Local optima networks (LONs) are a compact graph-based visualisation and characterisation approach to represent the fitness landscape of an optimisation problem. LONs are most frequently generated for combinatorial problems, where neighbourhoods can be crisply defined. A handful of approaches exist for continuous spaces, e.g. using derivatives-based local search approaches and basin-hopping, or by discretising the continuous space via gridding. Here we propose a new approach. Neighbourhoods are defined as balls around quasi-random samples from the search space. Basins and local optima are identified by greedily traversing these sampled neighbourhoods. One interpretation of such a formulation is that it approximates the LON induced by a \((1+\lambda )\) –Evolution Strategy (ES) with a ball mutation. The proposal allows the generation of LONs for problems with non-linear constraints, and discontinuous functions. We detail construction methods and illustrate the effective landscapes for some different objective functions using both the proposed methodology and derivatives-based alternatives.