VISUALISATION OF GEOMETRIC REGIONS OF COMPLEX SHAPES IN SHARED MEMORY PARALLEL COMPUTERS ; ВІЗУАЛІЗАЦІЯ ГЕОМЕТРИЧНИХ ОБЛАСТЕЙ СКЛАДНОЇ ФОРМИ В ПАРАЛЕЛЬНИХ ОБЧИСЛЮВАЛЬНИХ СИСТЕМАХ ЗІ СПІЛЬНОЮ ПАМ’ЯТТЮ

Using of the numerical methods for the solution of boundary value problems requires the making of discrete models of geometric regions of complex shape. The problem of generating a mesh can be divided into two independent tasks: 1) creating a formal description of the initial geometric region and 2) building its discrete model based on this description. The most difficult is the first stage, especially for geometric areas of irregular shape. A universal way to parametrically describe a geometric region of arbitrary shape is to use R-functions, which allow using logical operations of inversion, conjunction, and disjunction over elementary mathematical relations to construct implicit functions that uniquely describe the boundary of an arbitrary geometric object. The practical application of R-functions is quite complicated due to their implicit nature. To visualize the geometric regions described using implicit functions, you must first find a set of reference points that belong to the boundary of the original region, and then construct a voxel or boundary model for this set. The problem of effective finding points that belong to the boundary of the geometric region described using the implicit R-function is relevant today and requires the development of appropriate approaches and algorithms. This article describes a parallel algorithm for constructing and visualizing geometric models of regions described by implicit functions in computing systems with shared memory. This algorithm was implemented using the С++ standard library (C++11). A series of computational experiments were carried out, showing the effectiveness of the proposed algorithm on computers with various types of processors. ; Практичне застосування чисельних методів для розв’язання крайових задач потребує створення дискретних моделей геометричних областей складної форми. Проблему генерації сіткової моделі можна розбити на дві окремі задачі: 1)створення формального опису вихідної геометричної області та 2)побудову її дискретної моделі на основі цього ...