Abstract: Tessellation of CAD models is essential in engineering applications and scientific research, providing foundational data for model visualization and serving as input for CAD downstream applications such as CAE and CAM. This study introduces a rapid tessellation algorithm for CAD models based on an anisotropic quadtree background grid. The algorithm, building from the bottom up, ensures that the results are two-dimensional manifolds. It incorporates a size function based on curvature and its first derivative for identifying features with controllable tolerance during curve discretization. In the adaptive quadtree stage for rapid surface tessellation, the design minimizes mesh elements while maintaining consistency with the original CAD input through a posteriori hybrid multi-order tolerance conditions. Comparative numerical experiments demonstrate that this algorithm surpasses open-source software like OCC and Gmsh, as well as commercial offerings like Ansys, in terms of geometric conformal accuracy, background grid scale, and computational efficiency, highlighting its potential for practical engineering applications.