Do you mean you have curvatures instead of second derivatives or in addition to them?Hi, I found this example below on how to fit a curve by points and derivatives. Is it possible to something similar if If I have some points and curvature k? or if I know the osculating circle? y/n
thanks in advance
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Hi thanks, I am trying to find "g2" continuity:Do you mean you have curvatures instead of second derivatives or in addition to them?
Since curvature can be expressed through the first two derivatives you can, conversely, express the second derivatives through the first one and the curvature and thus reduce the problem to the one you've posted.
The system the book is describing is known as Ordinary Least Square (OLS), more commonly known as Multiple Linear Regression (MLR).
[math]\hat{y}=X\beta+\epsilon[/math]
As the name suggests, the OLS seeks the least square. In other words, minimize the residual error [imath]\epsilon[/imath] of the curve, so it doesn't take the curvature into account.
However, you can compare the fitted and the known curvature simply by looking at their ratios. If it's close to 1, it indicates a good fit.
Suppose [imath]K[/imath] is the known curvature, and [imath]K'[/imath] is the fitted curvature.Divide one by the other i.e. their ratio: [imath]\frac{K}{K'}[/imath].thanks for the reply, what do you mean by "ratios"
thanks
Just realized that my previous post is not really correct because in this thread the derivatives are given in different points, i.e. [imath]x_{2,i}[/imath] for the 1st and [imath]x_{3,j}[/imath] for the second.Do you mean you have curvatures instead of second derivatives or in addition to them?
Since curvature can be expressed through the first two derivatives you can, conversely, express the second derivatives through the first one and the curvature and thus reduce the problem to the one you've posted.