Abstract
The problem of imaging by ray tracing of triangulated surfaces smoothed by the spherical interpolation method was solved. The method of spherical interpolation was mainly designed to interpolate the triangulated surface with the subsequent aim of imaging this surface by the method of ray tracing. This approach makes it possible to combine the method of ray tracing with the accumulated base of models with a triangulated surface. The method of spherical interpolation is universal and enables construction of plane and spatial smooth curves drawn through arbitrarily set points. The proposed interpolation algorithm is based on a simple algebraic surface, sphere, and does not use algebraic polynomials of the third and higher orders. Analytical relations for realization of each stage of construction of an interpolating surface by this method were given. For imaging the interpolating surface, an iterative algorithm (ITA) of calculation of the point of intersection of a projection ray with this surface was constructed. The proposed ITA has an ability of a broad paralleling of computations. An algorithm of constructing points of an interpolating surface was developed with its step coinciding with the step of the iterative computation process which makes it possible to execute the algorithm of imaging and construct the surface point in a single ITA pass. The study results were confirmed by simulation of the imaging process in the Wolfram Mathematica package. Thus, the problem of combining new methods of constructing smooth geometric forms of triangulated surfaces and the method of ray tracing was solved which, in general, will improve realism of synthesized scenes in computer graphics
Highlights
In modern computer graphics, methods of rasterization and ray tracing are applied to synthesize images of 3D objects [1, 2]
The unresolved issues mentioned above restrain widespread use of the highly realistic method of ray tracing in computer graphics
This will make it possible to improve realism of image synthesis by the method of ray tracing with the use of the base of models of objects with triangulated surfaces accumulated in computer graphics
Summary
Methods of rasterization and ray tracing are applied to synthesize images of 3D objects [1, 2]. The ray tracing method has been actively developed in recent years It enables synthesis of images of analytically described surfaces without their prior triangulation which significantly improves realism of the synthesized object images. Combination of the ray tracing method with the accumulated database of object models and software must be implemented while preserving features of high realism of the method This problem can be solved if interpolation of triangle illumination is eliminated and replaced by interpolation of a triangle with a certain curved surface. Such an approach makes it possible to improve realism of the synthesized polygonal object images. Search for new methods for modeling smooth geometric shapes of polygonal surfaces for the purpose of further imaging with application of the ray tracing method is still an urgent task at this stage of the computer graphics development
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