Matlab Code: Spline or Not

Today I had a short discussion with my officemate Roy, who is a senior PhD student in my program. The topic we discussed was the method of deaggregation. To draw a smooth line connecting the six given points (from USGS data), spline method is preferred. But I had problem on producing a series of smooth lines for each magnitude. There are weird curvature of the curves when the PGA values are within a 0.01g to 0.1g. After the evaluation with Roy, I figured out I need to change my interpolation process to make sure the curve is reasonable. Here is the summary from our meeting. (I write it down here to help me remember.)

• Apply spline once and only once to the total seismic hazard curve.
• Estimate the probability of Mw for six return period, then construct the deaggregation points for each Mw.
• Assume the probability between every two points from original six points (USGS data) is linear relationship.
• Assume the lines are parallel with each other when the PGA is smaller or greater than the smallest or greatest one of the six points (USGS data) separately.
  

So far the idea looks fine. I need to test the idea in Matlab to see what the result is.