Open Geoscience, Vol. 10, iss. 1(2018), s. 395-402
The paper discusses limitations of analytical
attainment of the attitude of a geological plane by using
three non-collinear points. We present problems that
arise during computing the orientation of a plane generated
by almost collinear points. We referred these errors
to floating-point arithmetic inaccuracies. To demonstrate
the problem, we examined a surface of constant orientation.
We used Delaunay triangulation to calculate its local
orientation parameters. We introduced a new measure of
collinearity applicable for collecting attitude of planar triangles.
Using this measure we showed that certain planes
generated by the triangulation cannot be treated as a reliable
source of measurement. To examine the relationship
between collinearity and orientation, we used a combinatorial
algorithm to obtain all possible planes from the
given set of points. A statistical criterion of rejecting almost
collinear planes was suggested.