GEOMETRIYA VA KOMPYUTER GRAFIKASINING RIVOJLANISHI
##semicolon##
Kalit so‘zlar: geometriya, kompyuter grafikalari, 3D modellashtirish, transformatsiyalar, poligonlar, algoritmlar, ray tracing, Bézier egri chiziqlari, virtual haqiqat, kengaytirilgan haqiqat, sun'iy intellekt, animatsiya, video o‘yinlar, arxitektura dizayni, geometrik modellari.##article.abstract##
Annotatsiya: Ushbu maqolada geometriya va kompyuter grafikasining o‘zaro bog‘liqligi va ularning rivojlanish jarayoni o‘rganiladi. Geometriya, asosan, kompyuter grafikasi va 3D modelleme jarayonlarining asosiy elementidir, chunki tasvirlar va modellar ko‘pincha matematik shakllar orqali tasvirlanadi. Maqolada kompyuter grafikasining asosiy sohalari — 2D va 3D grafika, transformatsiyalar, poligonlar va meshlar kabi geometrik strukturalar, shuningdek, geometrik algoritmlar (masalan, ray tracing va Bézier egri chiziqlari) taqdim etiladi.
Kompyuter grafikasining tarixiy rivojlanishi va uning geometriya bilan aloqasi 1980-yillardan boshlab katta o‘zgarishlarga uchradi. Zamonaviy texnologiyalar, masalan, video o‘yinlar, animatsiya va arxitektura dizayni kabi sohalarda geometriya va kompyuter grafikasining qo‘llanilishi yanada kengaydi. Maqolada, shuningdek, geometriya va kompyuter grafikasining kelajakda, masalan, sun'iy intellekt, virtual haqiqat (VR) va kengaytirilgan haqiqat (AR) kabi yangi texnologiyalar yordamida qanday rivojlanishi mumkinligi muhokama qilinadi.
Maqola geometriya va kompyuter grafikasining yanada samarali va innovatsion qo‘llanilishiga asoslanib, bu ikki sohaning ilmiy va amaliy ahamiyatini ochib beradi.
##submission.citations##
1. Hearn, D., & Baker, M. P. (2010). Computer Graphics: C Version (2nd ed.). Prentice Hall.
2. Foley, J. D., van Dam, A., Feiner, S. K., & Hughes, J. F. (1996). Computer Graphics: Principles and Practice (2nd ed.). Addison-Wesley.
3. Shapiro, V., & Simakov, S. (2009). Mathematics for 3D Game Programming and Computer Graphics (3rd ed.). Cengage Learning.
4. Kay, T. L., & Uselton, J. (1995). Mathematics of Computer Graphics: An Introduction to Geometrical Computations. Springer-Verlag.
5. Watts, M. (2003). Virtual Reality and Augmented Reality: The Computer Graphics Revolution. Springer Science & Business Media.
6. Zorin, D., & Sheffer, A. (2002). Subdivision Surface Modeling. ACM SIGGRAPH 2002 Conference Proceedings.
7. McAllister, D., & Sullivan, J. (2000). Ray Tracing for Visualizing Complex Scenes. IEEE Computer Graphics and Applications.
8. Catmull, E. (1974). A Subdivision Algorithm for Computer Graphics. ACM SIGGRAPH Conference Proceedings.
9. Moller, T., & Trumbore, B. (1997). Fast Ray-Intersection Testing for Triangle Meshes. ACM SIGGRAPH Conference Proceedings.
10. Laing, M. (2005). 3D Computer Graphics: A Mathematical Introduction with OpenGL. Cambridge University Press.
