Alternative to ginput for finding curve intersections with unevenly spaced data in MATLAB

Is there a better way to determine the intersection of two curves in MATLAB, other than using ginput, especially when the data points are unevenly spaced and do not include the exact intersection point? How can I handle cases where one of my datasets forms two angled lines joined together, rather than a smooth curve?

Answer 1

[Matt J]

Use fminbnd or fzero,

x=sort(rand(1,12)*5);
y1=[0,1,-1*x(3:end)+3+2*x(3)];
y2=2*x-3;

f=@(z)  interp1(x,y1,z)-interp1(x,y2,z)  ;

xmin=fzero(f,[min(x),max(x)]); ymin=interp1(x,y1,xmin); %intersection

h=plot(x,y1,'--gx', x,y2,'--b+',xmin,ymin,'ro'); 
h(3).MarkerFaceColor=h(3).Color; h(3).MarkerSize=8;

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[Bo]

Instead of using sort, I use [X,ia,ic] = unique(x); y1 = y1(ia); other than that, both fzero, and fminbnd works well, really appreciated!

Answer 2

[Alan Stevens]

Create a function using interp1 for use with fzero. For example:

 yfn = @(X,Y,x) interp1(X,Y,x);
 X = [1,2,3,7,8,9];
 Y1 = X;
 Y2 = 15-X.^1.5;


x0 = 6;

xp = fzero(@(x0)fn(x0,X,Y1,Y2,yfn),x0);
disp(xp)

    4.5710

yp = yfn(X,Y1,xp);
plot(X,Y1,'-o',X,Y2,'-+',xp,yp,'ks'),grid
xlabel('x'), ylabel('y')

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function Z = fn(x,X,Y1,Y2,yfn)
         Z = yfn(X,Y1,x)-yfn(X,Y2,x);

end

Answer 3

[Star Strider]

Another approach —

x = [linspace(0, 2.4) linspace(5.2, 7, 8)].'*1E-3;

y1 = [x(x<=2.4E-3)*580/2.4E-3; 500*ones(size(x(x>2.5E-3)))];
y2 = x*580/2.4E-3 - 450;

idx = find(diff(sign(y2 - y1)))

idx = 100

idxrng = max(1,idx) : min(numel(x),idx+1)

idxrng = 1×2

100 101

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y2(idxrng)-y1(idxrng)

ans = 2×1

-450.0000 306.6667

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xi = interp1((y1(idxrng)-y2(idxrng)), x(idxrng), 0)

xi = 0.0041

yi = interp1(x, y1, xi)

yi = 532.4229

figure
plot(x, y1, '.-', DisplayName="y_1")
hold on
plot(x, y2, '.-', DisplayName="y_2")
plot(xi, yi, 'sr', DisplayName="Intersection")
hold off
grid
legend(Location='best')

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This approach finds the approximate index of the two lines and then interpolates to find the intersection points of the lines.

EDIT — (9 Feb 2025 at 1:43)

Corrected code.

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