How to fit points on a given t sequence to edges at different t moments on a known lattice

[wrx1990]

When I build scenario lattice like e.g
lattice_approximation([1,2,3,4,5],gaussian_path1D,1000000,2,1);
I will get the following image

I have a new t-series(gaussian_path1D) marked on the plot with a gray dot,how to get the nearest edge of each point at any t.