In a number of problems from reliability engineering, geosciences, insurance and beyond, it is of crucial importance to modellers and decision makers to estimate regions of controllable and/or uncontrollable parameters that lead to abnormal responses of systems of interest. This includes for instance engineering configurations and/or wind conditions leading to potential collapse of a bridge, physical conditions leading to a divergence of neutronic reactions in nuclear saftey, and sea and weather state variables combined with dyke properties potentially leading to floods. Nowadays, in all of these issues, numerical simulations are increasingly used in order to understand which regions of parameter space lead to situations ranging from acceptable (or even beneficial, in case the economical context) to potential catastrophes. At the user level, visualisation is essential in order to grasp what is sound from what is to be excluded, and understanding the geometry of the underlying parameter regions can be very useful for making well-informed or even optimal decisions. Here we investigate mathematical ICT approaches to the visualisation of such sets in dimensions higher than 3.