DOI: https://doi.org/10.15587/1729-4061.2018.145531

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

Vladimir Gusiatin, Maksim Gusiatin, Oleg Mikhal

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

Keywords


ray tracing; projection ray; modeling curves and surfaces; quadric; spherical interpolation

Full Text:

PDF

References


Hughes, F. J., Andries, V. D., Morgan, M., David, F. S., James, D. F., Steven, K. F., Kurt, A. (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: https://doi.org/10.1535/itj.0902.01

Romaniuk, O. N., Obidnyk, M. D., Melnykov, O. M. (2012). Sproshchennia protsedury vyznachennia vektoriv iz vykorystanniam sferychno-kutovoi interpoliatsiyi. Reiestratsiya, zberihannia i obrobka danykh, 14 (2), 14–24.

Efremov, A., Havran, V., Seidel, H.-P. (2005). Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces. Proceedings of the 21st Spring Conference on Computer Graphics – SCCG ’05. doi: https://doi.org/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.

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: https://doi.org/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: https://doi.org/10.1080/16864360.2006.10738412

Shi, H., Sun, Y. (2002). Blending of Triangular Algebraic Surfaces. MM MMRC, AMSS, Academia, Sinica, Beijing, 200–206.

Vyatkin, S. I. (2007). Modelirovanie slozhnyh poverhnostey s primeneniem funkciy vozmushcheniya. Avtometriya, 43 (3), 40–47.

Nagata, T. (2005). Simple local interpolation of surfaces using normal vectors. Computer Aided Geometric Design, 22 (4), 327–347. doi: https://doi.org/10.1016/j.cagd.2005.01.004

Gusyatin, V. M., Gusyatin, M. V. (2002). Vektornoe pole napravlyayushchih v zadache modelirovaniya krivolineynyh poverhnostey metodom sfericheskoy interpolyacii. Vymiriuvalna ta obchysliuvalna tekhnika v tekhnolohichnykh protsesakh, 1, 88–92.

Gusyatin, V. M., Gusyatin, M. V. (2013). Sglazhivanie triangulirovannoy poverhnosti metodom sfericheskoy interpolyacii v zadachah komp'yuternoy grafiki. Radioelektronni i kompiuterni systemy, 3 (62), 59–64.

Gusiatin, V., Gusiatin, M., Mikhal, O. (2017). Ray tracing synthesis of spatial curve images built by the spherical interpolation method. Eastern-European Journal of Enterprise Technologies, 3 (4 (87)), 4–9. doi: https://doi.org/10.15587/1729-4061.2017.103975

Gusyatin, V. M. (2001). Metod umen'sheniya iteraciy v algoritmah sinteza izobrazheniy real'nogo masshtaba vremeni. Radioelektronika i informatika, 1, 99–100.


GOST Style Citations


Computer Graphics. Principles and practice / Hughes F. J., Andries V. D., Morgan M., David F. S., James D. F., Steven K. F., Kurt A. Addison-Wesley Publishing Company, Inc., 2014. 1209 p.

Hurley J. Ray Tracing Goes Mainstream // Understanding the Platform Requirements of Emerging Enterprise Solutions. 2005. Vol. 9, Issue 2. doi: https://doi.org/10.1535/itj.0902.01 

Romaniuk O. N., Obidnyk M. D., Melnykov O. M. Sproshchennia protsedury vyznachennia vektoriv iz vykorystanniam sferychno-kutovoi interpoliatsiyi // Reiestratsiya, zberihannia i obrobka danykh. 2012. Vol. 14, Issue 2. P. 14–24.

Efremov A., Havran V., Seidel H.-P. Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces // Proceedings of the 21st spring conference on Computer graphics – SCCG '05. 2005. doi: https://doi.org/10.1145/1090122.1090144 

Sisojevs A., Glazs A. 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, 2011. P. 9–12.

Baramidze V., Lai M. J., Shum C. K. Spherical Splines for Data Interpolation and Fitting // SIAM Journal on Scientific Computing. 2006. Vol. 28, Issue 1. P. 241–259. doi: https://doi.org/10.1137/040620722 

Smooth Approximation to Surface Meshes of Arbitrary Topology with Locally Blended Radial Basis Functions / Pang M., Ma W., Pan Z., Zhang F. // Computer-Aided Design and Applications. 2006. Vol. 3, Issue 5. P. 587–596. doi: https://doi.org/10.1080/16864360.2006.10738412 

Shi H., Sun Y. Blending of Triangular Algebraic Surfaces. MM MMRC, AMSS, Academia, Sinica, Beijing, 2002. P. 200–206.

Vyatkin S. I. Modelirovanie slozhnyh poverhnostey s primeneniem funkciy vozmushcheniya // Avtometriya. 2007. Vol. 43, Issue 3. P. 40–47.

Nagata T. Simple local interpolation of surfaces using normal vectors // Computer Aided Geometric Design. 2005. Vol. 22, Issue 4. P. 327–347. doi: https://doi.org/10.1016/j.cagd.2005.01.004 

Gusyatin V. M., Gusyatin M. V. Vektornoe pole napravlyayushchih v zadache modelirovaniya krivolineynyh poverhnostey metodom sfericheskoy interpolyacii // Vymiriuvalna ta obchysliuvalna tekhnika v tekhnolohichnykh protsesakh. 2002. Issue 1. P. 88–92.

Gusyatin V. M., Gusyatin M. V. Sglazhivanie triangulirovannoy poverhnosti metodom sfericheskoy interpolyacii v zadachah komp'yuternoy grafiki // Radioelektronni i kompiuterni systemy. 2013. Issue 3 (62). P. 59–64.

Gusiatin V., Gusiatin M., Mikhal O. Ray tracing synthesis of spatial curve images built by the spherical interpolation method // Eastern-European Journal of Enterprise Technologies. 2017. Vol. 3, Issue 4 (87). P. 4–9. doi: https://doi.org/10.15587/1729-4061.2017.103975 

Gusyatin V. M. Metod umen'sheniya iteraciy v algoritmah sinteza izobrazheniy real'nogo masshtaba vremeni // Radioelektronika i informatika. 2001. Issue 1. P. 99–100.







Copyright (c) 2018 Vladimir Gusiatin, Maksim Gusiatin, Oleg Mikhal

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN (print) 1729-3774, ISSN (on-line) 1729-4061