Intepolate in 2D loop of points

Hi all,

I have a shape made up of regularly spaced data points in 2D. I want to increase the sampling of the points, i.e. interpolate between points as I need the outer edge in higher resolution than it is currently. I have tried intep etc, alphaShape and meshgrid but am struggling, so any help would be great. I have also tried just doing it for the points that make up the perimeter of the shape as this is what I'm interested in, but didn't get anywhere with that easier and thought it might be easier to do it as a whole object?

An example of a data set can be seen below.

    %-2.57812500000000  -2.92968750000000
-2.57812500000000  -3.04687500000000
-2.57812500000000  -3.16406250000000
-2.57812500000000  -3.28125000000000
-2.57812500000000  -3.39843750000000
-2.57812500000000  -3.51562500000000
-2.57812500000000  -3.63281250000000
-2.57812500000000  -3.75000000000000
-2.57812500000000  -3.86718750000000
-2.57812500000000  -3.98437500000000
-2.46093750000000  -2.81250000000000
-2.46093750000000  -2.92968750000000
-2.46093750000000  -3.04687500000000
-2.46093750000000  -3.16406250000000
-2.46093750000000  -3.28125000000000
-2.46093750000000  -3.39843750000000
-2.46093750000000  -3.51562500000000
-2.46093750000000  -3.63281250000000
-2.46093750000000  -3.75000000000000
-2.46093750000000  -3.86718750000000
-2.46093750000000  -3.98437500000000
-2.34375000000000  -2.57812500000000
-2.34375000000000  -2.69531250000000
-2.34375000000000  -2.81250000000000
-2.34375000000000  -2.92968750000000
-2.34375000000000  -3.04687500000000
-2.34375000000000  -3.16406250000000
-2.34375000000000  -3.28125000000000
-2.34375000000000  -3.39843750000000
-2.34375000000000  -3.51562500000000
-2.34375000000000  -3.63281250000000
-2.34375000000000  -3.75000000000000
-2.34375000000000  -3.86718750000000
-2.22656250000000  -2.46093750000000
-2.22656250000000  -2.57812500000000
-2.22656250000000  -2.69531250000000
-2.22656250000000  -2.81250000000000
-2.22656250000000  -2.92968750000000
-2.22656250000000  -3.04687500000000
-2.22656250000000  -3.16406250000000
-2.22656250000000  -3.28125000000000
-2.22656250000000  -3.39843750000000
-2.22656250000000  -3.51562500000000
-2.22656250000000  -3.63281250000000
-2.22656250000000  -3.75000000000000
-2.22656250000000  -3.86718750000000
-2.10937500000000  -2.46093750000000
-2.10937500000000  -2.57812500000000
-2.10937500000000  -2.69531250000000
-2.10937500000000  -2.81250000000000
-2.10937500000000  -2.92968750000000
-2.10937500000000  -3.04687500000000
-2.10937500000000  -3.16406250000000
-2.10937500000000  -3.28125000000000
-2.10937500000000  -3.39843750000000
-2.10937500000000  -3.51562500000000
-2.10937500000000  -3.63281250000000
-2.10937500000000  -3.75000000000000
-2.10937500000000  -3.86718750000000
-1.99218750000000  -2.34375000000000
-1.99218750000000  -2.46093750000000
-1.99218750000000  -2.57812500000000
-1.99218750000000  -2.69531250000000
-1.99218750000000  -2.81250000000000
-1.99218750000000  -2.92968750000000
-1.99218750000000  -3.04687500000000
-1.99218750000000  -3.16406250000000
-1.99218750000000  -3.28125000000000
-1.99218750000000  -3.39843750000000
-1.99218750000000  -3.51562500000000
-1.99218750000000  -3.63281250000000
-1.99218750000000  -3.75000000000000
-1.87500000000000  -2.34375000000000
-1.87500000000000  -2.46093750000000
-1.87500000000000  -2.57812500000000
-1.87500000000000  -2.69531250000000
-1.87500000000000  -2.81250000000000
-1.87500000000000  -2.92968750000000
-1.87500000000000  -3.04687500000000
-1.87500000000000  -3.16406250000000
-1.87500000000000  -3.28125000000000
-1.87500000000000  -3.39843750000000
-1.87500000000000  -3.51562500000000
-1.87500000000000  -3.63281250000000
-1.87500000000000  -3.75000000000000
-1.75781250000000  -2.34375000000000
-1.75781250000000  -2.46093750000000
-1.75781250000000  -2.57812500000000
-1.75781250000000  -2.69531250000000
-1.75781250000000  -2.81250000000000
-1.75781250000000  -2.92968750000000
-1.75781250000000  -3.04687500000000
-1.75781250000000  -3.16406250000000
-1.75781250000000  -3.28125000000000
-1.75781250000000  -3.39843750000000
-1.75781250000000  -3.51562500000000
-1.75781250000000  -3.63281250000000
-1.75781250000000  -3.75000000000000
-1.64062500000000  -2.46093750000000
-1.64062500000000  -2.57812500000000
-1.64062500000000  -2.69531250000000
-1.64062500000000  -2.81250000000000
-1.64062500000000  -2.92968750000000
-1.64062500000000  -3.04687500000000
-1.64062500000000  -3.16406250000000
-1.64062500000000  -3.28125000000000
-1.64062500000000  -3.39843750000000
-1.64062500000000  -3.51562500000000
-1.64062500000000  -3.63281250000000
-1.64062500000000  -3.75000000000000
-1.52343750000000  -2.46093750000000
-1.52343750000000  -2.57812500000000
-1.52343750000000  -2.69531250000000
-1.52343750000000  -2.81250000000000
-1.52343750000000  -2.92968750000000
-1.52343750000000  -3.04687500000000
-1.52343750000000  -3.16406250000000
-1.52343750000000  -3.28125000000000
-1.52343750000000  -3.39843750000000
-1.52343750000000  -3.51562500000000
-1.52343750000000  -3.63281250000000
-1.40625000000000  -2.46093750000000
-1.40625000000000  -2.57812500000000
-1.40625000000000  -2.69531250000000
-1.40625000000000  -2.81250000000000
-1.40625000000000  -2.92968750000000
-1.40625000000000  -3.04687500000000
-1.40625000000000  -3.16406250000000
-1.40625000000000  -3.28125000000000
-1.40625000000000  -3.39843750000000
-1.40625000000000  -3.51562500000000
-1.40625000000000  -3.63281250000000
-1.28906250000000  -2.57812500000000
-1.28906250000000  -2.69531250000000
-1.28906250000000  -2.81250000000000
-1.28906250000000  -2.92968750000000
-1.28906250000000  -3.04687500000000
-1.28906250000000  -3.16406250000000
-1.28906250000000  -3.28125000000000
-1.28906250000000  -3.39843750000000
-1.28906250000000  -3.51562500000000
-1.28906250000000  -3.63281250000000
-1.17187500000000  -2.69531250000000
-1.17187500000000  -2.81250000000000
-1.17187500000000  -2.92968750000000
-1.17187500000000  -3.04687500000000
-1.17187500000000  -3.16406250000000
-1.17187500000000  -3.28125000000000
-1.17187500000000  -3.39843750000000
-1.17187500000000  -3.51562500000000
-1.17187500000000  -3.63281250000000
-1.05468750000000  -2.81250000000000
-1.05468750000000  -2.92968750000000
-1.05468750000000  -3.04687500000000
-1.05468750000000  -3.16406250000000
-1.05468750000000  -3.28125000000000
-1.05468750000000  -3.39843750000000
-1.05468750000000  -3.51562500000000
-1.05468750000000  -3.63281250000000
-0.937500000000000  -2.92968750000000
-0.937500000000000  -3.04687500000000
-0.937500000000000  -3.16406250000000
-0.937500000000000  -3.28125000000000
-0.937500000000000  -3.39843750000000
-0.937500000000000  -3.51562500000000
-0.937500000000000  -3.63281250000000
-0.820312500000000  -3.04687500000000
-0.820312500000000  -3.16406250000000
-0.820312500000000  -3.28125000000000
-0.820312500000000  -3.39843750000000
-0.820312500000000  -3.51562500000000
-0.820312500000000  -3.63281250000000
-0.703125000000000  -3.28125000000000
-0.703125000000000  -3.39843750000000
-0.703125000000000  -3.51562500000000
-0.703125000000000  -3.63281250000000
  end

