BACKGROUND GRID METHOD FOR PLANE SHAPES TRIANGULATION IN FUNCTIONAL APPROACH

Abstract

In herein paper is described the problem of triangular mesh generation for complex geometrical domain. Functional approach is used for a geometrical object representation. Vladimir Rvachev’s R functions are used also. Functional approach is based on implicit functions and logical operations (negation, conjunction and disjunction) over these functions. Logical operation is a special real-value function that at inner point is greater than zero and at outer point is less than zero. Thus standard triangulations techniques, which based on predefined boundary discreet model, is less efficient. During background grid method for triangulation, triangles are built in domain directly. Presented method starts with a mesh that can be relatively easy generated (e.g. uniform mesh). Next, initial mesh is defined as a set of all inner elements. The last one generates a layer of elements near boundary (adaptation step). Adaptive method generates meshes that are close to uniform for structured background grids.