geometry processing

Bloomenthal’s survey situates ray marching inside the wider language of implicit modeling instead of treating SDFs as an isolated graphics trick. It gives a careful explanation of implicit functions, regularity, and the geometric meaning of the gradient, including why the normalized gradient provides a surface normal and how numerical differencing approximates that gradient when an analytic derivative is unavailable. That makes it one of the strongest references for the conceptual link between scalar fields, isosurfaces, and shading.

It is also particularly useful because it connects rendering to modeling operations. The survey covers constructive solid geometry, blending, and the broader convenience of implicit representations for boolean composition and shape design, including cases where hard-edged junctions challenge polygonal approximations. For a research page, that breadth matters: it helps explain why SDF workflows are appealing not only because they ray march well, but because implicit surfaces are naturally compositional and support operations that are awkward in mesh-first representations.