Solved
Spline
Why we have 3 functions lspline, pspline and cspline? Can we have only one spline?
Hi,
The second derivative at the endpoints for each function is as follows:
cspline—Determined by the straight line through the nearest two points.
lspline—Equals to 0.
pspline—Equals to the value of the next nearest point.
There is a fourth spline possibility. Call it a dspline? A spline can be put through n points in the XY plane if you also specify the derivatives or slope at each end point of the spline. I used to do this with roller coasters so the curved track could match slope of straight portions at start/finish. Using this method no extrapolation is possible.
The four splines looking closely at first two points. Each is subtly different.
