我试图计算一个由点数组(x，y，z)给出的曲面的曲率。最初我试图拟合一个多项式方程z=a+bx+cx^2+dy+exy+fy^2)

然后计算高斯曲率$ K = \frac{F_{xx}\cdot F_{yy}-{F_{xy}}^2}{(1+{F_x}^2+{F_y}^2)^2} $

但是，如果曲面是复杂的，则问题是拟合的。我找到了这个Matlab程序来数值计算曲率。我想知道如何在Python中做同样的事情。function [K,H,Pmax,Pmin] = surfature(X,Y,Z),

% SURFATURE - COMPUTE GAUSSIAN AND MEAN CURVATURES OF A SURFACE

% [K,H] = SURFATURE(X,Y,Z), WHERE X,Y,Z ARE 2D ARRAYS OF POINTS ON THE

% SURFACE. K AND H ARE THE GAUSSIAN AND MEAN CURVATURES, RESPECTIVELY.

% SURFATURE RETURNS 2 ADDITIONAL ARGUEMENTS,

% [K,H,Pmax,Pmin] = SURFATURE(...), WHERE Pmax AND Pmin ARE THE MINIMUM

% AND MAXIMUM CURVATURES AT EACH POINT, RESPECTIVELY.

% First Derivatives

[Xu,Xv] = gradient(X);

[Yu,Yv] = gradient(Y);

[Zu,Zv] = gradient(Z);

% Second Derivatives

[Xuu,Xuv] = gradient(Xu);

[Yuu,Yuv] = gradient(Yu);

[Zuu,Zuv] = gradient(Zu);

[Xuv,Xvv] = gradient(Xv);

[Yuv,Yvv] = gradient(Yv);

[Zuv,Zvv] = gradient(Zv);

% Reshape 2D Arrays into Vectors

Xu = Xu(:); Yu = Yu(:); Zu = Zu(:);

Xv = Xv(:); Yv = Yv(:); Zv = Zv(:);

Xuu = Xuu(:); Yuu = Yuu(:); Zuu = Zuu(:);

Xuv = Xuv(:); Yuv = Yuv(:); Zuv = Zuv(:);

Xvv = Xvv(:); Yvv = Yvv(:); Zvv = Zvv(:);

Xu = [Xu Yu Zu];

Xv = [Xv Yv Zv];

Xuu = [Xuu Yuu Zuu];

Xuv = [Xuv Yuv Zuv];

Xvv = [Xvv Yvv Zvv];

% First fundamental Coeffecients of the surface (E,F,G)

E = dot(Xu,Xu,2);

F = dot(Xu,Xv,2);

G = dot(Xv,Xv,2);

m = cross(Xu,Xv,2);

p = sqrt(dot(m,m,2));

n = m./[p p p];

% Second fundamental Coeffecients of the surface (L,M,N)

L = dot(Xuu,n,2);

M = dot(Xuv,n,2);

N = dot(Xvv,n,2);

[s,t] = size(Z);

% Gaussian Curvature

K = (L.*N - M.^2)./(E.*G - F.^2);

K = reshape(K,s,t);

% Mean Curvature

H = (E.*N + G.*L - 2.*F.*M)./(2*(E.*G - F.^2));

H = reshape(H,s,t);

% Principal Curvatures

Pmax = H + sqrt(H.^2 - K);

Pmin = H - sqrt(H.^2 - K);