The concept of continuous scatterplot (CSP) is a modern visualization technique. The idea is to define a scalar density
value based on the map between an n-dimensional spatial domain and an m-dimensional data domain, which describe the CSP space.
Usually the data domain is two-dimensional to visually convey the underlying, density coded, data. In this paper we investigate kinds
of map-based discontinuities, especially for the practical cases n = m = 2 and n = 3 | m = 2, and we depict relations between them
and attributes of the resulting CSP itself. Additionally, we show that discontinuities build critical line structures, and we introduce
algorithms to detect them. Further, we introduce a discontinuity-based visualization approach – called contribution map (CM) – which
establishes a relationship between the CSP’s data domain and the number of connected components in the spatial domain. We show
that CMs enhance the CSP-based linking & brushing interaction. Finally, we apply our approaches to a number of synthetic as well
as real data sets.