When using Hermite Interpolation for smooth curves, does it mean the curve function would have the order of 2x points on the curve? For example, here there would be 8 parameters (4 values and 4 derivatives), will that result in a Hermite Interpolation of max power = 7 polynomial? If that's the case, the interpolation process would have a runtime extremely high, O(n^3) I guess?
buggy213
I believe that it is done piecewise, so in this instance if we label the points 0, 1, 2, 3, then the segments from 0 to 1, 1 to 2, and 2 to 3 are all interpolated separately. To ensure that you get a continuous curve, you have to set constraints on the endpoints / derivatives of each segment. This can be a big issue for bezier curves, where trying to maintain C2 continuity leads to nonlocal effects when editing a control point as it forces all of the other ones to move to satisfy constraints.
llejj
To implement hermite splines, would we calulate derivatives numerically?
When using Hermite Interpolation for smooth curves, does it mean the curve function would have the order of 2x points on the curve? For example, here there would be 8 parameters (4 values and 4 derivatives), will that result in a Hermite Interpolation of max power = 7 polynomial? If that's the case, the interpolation process would have a runtime extremely high, O(n^3) I guess?
I believe that it is done piecewise, so in this instance if we label the points 0, 1, 2, 3, then the segments from 0 to 1, 1 to 2, and 2 to 3 are all interpolated separately. To ensure that you get a continuous curve, you have to set constraints on the endpoints / derivatives of each segment. This can be a big issue for bezier curves, where trying to maintain C2 continuity leads to nonlocal effects when editing a control point as it forces all of the other ones to move to satisfy constraints.
To implement hermite splines, would we calulate derivatives numerically?