Intersection of line and curve from thier points

Question

Mohamed Ameen 2017-12-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/371799-intersection-of-line-and-curve-from-thier-points

评论： Juan Sebastián Gómez Chitiva 2021-1-24

采纳的回答： Star Strider

在 MATLAB Online 中打开

I have a line with 2 points on it and a curve with 4 points on it

For the line we have :

x_line = [7020 0]
y_line = [0 250000]

For the curve we have :

x_curve = [5620 4850 4290 3600]
y_curve = [0 100000 200000 300000]

I need to know the intersection point of the line and the curve

Any help will be appreciated.

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Answer 1

Star Strider 2017-12-8

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https://ww2.mathworks.cn/matlabcentral/answers/371799-intersection-of-line-and-curve-from-thier-points#answer_295273

在 MATLAB Online 中打开

Try this:

x_line = [7020 0];
y_line = [0 250000];
x_curve = [5620 4850 4290 3600];
y_curve = [0 100000 200000 300000];
b_line = polyfit(x_line, y_line,1);                     % Fit ‘line’
y_line2 = polyval(b_line, x_curve);                     % Evaluate ‘line’ At ‘x_curve’
x_int = interp1((y_line2-y_curve), x_curve, 0);         % X-Value At Intercept
y_int = polyval(b_line,x_int);                          % Y-Value At Intercept
figure(1)
plot(x_line, y_line)
hold on
plot(x_curve, y_curve)
plot(x_int, y_int, '+r')                                % Plot Intercept Point
hold off

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Juan Sebastián Gómez Chitiva 2021-1-24

exactly what i need!!! Thanks!!!!

this is the best answer i've seen

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Answer 2

Mohamed Ameen 2017-12-8

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https://ww2.mathworks.cn/matlabcentral/answers/371799-intersection-of-line-and-curve-from-thier-points#answer_295274

Thank you very much, it worked... But if you could explain the steps a little more, that will be great.

Thanks again for your help.

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Star Strider 2017-12-8

As always, my pleasure.

First, ‘line’ is a linear function, so creating an equation for it (using polyfit) is straightforward. I cannot compare the y-values for ‘y_line’ and ‘y_curve’ directly, so I evaluate ‘line’ at the ‘x_curve’ points to create y-values at those points as ‘y_line2’. I then subtract ‘y_curve’ from them, and use interp1 to find the x-value (as ‘x_int’) where they are 0. I then use polyval with ‘x_int’ to get the y-value at the interception, ‘y_int’.

The plots are then straightforward.

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Answer 3

Mohamed Ameen 2017-12-8

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https://ww2.mathworks.cn/matlabcentral/answers/371799-intersection-of-line-and-curve-from-thier-points#answer_295276

Thanks a lot Mr. Strider, that's really helpful

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Star Strider 2017-12-8

As always, my pleasure.

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Answer 4

Jamie Hetherington 2019-12-24

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https://ww2.mathworks.cn/matlabcentral/answers/371799-intersection-of-line-and-curve-from-thier-points#answer_407548

Starstrider this solution was excellent. I needed a method to identify the point of intersection between a straight line and a plotted curve of residuals. I was thinking it could be done solving simulatenous equations but would've taken more time to create and implement.

Great stuff!