Subject of this paper is triangulation of given domain also called as mesh generation. Overview of main mesh types (structured, unstructured and hybrid) is given. Groups of triangulation methods are defined and include collective triangulation, incremental triangulation, pliant mesh generation with post-triangulation and plaint mesh generation with retriangulation. Delaunay triangulation is described in greater detail and variuos Delaunay triangulation algorithms are presented including use of Delaunay triangulation for anisotropic mesh generation and method to generate Constrained Delaunay triangulation. Greedy insertion Delaunay and data dependent allgorithms are developed for hight fields surface aproximation. Significant improvements are made to these algorithms including faster recalculation, node selection and use of supplementary data sets in order to maximise efficiency of calculations. Main criteria to evaluate developed algorithms is overall error of approximation and speed of calculation. Data dependent algorithm generates better quality mesh (less approximation error), however Delaunay triangulation algorithm is significantly faster. Results and conclusions are presented at the end of paper.