Linear interpolation inside a 3D triangle

Question

I have data at the nodes of a 3D triangle, and I need to interpolate to get data inside the triangle.

here is what i tried to do:

  x=[0,1,0];
 y=[1,0,1];
 z=[0,2,-1];
 [X,Y,Z]=meshgrid(x,y,z);
 v=[2,5,-1];
 xs=linspace(0,1,.1);
 ys=linspace(0,1,.1);
 zs=linspace(-1,2,.1);
 Vs = interp3(X,Y,Z,v,xs,ys,zs,'linear');

i get an error: The number of input coordinate arrays does not equal the number of dimensions (NDIMS) of these arrays.

what is wrong?

StefanM · Answer 1 · 2016-09-27T15:44:56.553

1

Let Xcontain the x-coordinates of your nodes, Y the y-coordinates, Z the z-coordinates of your nodes. Store the value/data at your nodes in V. Now you can specify where you want to interpolate the data by saving the x,y and z-coordinates of these points in Xs,Ys and Zs. The value of your data at these points is:

Vs = interp3(X,Y,Z,V,Xs,Ys,Zs,'linear');

You can take a look at the Matlab documentation.

Edit: As you added your code: The error seems to be that the dimension of your V is wrong. If you take a look at the example Matlab Docu -> interp3 -> Evaluate Outside the Domain of X, Y, and Z you will see, that Vhas to have the dimension as X, Yand Zcombined. From the documentation: size(V) = [length(Y) length(X) length(Z)] for vectors X ,Yand Z.

Here is an example:

X = linspace(-1,2,5);
Y = linspace(-1,7,23);
Z = linspace(3,9,23);
V = rand(23,5,23);

xq = linspace(0,1,34);
yq = linspace(0,2,34);
zq = linspace(4,5,34);
vq = interp3(X,Y,Z,V,xq,yq,zq,'linear',-1);

edited Sep 27 '16 at 15:44

answered Sep 27 '16 at 12:39

StefanM

797
1
10
17

X Y and Z should be gridded using meshgrid? Xs Ys Zs should be vectors? – user2600366 Sep 27 '16 at 13:34
X,Y and Z can also be vectors (Matlab documentation -> interp3 -> input arguments). So X(1) is the x coordinate of your first node, X(2) of your second node,.... The same goes for Y and Z. – StefanM Sep 27 '16 at 13:41
The same for Xs,Ys and Zs they can also be vectors. – StefanM Sep 27 '16 at 13:42
i added my code to the question – user2600366 Sep 27 '16 at 14:28
if u can please help me to find out whats wrong in my code i will be grateful – user2600366 Sep 27 '16 at 15:21
@user2600366 I editted my answer. Hopefully it will help you. – StefanM Sep 27 '16 at 15:32
can u please write an example for a valid v ? what does each row and column f v means? remmber that each of my original point has 1 value – user2600366 Sep 27 '16 at 15:34
Example has been added. If you look at the dimension of `vq` you'll see that every point in this example only has one value assigned. – StefanM Sep 27 '16 at 15:51
my last issue, if i want that matrix V will have the value 1 at x=y=z=0, i should put it in v(0,0,0) and so on – user2600366 Sep 27 '16 at 16:33
I found a detailed explanation of this function here - http://stackoverflow.com/questions/24766557/three-dimensional-3d-matrix-interpolation-in-matlab – StefanM Sep 27 '16 at 16:35

Linear interpolation inside a 3D triangle

1 Answers1