Intersection of line and curve from thier points

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.

Answer 1

[Star Strider]

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

[Juan Sebastián Gómez Chitiva]

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

this is the best answer i've seen

Answer 2

[Mohamed Ameen]

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.

[Star Strider]

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.

Answer 3

[Mohamed Ameen]

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

[Star Strider]

As always, my pleasure.

Answer 4

[Jamie Hetherington]

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!