Answer 1

[Robert]

If I were you, I would throw away the data that is not on the edges by finding the min and max of each of your columns of data points. This takes advantage of the even spacing in your example dataset. If you don't have that nice spacing in your real data you could bin the values in x to achieve the same result.

Once you have two curves describing the top and bottom edges you can do whatever interpolation or smoothing you like. The code below will demonstrate a few options available to you.

    % your example data is stored in the variable x (a 176x2 double array)

    clf
    plot(x(:,1),x(:,2),'.')

    x0 = unique(x(:,1)); % get one value for each "column" of data

    for ii = length(x0):-1:1 % for each column of data
        these = x(:,1)==x0(ii); % find the corresponding indices
        y0_lo(ii) = min(x(these,2)); % get the min y value (second column of x)
        y0_hi(ii) = max(x(these,2)); % get the max y value 
    end

    hold all
    plot(x0,y0_lo,x0,y0_hi)

    % interpolate to 100 points
    x1 = linspace(min(x0),max(x0),100);
    y1_lo = interp1(x0,y0_lo,x1,'spline');
    y1_hi = interp1(x0,y0_hi,x1,'pchip');

    plot(x1,y1_lo,x1,y1_hi)

    % moving average with width 3 (from the Curve Fitting Toolbox)
    y2_lo = smooth(y0_lo,3);
    y2_hi = smooth(y0_hi,3);

    plot(x0,y2_lo,x0,y2_hi)
    hold off

[awinka]

Hi Robert,

Thanks this was the approach I'd gone for, but then got stuck with performing the actual interpolation. Will have a good now and let you know Thanks very much, Lou

[awinka]

Hi Robert, having initially thought this did what I needed, I actually need the entire loops to be interpolated - this does the top and bottom points, but I also need the side points if you understand. I have uploaded a picture with the points which are just along the top to try and help.

Any further advice would be much appreciated. Lou

[Robert]

In your example dataset your sides are just straight lines. With no other constraints, I would suggest you simply take those min/max x values as your sides.

What you decide to do will depend on what your data means and what you intend to do with it, so I don't have enough information to guess what option would be best for you.

I can suggest that if you want a more round shape you could use polar coordinates. Take the mean of your values as the origin and convert the data to polar coordinates. Then bin your data by angle, take the max distance in each bin, and interpolate over those values. (Duplicate the first value or few values on the end of the list to make the result smooth at your loop's start/end.)