Cutting-edge techniques in 3D modeling and animation: Leveraging mathematical models and advanced software tools

Abstract. This paper explores the advancements in computer animation technology, focusing on 3D modeling and animation. It delves into the core aspects of character design, environment modeling, and animation rigging, emphasizing the mathematical models and algorithms that enhance realism and efficiency. Key techniques discussed include Bezier curves and spline interpolation for anatomy and proportions, Perlin noise and fractal algorithms for texturing, and Inverse Kinematics (IK) and Forward Kinematics (FK) for rigging. Additionally, the paper examines procedural generation and fluid dynamics simulations for environment modeling and the integration of motion capture data. The use of software tools like Blender, Autodesk Maya, and Houdini is highlighted. This study aims to provide a comprehensive understanding of the current state of 3D animation technology and its future directions.