OPTIMALIZATION OF TRIANGULAR IRREGULAR
NETWORKS FOR MODELING OF GEOMETRICAL STRUCTURE OF GEORELIEF
The main aim of paper is to show that triangular irregular network has to fulfil condition of correct configuration as much as possible to be more accurate model of georelief (or other surface) used for visualization and like a base for further modelling.
The idea of condition of correct triangle configuration is based on fact that for exact representation of part of georelief surface (including first partial derivatives, slope and aspect) suppose that normal vector of triangle plain and real normal vector of modelled surface in place of triangle centroid are the same.
So, the main consequence of not fulfilling the condition of correct configuration of triangle is that normal vector computed based on triangle plane is other than real normal vector of georelief surface in that place. The normal vector is very important parameter for visualization especially for computing illumination. Therefore an offset of normal vectors produce none accurate model of georelief surface for visualization and also for processes modelling.
We want to present properties of condition of correct configuration of triangle depending on modelled surface, ways to fulfilling this condition. We want to present experiment for minimizing offset of normal vectors of triangular irregular network created by Delaunay triangulation by Lawson local optimalization which created more accurate model of georelief surface for visualization and other purposes.
One of the most important advantages of triangular irregular networks (TIN) is the possibility to adjust its shape to the shape of georelief (terrain) surface. Therefore TIN is preferred in some kinds of digital terrain model. In complex digital model of georelief we want to model not only its basic shape (elevation) but also its geometrical structure (with the first and the second partial derivatives and from them derived morphometric variables – slope, aspect and curvatures).
Therefore for exact modelling the triangles have to fulfil some conditions: the condition of representativeness, the basic condition for location and density of input point field – triangle vertices, and also the condition of correct configuration for the most accurate modelling of partial derivatives and morphometric variables.
We present the condition of correct configuration that is based on relation between georelief surface and plane of triangle. Simplifying of georelief surface in small neighbourhood of triangle centroid by osculating paraboloid we get simple geometrical relation between georelief surface and plane of triangle.
We can use this in (data-depend) triangulation; we show the way for identifying of positional shift which creates numerical error of the first partial derivatives, slope and aspect, so we can choose the most accurate triangle of possible triangles.
If there is dense grid as input, we can choose almost arbitrary point for constructed triangles. We present algorithm for geometrically ordaining of position of searched the third vertex for two known vertices, to create triangle fulfilling the condition of correct configuration.
The disadvantage of the presented methods is need to know the shape of georelief surface to represent, but that is just it for exact representation. The advantage is direct calculation of position of searching point, we do not need searching algorithm. Created TIN is well suited for exact modelling of geometrical structure of georelief, so it is assumption it will be used in some type of models.