Equidistant forward interpolation from the inertial real grid onto the comoving real grid using the fine grids. Real knots (•) are marked on the real and the fine grids; virtual knots (°) are marked on the fine grids. Knots i−1, i, and i + 1 are projected from the inertial real onto inertial fine grid using the map array (m_L, m_C, m_R) and corrected for the shift s to obtain the corresponding nearest-right neighbors n_L, n_C, and n_R in the comoving fine grid. In the comoving fine grid, two scans with running index n are done to find real knots on the intervals [m_L,m_C] and [m_C,m_R]: from n_C to n_R−1 using the next_real array (solid orange line), and from n_C−1 to n_L using the prior_real array (dotted orange line). When a real knot is found, we find the corresponding real comoving grid index j using the unmap array. The desired l.h.s. ξ (sloped black solid line) or r.h.s. 1−ξ (sloped black dotted line) weights are computed from n, n_L, n_C, n_R, and 4.