lspline | R package : Linear Splines with Convenient Parametrisations

I'm trying to calculate y values based on x values and a series of curves defined by a set of vertices. I'm pretty new to R, and couldn't find a direct way to do this. I've found a couple of methods, but I am looking for a better method to generate a formula I can then apply to a series of data frames, to use in further transformations. The curves and vertices are literature values, and I need to use them as they are (linear line segments going through each vertex), rather than interpreting a model based on the points and then adding predictions.