Abstract: The object of the study is a method of direct rendering of complex three-dimensional objects based on perturbation functions using graphics processors, using a variety of streaming multiprocessors. Direct rendering means that the visualization of functionally defined models takes place without their preliminary conversion to other formats, for example, into triangle grids. The research method is based on analytical geometry in space, differential geometry, interpolation theory and matrix theory, based on mathematical modeling and the theory of computing systems. The main conclusions of the study are: the possibility of direct rendering of functionally specified objects, when rendering it is important that the computing processors are not idle. The first problem that was solved was that different GPUs have different numbers of streaming multiprocessors. Therefore, it was necessary to choose during execution the optimal stage from which the work began. Thus, you can partially get rid of the problem with unused computing resources. The second problem, the balancing problem, was solved by using a large number of computing processors. For implementation, the CUDA parallel programming model was used, which, together with a set of software tools, allows implementing programs in the C language for execution on a GPU. The resulting system visualizes complex functionally defined objects with high resolution interactively. The dependence of performance on the computing power of graphics processors is investigated.

Abstract: The object of research is a new way of defining and visualizing a photorealistic terrain. The method to render a terrain as easily as a texture is proposed. A terrain model is coded as differential height map, i.e. the carrier surface is defined by algebraic means and only deviation from this basic surface is stored in the each node. Such a modeling method simplifies creation of smooth detail levels and shading. The data of height grid is not a subject to geometry transformations as the triangle vertices are. The geometry transformations are only required for the carrier surface. During the recursive voxel subdivision on each level, we project the centers of the voxels onto basic plane. The computed coordinates, as well as in the case of ordinary RGB texture map, will define address in the so called "altitude map" or "shape texture". The altitude corresponding to this address and a level of details is calculated, and are used to modify coefficients of the base plane equation. As a result will be obtained a surface modulated with the values from the altitude map. Visualization in real time on graphical accelerators is implemented. The method is based on the analytic geometry in space, differential geometry and vector algebra, interpolation theory and matrix theory, based on mathematical modeling and computer science. The main conclusions of the study are: the ability to generate the terrain using the same mechanism as for the texture color to display the terrain and changing levels of detail. The image interpolation is used for filtering heights dynamically similar to color texture. In comparison with the known methods the proposed method computation time substantially does not dependent on the resolution of the height map when generating a terrain.