how to Differentiate 3D points

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Kurt 2013-10-11

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评论： dpb 2013-10-12

Hi guys,

I have some 3D points of a 3D surface in x, y and z format. You can get the points here: http://textuploader.com/?p=6&id=EjEtc

Assuming 'M' is my 3D surface (i.e. made up of the 3D points), I would like to get the derivative of M with respect to the 'x' direction and the 'y' direction. That is, I want to differentiate M wrt to the x and y coordinates (i.e. gradient in x and y directions).

My data is not a uniform grid. Any ideas how to do this in Matlab ?

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Answer 1

dpb 2013-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/89919-how-to-differentiate-3d-points#answer_99336

在 MATLAB Online 中打开

See

doc gradient

maybe? Look at alternate syntax with spacing inputs not just minimum case.

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Kurt 2013-10-11

在 MATLAB Online 中打开

dpb,

To get a better undetanding of my problem. Here is my code which does the desired differentiation, but on a uniform XYZ grid. I have no idea how to adapt this for the non-grid 3D data I posted in the 1st post.

function Run_Differentiate_3D()
clc;clear all;close all
   % Generate data
   [X2,Y2] = meshgrid(-2:.2:2, -2:.2:2);                                
  % surf(X,Y,Z)
  X2= X2(:);
  Y2 = Y2(:);
  Z2 =zeros(size(X2),1)  ;
% data here is a Grid
Surface_3D = [X2 Y2 Z2];
% Cx is derivative wrt to x coordinates, likewise Cy for y coords.
[Cx,Cy]=SurfaceGrad3D(Surface_3D);
end
function [Cu,Cv]=SurfaceGrad3D(x)
   r=size(x,1);
   c=size(x,2);
   Cu=spalloc(r*c,r*c,r*c*2);
   Cv=spalloc(r*c,r*c,r*c*2);
    for j=1:c-1
       for i=1:r
           Cu((c-1)*r+i,(c-1)*r+i)=1;
             Cu((c-1)*r+i,(c-2)*r+i)=-1;
            Cu((j-1)*r+i,(j-1)*r+i)=-1;
  %          
            Cu((j-1)*r+i,(j)*r+i)=1;
   %Cu((c-1)*r+i,(c-2)*r+i)=-1;
  % Cu((j-1)*r+i,(j-2)*r+i)=-1;
  %Cu((j-1)*r+i,(j)*r+i)=1;
       end;
   end;
for i=1:r-1
    for j=1:c
          Cv((j-1)*r+r,(j-1)*r+r)=1;
         Cv((j-1)*r+r,(j-1)*r+r-1)=-1;
         Cv((j-1)*r+i,(j-1)*r+i)=-1;
           Cv((j-1)*r+i,(j-1)*r+i+1)=1;
            %Cv((j-1)*r+i,(j-1)*r+i-1)=-1;
         % Cv((j-1)*r+i,(j-1)*r+i+1)=1;
      end;
  end;
end

Kurt 2013-10-12

dpb,

what do you think of this fex, can it do the job? http://www.mathworks.com/matlabcentral/fileexchange/29312-diffxy/content/diffxy/html/demo_diffxy.html

dpb 2013-10-12

编辑：dpb 2013-10-13

Dunno--give it a go and see...you'll have to see what its assumptions are on data ordering, etc., ...

On the spline, if the data are a (relatively) smooth surface, the idea is that a piecewise cubic poly should be a good representation of same. Since it's a poly of low order, one can analytically compute the derivatives from the coefficients.

For globally-smooth data, response surfaces are often used as well for the same purpose or to reduce high-complexity models to simply-evaluated RSMs for such purposes as MC simulation where the actual evaluation would be excessively costly.

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how to Differentiate 3D points

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