Implicit surfaces provide many useful solutions for computer graphics tasks such as simple in/out queries, resolution independent representation and compact definition. However, rendering them robustly and efficiently provides a challenge especially for surfaces defined with complex field functions. In Part I, we introduce a real-time rendering method for skeleton-based integral surfaces. It relies on dynamically built A-buffers on GPU to discard empty spaces and reduce the number of skeleton primitives evaluation. The root finding is performed using rational quadratic interpolation to limit the number of field evaluations. Part II introduces per-primitive interval arithmetic for skeleton-based integral surfaces for real-time rendering and slicing, and finally in Part III we introduce a family of robust forward inclusion methods for rendering a wide family of implicits. Using linear and quadratic inclusion functions calculated either by bounding the first and second order derivatives, or building the bounds up from the basic algebraic operations that constitute the field function definitions, ray-surface intersections are calculated reliably and efficiently. The problem of creating infinite or invalid bounds are eliminated by reducing the interval sizes and bounding piece-wise defined functions. Example surfaces are given with skeleton-based implicits, convolution surfaces, Hermite radial basis implicits for real-time rendering and slicing for additive manufacturing.