<p>We present a computational comparison of B-spline interpolation and B-spline quasi-interpolation on full and sparse grids. Sparse grids offer an efficient framework for high-dimensional approximation by significantly reducing grid sizes while maintaining high accuracy, in contrast to the exponential complexity of full grids. Numerical experiments in two to five dimensions demonstrate that full grid approximations become increasingly impractical in higher dimensions due to rapid growth in memory and computation time. Our results also show that, somewhat surprisingly, constructing function interpolants and quasi-interpolants requires roughly the same computation time, even though quasi-interpolants are constructed locally without solving global systems of equations. Therefore, the main advantage of quasi-interpolation lies in its ability to evaluate function values locally at isolated points without constructing all grid components, while achieving nearly the same accuracy as spline interpolation. We further demonstrate the effectiveness of sparse spline quasi-interpolants as surrogate models in optimization, providing accurate approximations of local minimizers with reduced computational cost. Timing results highlight the trade-offs between grid setup and evaluation costs, reinforcing the limitations of full grids in high-dimensional settings. These findings support the use of sparse grids and quasi-interpolation as practical and scalable alternatives for high-dimensional computational tasks.</p>