The spline can be evaluated at query points using the da_interpolation_evaluate_? function. Multiple derivative orders can be requested at once. The requested values are returned in a flat array \(y_{\text{data}}\) of size \(n \times \text{dim} \times n_{\text{order}}\), always giving in contiguous memory all the values of a given dimension and order. The ordering can be visualized as follows:
\[\begin{split}\begin{aligned}
& S^0(x_0), \, S^0(x_1), \, \ldots, \, S^0(x_{n-1}) \curvearrowright && \text{(dimension 0, order 0)} \\
& S^1(x_0), \, S^1(x_1), \, \ldots, \, S^1(x_{n-1}) \curvearrowright && \text{(dimension 1, order 0)} \\
& \qquad \vdots && \vdots \\
& S^{\text{dim}}(x_0), \, S^{\text{dim}}(x_1), \, \ldots, \, S^{\text{dim}}(x_{n-1}) \curvearrowright && \text{(dimension dim, order 0)} \\
& \qquad \vdots && \vdots \\
& {S^{\text{dim}}}'(x_0), \, {S^{\text{dim}}}'(x_1), \, \ldots, \, {S^{\text{dim}}}'(x_{n-1}) \curvearrowright && \text{(dimension dim, order 1)} \\
& \qquad \vdots && \vdots \\
& {S^{\text{dim}}}''(x_0), \, {S^{\text{dim}}}''(x_1), \, \ldots, \, {S^{\text{dim}}}''(x_{n-1}) \curvearrowright && \text{(dimension dim, order 2)} \\
& \qquad \vdots && \vdots
\end{aligned}\end{split}\]