finite differences

This article takes a topic that is often reduced to a one-line code snippet and turns it into a real design space. Quilez starts from the geometric fact that the gradient of the field is perpendicular to the isosurface, then compares forward, backward, and central differences in terms that matter to shader authors: bias, cost, numerical behavior, and visual quality. That makes it more useful than a generic calculus explanation, because it directly answers how to choose a normal-estimation method in an actual SDF renderer.

The other distinctive feature is that it goes beyond the classic six-sample gradient and presents compact alternatives such as tetrahedral sampling, along with the reasoning behind them. That matters in practice because normals are evaluated constantly in realtime ray marchers, and small changes in sampling pattern affect both performance and artifact profile. For a research topic page, this is the best source to cite when discussing why normal estimation is not an afterthought but a central part of the visual quality and cost of SDF rendering.