How to populate 2D array from 2 vectors perpendicular to each other?

I have 2 files. Each file contains 4 columns. Column 1, 2 and 3 define the location of a point in x, y, and z-axis respectively, on a Cartesan coordinate. Column 4 is the Value of that point. 'Inline' and 'Crossline' are perpendicular to each other and intersect at (0,0) coordinate. How do I populate a 2D array from these 2 files? (The data below are simplified. The real data has finer resolution)

Inline =

   2.800000            0   15.0000    1.3678
   1.000000            0   15.0000    1.2000
          0            0   15.0000    1.0000
  -1.000000            0   15.0000    1.2000
  -2.500000            0   15.0000    1.5688

Crossline =

          0    -2.300000   15.0000    1.3546
          0    -1.000000   15.0000    1.1000
          0            0   15.0000    1.0000
          0     1.000000   15.0000    1.1500
          0     2.700000   15.0000    1.3558

[Matt J]

Populate it based on what rule?

[Yun Inn]

1. Inline data will be the main data to be duplicated.
2. Data to be duplicated for each Y-axis point available on Crossline
3. Duplicated 'Value' in column 4 should be scaled such that any original 'Value' from the 2 files remain the same

[Matt J]

Show the expected output given the simplified example data you gave above.

[Walter Roberson]

The sample matrices do not represent vectors.

[Yun Inn]

Expected output =

   2.800000     -2.300000   15.0000    1.3678*1.3546
   1.000000     -2.300000   15.0000    1.2000*1.3546
          0     -2.300000   15.0000    1.3546
  -1.000000     -2.300000   15.0000    1.2000*1.3546
  -2.500000     -2.300000   15.0000    1.5688*1.3546

   2.800000     -1.000000   15.0000    1.3678*1.1000
   1.000000     -1.000000   15.0000    1.2000*1.1000
          0     -1.000000   15.0000    1.1000
  -1.000000     -1.000000   15.0000    1.2000*1.1000
  -2.500000     -1.000000   15.0000    1.5688*1.1000

   2.800000            0    15.0000    1.3678
   1.000000            0    15.0000    1.2000
          0            0    15.0000    1.0000
  -1.000000            0    15.0000    1.2000
  -2.500000            0    15.0000    1.5688

   2.800000      1.000000   15.0000    1.3678*1.1500
   1.000000      1.000000   15.0000    1.2000*1.1500
          0      1.000000   15.0000    1.1500
  -1.000000      1.000000   15.0000    1.2000*1.1500
  -2.500000      1.000000   15.0000    1.5688*1.1500

   2.800000      2.700000   15.0000    1.3678*1.3558
   1.000000      2.700000   15.0000    1.2000*1.3558
          0      2.700000   15.0000    1.3558
  -1.000000      2.700000   15.0000    1.2000*1.3558
  -2.500000      2.700000   15.0000    1.5688*1.3558

[Walter Roberson]

Each of those groups is "V-shaped"; the inputs are not "two vectors perpendicular to each other".

[Yun Inn]

OK. So is it possible to get this sort of expected results?

Answer 1

[Roger Stafford]

This is my attempt to generalize your description. Let (x0,y0,z0) be the point of intersection of your two lines. (Note: The lines you gave intersected at (0,0,15).) I have abbreviated the names of the lines as 'I' and 'C'.

 [XI,XC] = ndgrid(I(:,1),C(:,1));
 [YI,YC] = ndgrid(I(:,2),C(:,2));
 [ZI,ZC] = ndgrid(I(:,3),C(:,3));
 [VI,VC] = ndgrid(I(:,4),C(:,4));
 OUT = [XI(:)+XC(:)-x0,YI(:)+YC(:)-y0),ZI(:)+ZC(:)-z0,VI(:).*VC(:)];

I depended entirely on your stated expected output, since I could not understand your verbal description of it at all. I gather you want to complete the "grid" consisting of all possible pairing of points on the two lines and at each grid point you want the value to be the product of the corresponding values given by the two lines.

Roger Stafford

[Walter Roberson]

Unfortunately the input does not actually form vectors; A(:,4) and B(:,4) are both V-shaped.

I went for the math approach first, and then when cross-checking found it was not suitable.

The scheme Yun Inn used was to replicate each (X,Y) combination, with the new 4th column being the product of the respective 4th columns.

[Roger Stafford]

The way I see it, the first three columns of "inline" and "crossline" do each constitute points along straight lines. These are in fact parallel to the x and y axes, respectively. In the output the x, y, z points are located in a rectangular gridwork based on intersections of lines which run through the points along each line and are parallel to the two respective lines. At least that is the way that seemed most likely. The explanation given was certainly not helpful.

[Yun Inn]

Roger's description is exactly what I wanted to achieve. Apology for my poor explanation.

Thank you for all the inputs. The solution works!

Answer 2

[Walter Roberson]

[a,b] = ndgrid(A(:,1), B(:,2));
c = bsxfun(@times, A(:,4), B(:,4).');
Output = [a(:), b(:), A(:,3)*ones(size(A,1)*size(B,1),1), c(:)];

[Andrei Bobrov]

[a,b,c] = ndgrid(A(:,1), B(:,2), A(:,3));
d = A(:,4)*(B(:,4).');
Output = [a(:), b(:), c(:), d(:)];