Published Paper Details:

Computer gaming graphics and animations are at the forefront of technological advancements in the entertainment industry. The development and implementation of these graphics rely heavily on various mathematical concepts and techniques. This research paper delves into the sophisticated mathematical frameworks that underpin the optimization of real-time computational techniques essential for interactive computer gaming and high-fidelity animation systems. By integrating advanced concepts from algebra, calculus, and discrete mathematics, the study aims to enhance rendering algorithms, physics engines, and artificial intelligence in gaming environments. The paper systematically explores the application of quaternions for 3D rotations, spline theory for smooth animations, and graph theory for efficient path finding and decision-making processes. Furthermore, it examines the implementation of partial differential equations in simulating realistic physical phenomena and the use of linear algebra in optimizing graphical transformations and lighting models. Through a series of case studies and computational experiments, this research demonstrates how these mathematical approaches can significantly improve performance, visual quality, and interactivity in modern computer games and animation, pushing the boundaries of what is currently achievable in digital entertainment and simulation industries.