Royko O. Modelling of surfaces with triangular mesh taking into account the discrete analogue of curvature

Thesis for the degree of candidate of technical sciences, specialty 05.01.01 - Applied geometry, engineering graphics. - Kyiv National University of Construction and Architecture, Kyiv, Ukraine, 2015. The thesis is devoted to developing algorithms of discrete surface modeling, taking into account local values of discrete analogues of curvature. In addition, there are considered the features, which arise in the implementation of the proposed algorithms. Developed the algorithm of triangular mesh refinement. It is performed according to the values of the discrete analogue of Gaussian or mean curvature. Managing the refinement is carried out using quadtree. It allows displaying an irregular mesh topology, searching related items, adding or removing necessary elements of mesh. Also developed triangular mesh simplification algorithm, which is obtained by scanning three-dimensional object, or is the result of the modeling program. For the ordering of information about mesh used BSP-tree. Because of simplifying obtained the mesh with less triangular cells on flat areas of the model. The algorithms are implemented as software that allows to perform refinement or simplifying triangular mesh, as well as to analyze and compare the three-dimensional model based on the values of discrete analogues of Gaussian or mean curvatures of the respective vertices.