Techniques are described for rendering objects formed by implicit surfaces using ray-tracing, where each implicit surface is defined by a surface equation. The techniques utilize presence of real-roots to determine which implicit surfaces are intersected by a ray. If all implicit surfaces classified as uncomplemented surfaces intersect the ray, and none of the implicit surfaces classified as completed surfaces intersect the ray, the techniques determine a maximum from among a set of real-root values of the surface equations for the uncomplemented surfaces to determine an intersection point of the ray. The techniques utilize the intersection point for further processing such as per-pixel color and depth processing.