Tessellation of computer-aided design (CAD) models plays a crucial role in engineering and scientific domains, offering foundational data for model visualization and serving as input for downstream CAD applications, including computer-aided engineering (CAE) and computer-aided manufacturing (CAM). This research presented a rapid tessellation algorithm for CAD models that employs an anisotropic quadtree background grid. The algorithm, constructed from the ground up, guaranteed the output as two-dimensional manifolds. It featureed a size function reliant on curvature and its first derivative to accurately identify geometric featureed within a controllable tolerance during curve discretization. During the adaptive quadtree phase for swift surface tessellation, it minimized mesh elements, ensuring alignment with the original CAD input through a posteriori hybrid multi-order tolerance criteria. Comparative numerical experiments indicate that this algorithm outperforms existing open-source software, such as OCC and Gmsh, and commercial solutions like Ansys, in geometric accuracy, background grid scale, and computational efficiency, highlighting its potential for practical engineering applications.