Interpolating [X Y Z V] values on cylinder surface

Question

Ionesco 2021-8-25

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1440489-interpolating-x-y-z-v-values-on-cylinder-surface

评论： Simson Hutagalung 2022-7-5

xyzvm_cylinder.mat

I have four 1D arrays: x,y,z and v, representing (x,y,z) coordinates on a cylinder and v, the value (temperature) measured in that respective (x,y,z) point.

What I would like is to show the temperature distribution on the surface of the cylinder by interpolating these values. Something like this:

What I have managed is to scatter those points on the surface of the cylinder:

For the interpolation, I tried to use meshgrid and griddata, but I can't make it work.

function plot3D(x,y,z,v,m)
ddx=(2*pi*max(x))/m;
ddy=(2*pi*max(x))/m;
ddz=(max(z)-min(z))/m;
dx = min(x):ddx:max(x);
dy = min(y):ddy:max(y);
dz = min(z):ddy:max(z);
Tmin = min(v);Tmax=max(v);
[xqX,yqX,zqX] = meshgrid(dx,dy,dz);
vqX = griddata(x,y,z,v,xqX,yqX,zqX);
surf(xqX,yqX,zqX,vqX),hold on,
caxis([Tmin Tmax]);colormap('jet');shading interp;colorbar; 
end

Any ideas if it is possible?

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Answer 1

Wan Ji 2021-8-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1440489-interpolating-x-y-z-v-values-on-cylinder-surface#answer_774244

编辑：Wan Ji 2021-8-25

在 MATLAB Online 中打开

Actually, scatteredInterpolant function is easy to implement what you think.

function plot3D(x,y,z,v,m)
% scatter3(x,y,z);
Tmin = min(v); Tmax = max(v);
radius = mean(sqrt(x.^2+y.^2)); % use mean radius as radius
theta = linspace(0, 2*pi,m+1); % divide theta to m segments
minZ = min(z); maxZ = max(z);
Z = linspace(minZ, maxZ, m+1); % divide z to m segments
[Z, T] = meshgrid(Z, theta); % create meshgrid with theta and z
X = radius.*cos(T); % calculate X and Y for mesh 
Y = radius.*sin(T);
F = scatteredInterpolant(x,y,z,v,'linear'); % create interp handle
V = zeros(size(X));
V(:) = F(X(:),Y(:),Z(:)); % interp the value
Vave = 0.5*(V(end,:)+V(1,:)); % fix the minor flaw (average the beginnig and the end of corresponding theta)
V(end,:) = Vave; % fix the minor flaw 
V(1,:) = Vave; % fix the minor flaw 
surf(X,Y,Z,V,'edgecolor','none')
caxis([Tmin Tmax]);colormap('jet');shading interp;colorbar; 

Now use this function to produce figure

load('xyzvm_cylinder.mat')
plot3D(x,y,z,v,40)

The result shows as following

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Wan Ji 2021-8-25

@Ionesco

Hi, friend,

There still exists a flaw in my code, and I have fixed it. This flaw is due to the case that 2*pi and 0 are the same position for theta, so I averaged them to provide a fixed value.

Yours

Wan Ji

Simson Hutagalung 2022-7-5