interest rates - How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries.

I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how to calibrate theta.

Is there any implementation that I could use (preferably matlab, r or c++) or a detailed description of the algorithm that I could use for reference? I have found some notes on the optimal form of theta*, but it's described in continuous rather than discrete terms, so it's of limited use in my case.