In optimiser analysis and design it is informative to visualise how a search point/population moves through the design space over time. Visualisable distance-based many-objective optimization problems have been developed whose design space is in two-dimensions, with arbitrarily many objective dimensions. Previous work has shown how disconnected Pareto sets may be formed, how problems can be projected to and from arbitrarily many design dimensions, and how dominance resistant regions of design space may be defined. Most recently, a test suite has been proposed using distances to lines rather than points. However, attention to visualisable problems has been limited This may be because the type of problem characteristics available has been relatively limited compared to many practical problems (and non-visualisable problem suites). Here we introduce the mechanisms required to embed several widely seen problem characteristics in a distance-based problem framework. These include local fronts, variable density of solutions in objective space, landscape discontinuities, varying objective ranges, neutrality in objective, space, and non-identical disconnected Pareto set regions. Furthermore we also provide an automatic problem generator (opposed to hand-tuned problem definitions). Additionally, example performance results are provided on some popular optimisers on sampled problem instances.