How can I interpolate x, y coordinate path with fixed interval?

I made x, y coordinate from A star path planning algorithm in matlab m file. And I need to interpolate this with fixed interval.

My final data set is

Path = [1 2; 1 3; 1 4; 1 5; 1 6; 1 7; 2 8; 3 9; 4 9; 5 8; 5 7; 5 6; 5 5; 5 4; 5 3; 6 2;7 2; 8 2; 9 3; 9 4;9 5; 9 6; 9 7; 9 8; 8 9];

And I want interpolated data set from initial point (1,2) to final point (8,9) with distance 0.1944. But I have no idea how to implement in m file code.

Is there anybody who can do this? I really appreciate it advance. Thank you!!

[Aw94]

I had a very similar problem with my data set. The difference is that I have xyz data instead of just xy. I tried this solution and I could not get the correct result. I could really use the help. Here is what I have:

format long g
fpath = 'Y:\Whaling\raw data\matlab\data cleaning\10m res\';
files = dir( fullfile(fpath,'txyzMLLW_*.txt') ); 
files = strcat(fpath,{files.name}');
f_txt=[];
for i=1:numel(files)
    data = importdata(files{i});
    total_length = arclength(data(:,2),data(:,3),data(:,4),'linear');
    if total_length>10
        newData= interparc(0:(10/total_length):1,data(:,2),data(:,3),data(:,4),'linear');
        f_txt=[f_txt;newData];
    else
        N=.5;
        newData= interparc(0:N:1, data(:,2), data(:,3),data(:,4),'linear');
        f_txt=[f_txt;newData];
    end
end
dlmwrite('10mres.txt',f_txt);

All of my files are text files organized with time in the first column, x coordinates (meters) in the second, y coordinates (meters) in the third, and depth (meters) in the fourth column. Each text file is a "path" of points. For each text file, I am attempting to get a new (interpolated) coordinate and depth every 10m along the path formed by the straight line distance calculated from one point to the next. If the total length of all the distances between points adds up to less than 10m, I used an else statement to just take the first and last coordinate and interpolate the point in the middle of the total length. Each point is on average, less than a centimeter apart. Ultimately, this will condense the final output file, 10mres.txt, from millions of points to tens of thousands. The problem is that the interpolated coordinates and depth is not 10m. As an example, here is the data from the last iteration:

>> test= newData([1,2],:)

test =

                   645042.18                 3257946.5                -1.9139999
            645046.405950062          3257954.01740637         -1.96472819711583

>> test_l= arclength(test(:,1),test(:,2),test(:,3))

test_l =

            8.62395650285223

test_l should equal 10, meaning that the distance between the first two interpolated coordinates and depth should be 10m. I'm not sure which part of my code is wrong or if this is even possible. I would greatly appreciate any help! I've included two text files that are included in the large number of files that my code should loop through. Thanks!

Answer 1

[John D'Errico]

Trivial. Using a couple of tools (arclength, interparc) on the file exchange...

The total length of the curve is...

format long g
total_length = arclength(path(:,1),path(:,2),'linear')
total_length =
          26.4852813742386

You want equally spaced points along the curve, at a spacing of 0.1944 ALONG the curve. I have no idea why you have chosen that number, but, I don't care. Note that the last point does not fall at the very end, since the total arc length along the curve is not an integer multiple of 0.1944.

interparc(0:(0.1944/total_length):1,path(:,1),path(:,2),'linear')
ans =
                       1                         2
                       1                    2.1944
                       1                    2.3888
                       1                    2.5832
                       1                    2.7776

... (I've cut out a few lines in the middle)

        8.30807325416077          8.69192674583923
        8.17061169589811          8.82938830410189
        8.03315013763544          8.96684986236456

[Image Analyst]

John's interparc is really good (though slow when I've used it) and is probably your best and easiest approach. I didn't think A* needed uniform spacing, but whatever... Mainly I wanted to say don't use Path as the name of your variable . I know MATLAB is case sensitive but it still seems risky to use a built-in variable/function as the name of your own variable.

