GPU rendering

This chapter translates the abstract sphere-tracing idea into a concrete GPU rendering problem. Instead of discussing implicit surfaces in the abstract, it uses per-pixel displacement mapping to show why fixed-step sampling is brittle on hardware: either you undersample and miss intersections, or you oversample and lose performance. The chapter’s real contribution is showing how a precomputed distance map gives exactly the missing information needed to advance aggressively through empty space while still converging near the displaced surface.

It is especially useful as an implementation-oriented reference. The text walks through the ray setup in tangent space, the normalization details needed because texture-space distances are anisotropic, and the shader structure that turns the method into a practical step-and-test loop for realtime graphics. Compared with more theory-first sources, this one is valuable because it explains why ray marching fit the GPU pipeline so well and how distance-guided stepping solved a specific production rendering problem rather than remaining a purely academic technique.