Ray tracing synthesis of images of triangulated surfaces smoothed by the spherical interpolation method

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.