I'm given a set of 25 points(x,y values). I need to curve fit these points using a parabolic blending. I'm not sure how to go about it. I read that we need to take 3 points at a time to ensure a unique parabola is obtained. I need to: take first 3 points(1,2,3) and fit a parabola to it. take the next 3 points (2,3,4) and do the same. This goes on till i reach my final point. The overlapping portions of any two parabolas is linearly blend using a cubic curve.
So, this looks more like a polyfit of third order except between point 1 and 2. Am i right in continuing on with a ployfit of order 3?