rendering, which allow for efficient rendering of complex scenes using ray marching.