Catenary Curve Generator

[docbrown]

I'm finally getting around to making tarps for my kids. I see multiple references to catenary curve templates and generators here and elsewhere on the internet, but most of those seem to either be broken or don't produce printable templates. I put the attached Matlab script together to create printable pdf files that are all sized accurately. The sequence of pdfs can be printed, cut out, and taped together to create a single contiguous template for arbitrary catenary curve parameters (with some caveats: If the sag is larger than 10", it won't fit neatly on a single page). So is case there is anyone besides me out there that both use Matlab and want to generate catenary curve templates, here you go.

Unfortunately, I can't upload .m files, so I'll drop the text of the script inline:

%%% Specify Catenary Parameters
h = 6;  % sag
H = 60; % width between catenary endpoints
unitsStr = 'inches'; % units for sag and width - options are {'inches','centimeters'}

%%% Output pdf file parameters
pdfFilename = '.\catCurve';
plotWidth = 9; % width of single plot on page (in current units)
pageOrientation = 'landscape'; % options are {'landscape', 'portrait'}

% The following code computes the catenary curve matching the inputs
aGuess = H^2 / (8*h);
a = fzero(@(x)(2*x*acosh((h+x)/x)-H), aGuess);
x = -(H/2):0.1:(H/2);
y = h + a - a*cosh(x/a);

% Create plots sized appropriately to fit the specified page width
p0 = min(x);
curPlt = 1;
while p0 < (H/2)
    figure; plot(x,y,'LineWidth',2);
    % force axes to have the correct size
    axis equal; grid on;
    xlim([p0,p0+plotWidth]);
    ylim([0,h]);
    set(gca,'LooseInset',get(gca,'TightInset'));
    set(gcf,'units',unitsStr,'position',[1,1,plotWidth,h]);
    axesPos = get(gca,'Position');
    set(gcf,'position',[1,1,plotWidth/axesPos(3),h/axesPos(4)]);
    % print current figure to pdf
    set(gcf,'PaperOrientation',pageOrientation);
    set(gcf,'PaperPositionMode','auto');
    newFname = sprintf('%s%d.pdf', pdfFilename, curPlt);
    print(newFname, '-dpdf');
    close(gcf);
    fileList{curPlt} = newFname;
    p0 = p0 + plotWidth;
    curPlt = curPlt + 1;
end

[mattnin]

Thanks for this by the way. I'm making yet another tarp but this time based on Shug's black crow and I've been trying to find a way to print out the cat curve and this worked perfectly. I made a free account with matlab (never used it before) and just did a simple cut and paste of your code

[FlyingAvocado]

Oh, this is interesting!

I am working on a tarp design as well, and just did the sketch in on-shape last night using conic curves since that's the tool they provide. If the curvature math is different enough it probably would be worth my time to try and convert your matlab algorithm into an onshape Featurescript.

Unfortunately the math here is a little beyond my level of comfort, do you happen to know if there is much difference there is between a conic and catenary curve?