Is it possible to make a surface perfectly proper?

Dear All,

I am getting the graph you see through the code below.

Can I get a plane-like surface with a proper shape like in the attached image without changing the points? I need a proper more evenly shaped surface, even if the surface does not pass through one-to-one points.

D = [288 2.79 7.55;

318 4.64 14.28;

127 2.31 8.31;

132 7.16 17.27;

264 2.31 4.32;

200 2.60 6.74;

268 3.06 15.12];

X = D(:,1);

Y = D(:,2);

Z = D(:,3);

% Create 100x100 grid mesh (x,y) points

[xGrid,yGrid] = meshgrid(linspace(min(X),max(X)),linspace(min(Y),max(Y)));

% Interpolation

zGrid = griddata(X(:),Y(:),Z(:),xGrid(:),yGrid(:),'cubic');

zGrid = reshape(zGrid,size(xGrid));

% Fig.1 Contour plot with original data points

figure

contour(xGrid,yGrid,zGrid,'ShowText','on')

hold on

scatter(X,Y,'ro')

grid on

colorbar

% Fig.2 Surf plot

figure

surf(xGrid,yGrid,zGrid)

colormap(jet)

colorbar

Thanks,

Ege

[Image Analyst]

Do you mean that you want to find the best-fit plane that goes through all those wildly varying points?

[Ege Ulus]

Yes, best fit hyperbolic paraboloid, elliptical, etc. surfaces are also accepted.

Answer 1

[Burhan Burak AKMAN]

You can change interpolation method.

zGrid = griddata(X(:),Y(:),Z(:),xGrid(:),yGrid(:),'v4');

[Ege Ulus]

Thanks, it helped!

Answer 2

[Simon Chan]

You may adjust the value of variable 'spacing' in the following code to meet your needs.

I use spacing = 5 as an example, you may try to use 10.

D =     [288            2.79            7.55;
  318            4.64            14.28;
  127             2.31            8.31;
  132           7.16             17.27;
  264           2.31             4.32;
  200           2.60             6.74;
  268           3.06             15.12];
X = D(:,1);
Y = D(:,2);
Z = D(:,3);
% Create 100x100 grid mesh (x,y) points
[xGrid,yGrid] = meshgrid(linspace(min(X),max(X)),linspace(min(Y),max(Y)));
% Interpolation
zGrid = griddata(X(:),Y(:),Z(:),xGrid(:),yGrid(:),'cubic');
zGrid = reshape(zGrid,size(xGrid));
% Fig.2 Surf plot
spacing = 5;                % Added this variable
figure
surf(xGrid(1:spacing:end,1:spacing:end),yGrid(1:spacing:end,1:spacing:end),zGrid(1:spacing:end,1:spacing:end))
colormap(jet)
colorbar

Answer 3

[Image Analyst]

Try John D'Errico's polyfitn()

https://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn?s_tid=srchtitle

It will fit your data to a 2-D polynomial of the order you want, like a plane or parabola.