polynomial function 3D
显示 更早的评论
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 个评论
Bjorn Gustavsson
2021-1-29
Question to you: Is the curvature constant along a polynomial?
Christoph Thorwartl
2021-1-29
Christoph Thorwartl
2021-1-29
采纳的回答
Bjorn Gustavsson
2021-1-29
1 个投票
更多回答（1 个）
Walter Roberson
2021-1-29
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.
类别
在 帮助中心 和 File Exchange 中查找有关 Polynomials 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