Answer 2

[Pol van Rijn]

Dear all,

We import a pitch signal with Matlab. The intervals are not equally spaced. We want to interpolize the signal into evenly spaced points for a fixed number of points (e.g. nbLandmarks = 100).

The code bellow exemplifies the problem:

    x = [0.0443877551020408,0.0543877551020408,0.0643877551020408,0.0743877551020408,0.0843877551020408,0.0943877551020408,0.104387755102041,0.114387755102041,0.124387755102041,0.204387755102041,0.214387755102041,0.224387755102041,0.234387755102041,0.244387755102041,0.254387755102041,0.264387755102041,0.274387755102041,0.284387755102041,0.294387755102041,0.304387755102041,0.314387755102041,0.324387755102041,0.334387755102041,0.344387755102041,0.354387755102041,0.364387755102041,0.374387755102041,0.384387755102041,0.394387755102041,0.404387755102041,0.414387755102041,0.424387755102041,0.434387755102041,0.444387755102041,0.454387755102041,0.464387755102041,0.474387755102041,0.484387755102041,0.494387755102041,0.504387755102041,0.514387755102041,0.524387755102041,0.534387755102041,0.544387755102041,0.554387755102041,0.564387755102041,0.574387755102041,0.584387755102041,0.594387755102041,0.604387755102041,0.614387755102041,0.624387755102041,0.634387755102041,0.644387755102041,0.654387755102041,0.664387755102041,0.674387755102041,0.684387755102041,0.694387755102041,0.704387755102041,0.714387755102041,0.724387755102041,0.734387755102041,0.744387755102041,0.754387755102041,0.764387755102041,0.774387755102041,0.784387755102041,0.794387755102041,0.804387755102041,0.814387755102041,0.824387755102041,0.834387755102041,0.844387755102041,0.854387755102041,0.864387755102041,0.874387755102041,0.884387755102041,0.974387755102041,0.984387755102041,0.994387755102041,1.00438775510204,1.01438775510204,1.02438775510204,1.03438775510204,1.04438775510204,1.05438775510204,1.06438775510204,1.07438775510204,1.08438775510204,1.09438775510204,1.10438775510204,1.11438775510204,1.12438775510204,1.13438775510204,1.14438775510204,1.15438775510204,1.16438775510204,1.17438775510204,1.18438775510204,1.19438775510204,1.20438775510204,1.21438775510204,1.22438775510204,1.23438775510204,1.24438775510204,1.25438775510204,1.26438775510204,1.27438775510204,1.28438775510204,1.29438775510204,1.30438775510204,1.31438775510204,1.32438775510204,1.33438775510204,1.34438775510204,1.39438775510204,1.40438775510204,1.41438775510204,1.42438775510204,1.43438775510204,1.44438775510204,1.45438775510204,1.46438775510204,1.47438775510204,1.48438775510204,1.49438775510204,1.50438775510204,1.51438775510204,1.52438775510204,1.53438775510204,1.54438775510204,1.55438775510204,1.56438775510204,1.57438775510204,1.58438775510204,1.59438775510204,1.60438775510204,1.61438775510204,1.62438775510204,1.63438775510204,1.64438775510204,1.65438775510204,1.66438775510204,1.67438775510204,1.68438775510204,1.69438775510204,1.70438775510204,1.71438775510204];
    y = [178.501287711490,178.813817319272,189.577320314237,198.531890111164,206.084842988324,210.772659446790,211.335281417129,225.730598341740,225.901977654885,306.196606301549,311.753166263343,306.529882118809,302.572283702370,299.243503200983,291.095074651409,279.481854772107,248.159722754787,214.034507246777,212.647142436683,214.577255800419,205.337286514298,193.497692372285,183.975721348776,184.194731172757,186.922051071877,197.014092067936,205.554295519911,198.012819197895,182.283425886289,173.663152149703,173.548841891897,185.041868348116,181.674858747520,190.872306020846,204.750027549473,217.903703680010,228.724275241253,247.757437675443,274.544838049364,291.329733811144,305.243226052746,314.228480296518,322.314347343363,323.565427408769,328.346912028903,344.803772784512,355.638316302583,365.371138780059,370.612820310853,373.468384184022,368.251725308925,364.370906526989,359.915275206608,349.382417137670,340.756437859346,334.161057959999,327.541751925761,319.936718164203,306.200374198362,299.791516056024,291.801696534321,284.316665363165,275.191681773465,262.431033660143,245.531853644526,233.993133040364,263.035204764925,275.410716045634,278.801012495933,276.075947645212,270.525890004624,265.883974511083,260.488758878041,253.327880797132,235.378716127273,222.297294573365,205.531760297487,195.800381677558,260.847505424418,255.422377848489,252.998437535703,241.663088823371,238.130803984018,231.174450559706,231.272951661193,227.954282074205,224.273074967619,220.502578201465,215.908811382127,213.115791000171,210.694882117113,210.191410569382,208.331620587344,206.889418207533,209.508138301982,198.845889904302,194.214615751282,190.323077342336,187.747212018961,186.247368793523,185.378465024959,183.800566689203,183.487596528727,183.130097319624,182.972172520995,182.949136038847,184.255952332459,185.511207552205,186.796049387191,187.956127411674,188.083790019697,182.699706588926,182.656205931429,167.955624245799,161.730237334813,164.334140324580,222.228845242497,188.486774766025,185.653134577677,183.722858436240,181.215446829656,178.628665268127,176.502654025668,174.724525577723,173.261084454337,171.311040476288,169.415204605069,167.454558556174,165.794225884532,163.878190839415,162.069203412894,159.845921980463,156.699464668517,154.334356064799,152.524246385702,151.462151275399,149.289694397227,147.666645346538,146.250525583130,144.097828914436,142.148718181077,141.300116362692,140.362078497336,139.312279921538,143.015388437532,143.510794105153,142.452192935977,136.907902687353,140.508000973869];
    % given is raw pitch data, x is time, y is pitch

