B\'ezier Curve

Bézier curves are parametric polynomial curves widely used in computer graphics and robotics for representing smooth, controllable paths. Current research focuses on optimizing Bézier curve generation and manipulation for various applications, including trajectory prediction (using probabilistic models and composite curves), motion planning (leveraging graph-theoretic approaches and safe corridor constraints), and 3D point cloud segmentation (via deep learning frameworks like BPNet). These advancements improve the efficiency and accuracy of Bézier curve applications in diverse fields, ranging from autonomous vehicle navigation and robotic control to the generation of synthetic datasets for machine learning.