surf indices reversed?

Quick question: It seems surf and surfl have indices reversed. Is this correct? For example, if I type

x=0:pi/10:pi
y = 0:pi/10:2*pi
for i = 1:11 
    for j = 1:21
        z(i,j) = sin(x(i))*sin(y(j))
    end
end
surfl(x,y,z)

I get the standard: Error using surfl (line 94)

The lengths of X and Y must match the size of Z.

error. If I use z' in place of z it runs. But shouldn't the first indiex be the x and the second the y? This is completely unintuitive to me.

[Stephen23]

" It seems surf and surfl have indices reversed. Is this correct? "

Yes.

"But shouldn't the first indiex be the x and the second the y?"

No.

It is due to an inconsistency between mathematical practice and graphics-plotting expectations, you can find a good explanation here:

https://blogs.mathworks.com/loren/2007/06/21/indexing-terminology/

This not just something that MATLAB has to contend with, see the indexing option here:

https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html

and another blog, apparently written by someone with a graphics background:

https://eli.thegreenplace.net/2014/meshgrids-and-disambiguating-rows-and-columns-from-cartesian-coordinates/

[Craig]

Thanks, Stephen. I see this. I expect the indices to line up. I am used to the idea that in matrices, the first index is vertical, and down, and the second index across. In lotting, the first index is across, and the second index up. I want to to be able to access a coordinate, say (3,7) and think of that as both the coordinates and the location in the matrix, even though when you write out the matrices, the numbers are rotated -90 degrees from the plot.

But even surf by default doesn't do what you have done. It flips the y-values so they go up.

Anyway, the issue is just a difference between the indexing conventions in matrices and plotting. I understand. It's just less logical to me. I guess I'm not "most users".

I like how the Python scripts have the option to change conventions. Does Matlab do anything similar?

[Image Analyst]

Craig, if the axis direction defaults don't do it the way you'd like, you can flip the direction of the y axis with

axis ij
axis xy

Use whichever does it the way you want.

[Craig]

Thanks!

Answer 1

[Matt J]

Yes, the x-axis traverses the rows of z and the y-axis traverses the columns.

For some reason, many people prefer their x-axis to be horizontal.

[Craig]

Not quite saure I understand the answer. As a matrix, x should traverse the rows (the first index). But it's not. It's traversing the columns. The matrix z above has 11 rows and 21 columns. But when I plot (x,y,z), it tries to plot (y,x,z), and hence the dimensions don't match.

There's the obvious conversion problem from conversion from matrices, where the first index is going down and the second index across, to a Cartesian graph, where the first index goes across and the second up, but anyone familiar with plotting matrix data figures out that you rotate 90 degrees from matrix to plot. There seems a real issue, though, when you give the function (x,y,z) and it plots (y,x,z).

[Matt J]

As a matrix, x should traverse the rows (the first index). But it's not.

When I say "traverse the rows", I mean you move along a row as x varies.

but anyone familiar with plotting matrix data figures out that you rotate 90 degrees from matrix to plot.

I'm not sure what language requires that you rotate 90 degrees. Regardless, here you have a very similar situation, except that you are required to transpose instead of rotate. The need to do either one is unappealing, IMHO.

The bottom line is, your conjecture is right. The surf() routines view z(i,j) such that y varies with i and x varies with j. The same is true for interp2(), meshgrid(), and nearly all Image Processing Toolbox functions.

[Craig]

Thanks, Matt. And thanks for your first answer, too. My first comment was a little short.

Yes, when I read "traverse the rows" I parsed that as moving from row to another ("traverse a row" I would have read as going down one row, from one column to the next. Don't know if that is right, but what you said makes sense now).

The rotation is not a language, just mathematical conventions. When you access the i-jth entry of a matrix z ( z(i,j) in Matlab), you go down to the ith row and across to the jth column. In a function z(x,y), for z(x_i, y_j) you would go across the x-axis to the ith entry on our grid, then up to the jth entry on the grid. Anyway, the different conventions for plotting and matrix entries cause some confusion, but I understand what Matlab is doing now. Not intuitive to me, but I can use it.

Answer 2

[Sean de Wolski]

I think you're seeing the difference between meshgrid and ndgrid. Meshgrid is used for plotting, ndgrid for matrix/tensor work

[rr,cc] = ndgrid(1:3,1:4)

rr = 3×4

1 1 1 1 2 2 2 2 3 3 3 3

cc = 3×4

1 2 3 4 1 2 3 4 1 2 3 4

[xx,yy] = meshgrid(1:3,1:4)

xx = 4×3

1 2 3 1 2 3 1 2 3 1 2 3

yy = 4×3

1 1 1 2 2 2 3 3 3 4 4 4

When I was heavily involved in 3d image processing in grad school I tried to be very very consistent and always use row/col as: the convention, notation, and variable names.

[Image Analyst]

Oh, so that's the difference. I never knew. I just always used meshgrid() for everything since I knew that one and didn't want to learn another function. But I can see how ndgrid() could be useful in some situations.

[Craig]

Thanks, Sean!

Answer 3

[Image Analyst]

Craig, you do know that matrices in MATLAB are indexed (row, column), right? Apparently not since if I

choose better names for your loop iterators we get this:

x = 0:pi/10:pi

y = 0:pi/10:2*pi

for xIndex = 1:11

for yIndex = 1:21

z(xIndex,yIndex) = sin(x(xIndex))*sin(y(yIndex))

end

end

Why are you indexing z like that? Well since row is y, M(row, column) is M(y, x). Matrices are not indexed like M(x, y). You should have z(yIndex, xIndex). The obvious solution is to just label the axes:

xlabel('X', 'FontSize', 25);

ylabel('y', 'FontSize', 25);

zlabel('Z', 'FontSize', 25);

axis equal

But make sure you do it right. You can also use meshgrid(), which you should. I don't have surfl() so I used surf():

x = 0:pi/10:pi;
y = 0:pi/10:2*pi;
for xIndex = 1: length(x) 
    for yIndex = 1: length(y)
        z(yIndex,xIndex) = sin(x(xIndex))*sin(y(yIndex));
    end
end
[X, Y] = meshgrid(x, y);
surf(X, Y, z);
% Label the first argument to surf(), which is the columns or x values.
xlabel('X', 'FontSize', 25);
% Label the second argument to surf(), which is the rows or y values.
ylabel('Y', 'FontSize', 25);
zlabel('Z', 'FontSize', 25);
axis equal
g = gcf;
g.WindowState = 'maximized';

[Craig]

Thanks, image analyst. I do know that matrices are labeled row, column. The "apparently not" comment sounds to me condescending, but it's easy to misinterpret things online so I won't worry about it.

Read the last response to Matt above. The issue is with the different conventions for matrices compared to plotting. If I give you a point (4,2,3), you x=4, y=2, and z =3 (across 4 units, then up, then out of the page in my mind, or across, back, up). But in matrix z, z(4,2)=3 you go down to the 4th row, the across to the seocnd column, and input 3.