Development of Algorithm and Data Structure for 2D Regions Discrete Model Elements Accelerated Search

Abstract

This paper is devoted to improving the search request processing productivity for planar discrete models used in engineering software. A data structure has been developed to accelerate the search for discretization elements based on a hierarchical triangular mesh. The developed indexing structure is built by a downward iterative algorithm, which constructs each new level of the hierarchy based on the previous level or indexed triangulation by simplifying it, which ensures that the morphology of the triangulation mesh is preserved throughout all levels of the hierarchical indexing structure. The developed building algorithm ensures the presence of tree-like connections between the levels of the hierarchical triangulation mesh, which allows downward navigation between geometrically close triangles. Search acceleration is achieved by performing a directed search in the top level of the indexing structure and then navigating between levels using downward links until the indexed triangle is found. The program implementation was carried out using C++17, and visualization of triangulation grids and isolines was carried out using the ObjectARX library. Based on the software implementation, an executive library was created.