How can i find the intersection of two lines between points? One of the lines isnt well behaved

x = linspace(0, 1, 40);                                     % Create Data
y1 = 1.0592*ones(size(x));                                  % Create Data
y1(18) = 1.0251;                                            % Create Data
y2 = 0.093*x + 1;
xi = linspace(min(x), max(x), numel(x)*100);                % Interpolation Vector
y1i = interp1(x, y1, xi);                                   % Interpolate
y2i = interp1(x, y2, xi);                                   % Interpolate
yd = y1i - y2i;                                             % Difference
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);        % Returns Approximate Zero-Crossing Indices Of Argument Vector
ydi = zci(yd);                                              % Zero-Crossing Indices
for k = 1:2
    ix = (ydi(k)-1):(ydi(k)+1);
    xv = xi(ix);
    yv = yd(ix);
    B = [xv(:), ones(size(xv(:)))] \  yv(:);
    xval(k) = -B(2)/B(1);                                   % Intersection X-Coordinates <—
end
y2r = [x(:) ones(size(y2(:)))] \ y2(:);                     % Regression For ‘y2’
yval = [xval(:) ones(2,1)] * y2r;                           % Intersection Y-Coordinates <—
figure
plot(xi, y1i)
hold on
plot(xi, y2i)
plot(xval, yval, 'pg')
hold off
grid

Here ‘xval’ are the x-values of the intersection. This computes the associated ‘yval’ vector and plots the points as well.

How can i find the intersection of two lines between points - 2019 08 21.png

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Star Strider 2019-8-22

在 MATLAB Online 中打开

As always, my pleasure!

One of the problems with simple anonymous function implementation of ‘zci’ is that if the end of a vector has a different sign than the beginning of the vector, it will pick that up as a zero-crossing, because of the ‘wrap-around’ effect of circshift operation. Logic to detect that and correct for it, in this context is:

if yd(1)*yd(end) < 1                                        % Check For ‘Wrap-Around’ Effect
    ydi = ydi(1:end-1)
end

and the slightly revised version of my code then becomes:

x = linspace(0, 1, 40);                                     % Create Data
y1 = 1.0592*ones(size(x));                                  % Create Data
y1(18) = 1.0251;                                            % Create Data
y2 = 0.093*x + 1;
xi = linspace(min(x), max(x), numel(x)*100);                % Interpolation Vector
y1i = interp1(x, y1, xi);                                   % Interpolate
y2i = interp1(x, y2, xi);                                   % Interpolate
yd = y1i - y2i;                                             % Difference
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);        % Returns Approximate Zero-Crossing Indices Of Argument Vector
ydi = zci(yd);                                              % Zero-Crossing Indices
if yd(1)*yd(end) < 1                                        % Check For ‘Wrap-Around’ Effect
    ydi = ydi(1:end-1)
end
for k = 1:numel(ydi)
    ix = (ydi(k)-1):(ydi(k)+1);
    xv = xi(ix);
    yv = yd(ix);
    B = [xv(:), ones(size(xv(:)))] \  yv(:);
    xval(k) = -B(2)/B(1);                                   % Intersection X-Coordinates <—
end
y2r = [x(:) ones(size(y2(:)))] \ y2(:);                     % Regression For ‘y2’
yval = [xval(:) ones(size(xval(:)))] * y2r;                 % Intersection Y-Coordinates <—
figure
plot(xi, y1i)
hold on
plot(xi, y2i)
plot(xval, yval, 'pg')
hold off
grid