This is a first approach to solve the problem (it uses the interparc by John) % number of different points we want to draw on the spline nbLandmarks = 100;

    figure % make a figure
    numPlots = 3;
    ax1 = subplot(numPlots,1,1);
    plot(ax1,x,y, 'o-') % plot raw data
    title(ax1,'Raw data, fundamental frequency')
    ylabel(ax1,'Frequency (Hz)')
    xlabel(ax1,'Time')

    % first approach
    interpolatedXY = interparc(linspace(0, 1, nbLandmarks), x,y,'lin');

    ax2 = subplot(numPlots,1,2);
    plot(ax2,interpolatedXY(:,1), interpolatedXY(:,2), 'o-')
    title(ax2,'First try with the interparc function, no luck...')
    ylabel(ax2,'Frequency (Hz)')
    xlabel(ax2,'Time')

This is a second approach I found on one of the Matlab forums, but you get the same result...

    % second approach
    pathXY = [x;y]'; % merge new x and y coordinates in one table

    stepLengths = sqrt(sum(diff(pathXY,[],1).^2,2));
    stepLengths = [0; stepLengths]; % add the starting point
    cumulativeLen = cumsum(stepLengths); % Cumulative sum of all items --> last item contains total length
    finalStepLocs = linspace(0,cumulativeLen(end), nbLandmarks);
    finalPathXY = interp1(cumulativeLen, pathXY, finalStepLocs);

    ax3 = subplot(numPlots,1,3);
    title(ax3,'Second try, still not working')
    ylabel(ax3,'Frequency (Hz)')
    xlabel(ax3,'Time')
    plot(ax3, finalPathXY(:,1),finalPathXY(:,2), 'o-')

I've been puzzled since days, why the code doesn't work for my data (both approaches work for different examples used in forums). Might it be the case that my data is too noisy?

Any help would be very appreciated!!

Answer 3

[Gilwon Seo]

Thank you John!! It works perfectly. You just saved one man. :) Have a great day!!