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The relationships between patterns and processes lie at the core of modern landscape ecology. These dependences
can be quantified by using indices related to the patch-corridor-matrix model. This model conceptualizes
landscapes as planar mosaics consisting of discrete patches. On the other hand, relief variability is a key factor for
many ecological processes, and therefore these processes can be better modeled by integrating information concerning
the third dimension of landscapes. This can be done by generating a triangle mesh which approximates
the original terrain. The aim of this methodological paper is to introduce two new constructions of triangulations
which replace a digital elevation model. These approximation methods are compared with the method which was
already used in the computation of 3D-landscape metrics (firstly for parameterized surfaces and secondly for two
landscape mosaics). The statistical analysis shows that all three methods are of almost equal sensitivity in reflecting
the relationship between terrain ruggedness and the patches areas and perimeters. In particular, either of the methods
can be used for approximating the real values of these basic metrics. However, the two methods introduced
in this paper have the advantage of yielding continuous approximations of the terrain, and this fact could be useful
for further developments.
