The recent developments in the research area have shown a significant focus on advancing numerical methods and approximations, particularly in the context of spline functions and polynomial interpolations. There is a notable trend towards enhancing the efficiency and accuracy of these methods, with researchers exploring novel approaches to scaling and quadrature rules. For instance, the integration of scaled Hermite functions has been shown to improve approximation performance, with a new framework proposed to optimize scaling factors. Additionally, advancements in quadrature rules for high-smoothness splines on refined triangles demonstrate a move towards more precise and adaptable numerical techniques. The field is also witnessing improvements in distance function approximations, leveraging convolutional and differential methods to achieve greater accuracy. Notably, some papers have introduced innovative solutions that not only advance the theoretical understanding but also offer practical computational benefits, such as the ability to balance error components and enhance convergence rates. These developments collectively indicate a push towards more sophisticated and efficient numerical tools that can be applied across various scientific and engineering disciplines.