为表面曲率计算提供正确的输入

Question

我想计算点云中某些点的平均曲率和高斯曲率。

我有 x、y、z，它们是坐标，是一维数组。我想使用下面的代码 ^src 但是在输入参数 X，Y 和 Z 是二维数组，我不知道那是什么意思，我怎么计算对应的二维数组

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);

Answer 1

您有办法将 x、y、z 数据转换为曲面矩阵/二维数组。方式取决于数据的方式和内容。

结构化网格数据：

(i)。如果您的 x,y,z 对应于结构化网格，那么您可以直接获取 x,y 的 unique 值，它给出沿 [=28 的点数=](nx,ny) 分别沿 x 轴和 y 轴。使用此 (nx,ny)，您需要将 x、y、z 数据分别重塑为矩阵 X、Y、Z 并使用您的函数.

(ii)。如果你对重塑不满意，你可以得到 min 和 max 值 x,y 使用 meshgrid 制作你自己的网格 并使用 griddata.
非结构化网格数据：如果你的数据是非结构化/分散的，获取min和max，使你的网格使用 meshgrid 并使用 griddata 、 scatteredInterpolant 进行插值。

也可以查看以下链接：

https://in.mathworks.com/matlabcentral/fileexchange/56533-xyz2grd

https://in.mathworks.com/matlabcentral/fileexchange/56414-xyz-file-functions

为表面曲率计算提供正确的输入

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