# How to convert matrix indexes to cartesian coordinates

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Tchilabalo on 24 Aug 2019
Commented: Tchilabalo on 25 Aug 2019
Given a matrix a shown above, i want to convert the cell indexes into cartesian coordinates. I am trying to figure out what these indexes represent: is it the center of the cell? or the left corner of the cell? Thanks.

It's both, it's neither... If this is for visualization, I'd prefer the center of the cell But generally its up to you to decide
Tchilabalo on 25 Aug 2019

Walter Roberson on 24 Aug 2019
Matrices are just arrays of values and there is no inherent Cartesian coordinates associated with them. They have rows and columns, not x and y.
If you use imshow() or image() or imagesc() to display an image, then you have the option to control how rows and columns map into data units. The default is a 1:1 mapping. The default for all three functions is that X=1 Y=1 will correspond to the center of the bottom left pixel and that X=columns Y=rows maps to the center of the upper-right pixel. Because the center are being referred to, the image would cover from (1/2,1/2) to (columns+1/2, rows+1/2)
There are other possibilities, such as georefferencing through the Mapping Toolbox, which provides some flexibility as to what coordinates mean, possibly including nonlinear projections. In such cases the person who created the dataset should have documented the transformation.
It is common for people to get confused with images and think that there should be a way to convert pixels into real world coordinates. Sometimes there are ways, but unless you are using a calibrated device such as MRI or confocal microscope, even if image has the appropriate headers then the headers are typically pretty wrong.

#### 1 Comment

Tchilabalo on 25 Aug 2019
Thanks for the clarification.

David Hill on 24 Aug 2019
n=3;%nxn matrix
a=1:n^2;
x=floor((a-.1)/n)+1;
y=mod(a,n);
y(find(y==0))=n;
plot(x,y,'LineStyle','none','Marker','o',"Color",'b');

#### 1 Comment

Tchilabalo on 25 Aug 2019
Thanks David.