polynomial function 3D
65 views (last 30 days)
Show older comments
Christoph Thorwartl
on 29 Jan 2021
Commented: Christoph Thorwartl
on 29 Jan 2021
Hello,
I would like to put a second order polynomial function through 9 points. The points are given in the form P(x,y,z).
Goal:
(1) Calculate polynomial function
(2) Calculate the mean curvature (= second derivative) of the function
Is there something similar to "p = polyfit(x,y,z,n)"?
Remark:
I can put a circle through three points in space and calculate the corresponding curvature of the circle. For this I use "circlefit3d(p1,p2,p3)". But I don't want to use only 3 of the 9 points for the curvature calculation.
I would be very pleased about a feedback.
3 Comments
Accepted Answer
More Answers (1)
Walter Roberson
on 29 Jan 2021
Is there something similar to "p = polyfit(x,y,z,n)"?
No. However, polyfit() constructs the Vandermode companion matrix and then uses \ for linear least squared computation of the coefficients. You can do the same thing;
X = x(:); Y = Y(:); Z = Z(:);
A = [X.^2, X.*Y, Y.^2, X, Y, ones(size(X))];
b = Z;
A\b
Assuming a*x^2 + b*x*y + c*y^2 + d*x + e*y + f = z .
In particular, assuming that there is no z^2 or x*z or y*z .
If there are higher order z, then at the moment I am not sure how to set up the problem without ending up with a companion matrix and all zeros on the right hand side, which unfortunately leads you to an all-zero solution instead of something useful.
See Also
Categories
Find more on Elementary Math in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!