Therefore, study of capabilities of synthesis by ray tracing of images of smooth spatial curves constructed by the method of spherical interpolation is a crucial issue.
Literature review and problem statementThe methods for constructing curves and surfaces that interpolate points set in space largely determine complexity of the algorithm for synthesizing images of objects and realism of the synthesized scene. Comparison of various ways of describing curves and surfaces in solving problems of image synthesis by the method of ray tracing is given hereinafter. Objects with a triangulated surface without smoothing are used alongside the method of ray tracing in [3]. A method was proposed for finding the point of intersection of a projection ray (PR) with a triangle. At the same time, this approach significantly worsens realism of synthesized objects since the surface geometry is violated and physically correct illumination cannot be calculated.One of convenient mathematical methods for describing curvilinear forms of objects consists in their representation with the help of pieces of parametric curves, surfaces or splines. Finding the point of intersection of a PR with such surfaces is not an easy task. An algorithm for finding point of intersection of a PR with NURBS splines was proposed in 4
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