Radiation fireballs are singular phenomena which involve severe thermal radiation and, consequently, they need to be duly assessed and prevented. Although the radiative heat transfer produced by a sphere is relatively well known, the shadowing measures implemented to control the fireball’s devastating effects have frequently posed a difficult analytical instance, mainly due to its specific configuration. The objective of this article is to develop a parametric algorithm that provides the exact radiative configuration factors for the most general case in which the fireball is located at any distance and height above the ground, partially hidden by a protective wall over an affected area at different positions with respect to the said fireball. To this aim we use methods based on Computational Geometry and Algorithm-Aided Design; tools that, departing from the projected solid-angle principle, provide exact configuration factors, in all cases, even if they do not present a definite analytical solution. This implies dealing with spatially curved radiative sources which had not been addressed formerly in the literature due to their mathematical difficulties. Adequate application of this method may improve the safety of a significant number of facilities and reduce the number casualties among persons exposed to such risks. As a similar radiative problem appears in volcanic explosions; we hope that further extensions of the method can be adapted to the issue with advantage.