# How do i make a line of datapoints between 2 points on map, and use their index for later.

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I am working with some glaciers in Greenland, where i have a matrix A of data that describes all x,y coordinates and the corresponding ice thickness. What i want is to create a straight line of data points between 2 different chosen x,y coordinates. Then, i want to find the indexes of these x,y points in the original matrix that lie on this straight line, so i can find the corresponding indexes of their respective ice_thickness data points.
The matrix A is a 64164x4 matrix, where the 1st column is the x-coordinates, the 2nd column is the y coordinates, the 3rd column is the height of the bedrock and the 4th column is the height of the ice-surface. So A(:,4)-A(:,3) gives us the ice thickness. This data is for an entire region of greenland, but i only want to find the x,y points along my chosen line, and then the corresponding ice thickness for those data points.
So far i've tried something like this;
a = [400000, -1050000]; %First point
b = [500000, -1115000]; %Second point
x = [a(1), b(1)]; % x-coordinates for our points.
y = [a(2), b(2)]; % y-coordinates for our points.
%We find all x points that lie between our chosen points;
X = a(1):b(1);
%We interpolate for our 2 points with all the points in X, and round.
*Y=interp1(x,y,X)
Y=round(Y)*
X2 = ismember(X,A(:,1)) %We find the indexes of the values in X that corresponds with our x-values in A.
X_A = X(X2) %We make a new vector only with the right indexes.
*Y2 = ismember(Y,A(:,2)) %same approach for Y.
Y_A = Y(Y2)*
%We end up with a vector for Y and X that is both 1x101 in size. This is fine, but i need to find the corresponding ice thickness indexes, for those values that match these x,y values. And this vector of ice thickness must be the same size, because i need to find the flux through this line with the formula below.
*for i=1:length(profilv_z)
*flux(i)=1.0 * profilv_z(i)*0.001 * profilv_dv(i)*0.001 * 0.917 ;*
end
Giga_ton_ice_per_year = sum(flux)*
%where profilv_z is the ice_thickness data. Also, i need to plot the ice_thickness through this line with the script below;
*figure(3)
subplot(2,1,1) * % plot ice_thickness through the flux line;
*plot(Y_A*0.001,profilv_z,'.-') % distance in km.
xlabel('distance in km')
ylabel('ice thickness - meters')*

Soumya Saxena on 16 May 2017
You compute the indexes of the values in X that corresponds with the x-values in A. You may consider using scattered interpolation. If x and y are your coordinates in A, i.e. A(:,1) and A(:,2), then let "v" be the thickness , which is the difference between A(:,3) and A(:,4). You can then create a model as:
F = scatteredInterpolant(x,y,v)
Then, you can use this to find thickness at any new query point, xq and yq as follows:
Vq = F(Pq)
Please refer to the following documentation:

Soumya Saxena on 9 May 2017
I understand that you want to compute the ice thickness using the third and fourth column. Please let me know why you are performing interpolation to compute Y

Chad Greene on 7 Jul 2017
There's an example of how to calculate the flux of Thwaites Glacier in Antarctica in the documentation for measures_interp here. Note you can't just multiply the local ice speed by thickness to get the ice flux unless the flux gate is perfectly orthogonal to ice flow.