What's the fastest way to get the points I want out of a huge blob?

In MATLAB I have a set of 5393280 points in the form of a decimal-valued vector (x,y,z). How do I represent them in a way that I can quickly collect all the points within some rectangular x-y domain?

Right now I'm representing them as a 3-column matrix, sorted by x-values, and using the following code to extract a rectangular region:

mtx_region = mtx_pointList( dxLowerBound  mtx_pointList(:,1) & ...
                            dyLowerBound  mtx_pointList(:,2), : );

However, I suspect that this is slowing my code down considerably.

What is a better way?

Prefiltering all relevant x-values with a binary search could speed up the process.

[a,A]=myFind2(mtx_region(:,1),dxLowerBound,dxUpperBound);

xpoints=mtx_region(a:A,:);
mtx_region = xpoints(     dyLowerBound  xpoints(:,2), : );

Binary search on sorted arrays is already discussed here.

function [b,c]=myFind2(x,A,B)
a=1;
b=numel(x);
c=1;
d=numel(x);
while (a+1<b||c+1<d)
    lw=(floor((a+b)/2));
    if (x(lw)<A)
        a=lw;
    else
        b=lw;
    end
    lw=(floor((c+d)/2));
    if (x(lw)<=B)
        c=lw;
    else
        d=lw;
    end
end
end

StackExchange Code Review Q#39409, answer score: 3