Looking for a function f(x,y,z) based on 3 points to calculate interpolat​ed/extrapo​lated values with a linear relation

Hello together, I am new to this forum and just starting using Matlab. Hope you could help me with my problem.

I have a "scattered" set of points with coordinates (x,y,z) that lie all in a plane.

For 3 points I have a certain measurement value. There is a linear relation between the measurement values.

Now I want to calculate the values for the remaining points.

I tried 'scatteredInterpolant', 'interpn' and 'griddatan' without any success.

Do you have any suggestions for the solution?

Thank you and regards

Eugen

Answer 1

[David Goodmanson]

HI Appli,

This is something Matlab does really well. I assume by 'linear relation' you mean that each point has a value

c = a1*x + a2*y + a3*z with the a's to be determined. Denoting the coordinates of the three known points by p,q,r rather than x,y,z, you have the three equations

a1*p1 + a2*q1 + a3*r1 = c1
a1*p2 + a2*q2 + a3*r2 = c2
a1*p3 + a2*q3 + a3*r3 = c3

i.e. the matrix eqn. P*A = C where

P = [p1 q1 r1;
     p2 q2 r2;
     p3 q3 r3] 

A = [a1; a2; a3]   % column vector
C = [c1; c2; c3]   % column vector

After constructing P and C with known values, this is solved in one line as

A = P\C

and once A is known, the rest of the C values (n of them, say) are determined by setting up the nx3 matrix

X = [x1 y1 z1;
    . ..
     xn yn zn]

Then

   C = X*A

provides the n the values of c.

[Appli Kation]

Hello David,

This is exactly what I was looking for.

Thank you very much for your support!