Ray tracing synthesis of spatial curve images built by the spherical interpolation method
DOI:
https://doi.org/10.15587/1729-4061.2017.103975Keywords:
ray tracing, projection ray, modeling of curves and surfaces, quadrics, spherical interpolationAbstract
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 solvedReferences
- Hughes, F. J., Van Dam, A., McGuire, M., Sklar, D. F., Foley, J. D., Feiner, S. K., Akeley, K. (2014). Computer Graphics (principles and practice). Addison-Wesley Publishing Company, Inc., 1209.
- Hurley, J. (2005). Ray Tracing Goes Mainstream. Understanding the Platform Requirements of Emerging Enterprise Solutions, 9 (2). doi: 10.1535/itj.0902.01
- Schmittler, J., Woop, S., Wagner, D., Paul, W. J., Slusallek, P. (2004). Realtime ray tracing of dynamic scenes on an FPGA chip. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware – HWWS ’04. doi: 10.1145/1058129.1058143
- Efremov, A., Havran, V., Seidel, H.-P. (2005). Robust and numerically stable Bezier clipping method for ray tracing NURBS surfaces. Proceedings of the 21st Spring Conference on Computer Graphics – SCCG ’05. doi: 10.1145/1090122.1090144
- Sisojevs, A., Glazs, A. (2011). An Efficient Approach to Direct NURBS Surface Rendering for Ray Tracing. The 19th International Conference on Computer Graphics, Visualization and Computer Vision WSCG'2011 proceedings. Plzen: University of West Bohemia, 9–12.
- Song, X., Aigner, M., Chen, F., Juttler, B. (2009). Circular spline fitting using an evolution process. Journal of Computational and Applied Mathematics, 231 (1), 423–433. doi: 10.1016/j.cam.2009.03.002
- Baramidze, V., Lai, M. J., Shum, C. K. (2006). Spherical Splines for Data Interpolation and Fitting. SIAM Journal on Scientific Computing, 28 (1), 241–259. doi: 10.1137/040620722
- Pang, M., Ma, W., Pan, Z., Zhang, F. (2006). Smooth Approximation to Surface Meshes of Arbitrary Topology with Locally Blended Radial Basis Functions. Computer-Aided Design and Applications, 3 (5), 587–596. doi: 10.1080/16864360.2006.10738412
- Shi, H., Sun, Y. (2002). Blending of Triangular Algebraic Surfaces. MM Research Preprints. MMRC, AMSS, Academia, Sinica, Beijing, 21, 200–206.
- Vyatkin, S. I. (2007). Modeling of complex surfaces using perturbation functions. Autometry, 43 (3), 40–47.
- Gusiatin, V. M., Gusiatin, M. V. (2013). Construction of a spatial curve by the method of spherical interpolation in problems of computer graphics. News of the Sumy State University. Series: Technical sciences, 2, 23–30.
- Gusiatin, V. M., Gusiatin, M. V. (2016). Synthesis of ray tracing of images of vector textures formed by the method of spherical interpolation. Radiotelektronnyi i komp'yuterny sistemi, 1 (75), 29–34.
- Gusiatin, V. M. (2001). Method of reduction of iterations in real-time image synthesis algorithms. Radioelectronics and Informatics, 1, 99–100.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Vladimir Gusiatin, Maksim Gusiatin, Oleg Mikhal
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.