Ray tracing synthesis of spatial curve images built by the spherical interpolation method - Gusiatin, Vladimir; Gusiatin, Maksim; Mikhal, Oleg (Eastern-European Journal of Enterprise Technologies, 2017)
The problem of visualization by ray tracing of spatial curves specified by interpolation points and smoothed by the method of spherical interpolation was solved. The method of spherical interpolation was developed mainly for interpolation of a triangulated surface with the purpose of further visualization of this surface by the method of ray tracing. This method is universal and enables the construction of flat and three-dimensional smooth curves drawn through arbitrarily set points. The paper presents analytical relationships for realization of each stage of construction of a spatial curve by this method. To visualize a spatial curve, an iterative process (IP) was developed for calculation of a point in the projection ray (PR) closest to some point of a mathematical spatial curve. To establish correspondence of the curve point to a pixel in a computer monitor screen, position of this point was determined relative to the space region bounded by the pyramid of pixel visibility. The proposed IP has a potential of wide parallelization of computations. An algorithm for constructing points of a spatial curve was developed with its step coinciding with the step of the iterative calculation process, which allows one to perform visualization algorithm and plot a curve point in a single pass of the IP. To this end, the point in the PR and the direction vector of the curve lie in the same plane perpendicular to the interpolated segment in each iteration step. This approach enables determination of the directing vector modulus for the subsequent stage of this iteration step. The proposed interpolation algorithm is based on the simplest algebraic surface, sphere, and does not use algebraic polynomials of the third and higher degrees. The results of the studies were confirmed by simulation of the visualization process using the Wolfram Mathematica software package. The problem of combining new methods for constructing smooth geometric shapes of spatial curves defined by straight lines and the method of ray tracing which on the whole will increase realism of the synthesized scenes in computer graphics was solved