I am curious if a spline can be both relaxed (second derivative = 0 at both endpoints) and clamped (first derivative is explicitly defined at both endpoints). This only needs to be true for a single spline between two end points. If this is not possible, what power (quartic, quintic, etc.) of spline would be required to fulfill these conditions?
Either way, how would I go about calculating a spline that fulfills these conditions?
I know very little about splines, so I may be missing something obvious. Any help or additional resources would be great. Thanks!
Since you have 6 equations (2 points, 2 first derivatives and 2 second derivatives) to satisfy, the interpolating spline will have 6 control points as well. This means that the spline could be a quintic Bezier curve, a quartic b-spline curve of 2 segments or a cubic b-spline curve of 3 segments.