Illustrative contents of the five auxilliary arrays: map, unmap, real_knot, prior_real, and next_real. Orange lines between elements of map and unmap indicate that the arrays store each other’s indices. Indices of map run on the real grid from i_red = 5 to i_blue = 9. Indices of unmap run on the fine grid from 1 to m_max = 11. Logical array real_knot contains true for real and false for virtual knots. Arrays next_real and prior_real contain fine grid indices of corresponding nearest real knots, illustrated by orange lines connected to the elements of real_knot. The last element of next_real points to m_max + 1, while the first element of prior_real points to 0. Note that the outmost knots i_red → m = 1 and i_blue → m = m_max always have to be real.