How do I find points of intersection between a curve and horizontal line?

I have a curve, not defined via a function handle, but evaluated at a number of points. I would like to find all the points of intersection of this curve with a horizontal line.

Answer 1

[MathWorks Support Team]

In general, the intersection points of a horizontal line and a curve can be found by looking for the changes in sign in the difference of the horizontal line and curve. For example,

X = (0:0.01:10)';
Y = sin(X); % curve
H = 0.5 + 0*X; % horizontal line

To determine the points of intersection, examine neighbouring x-values that flip the sign of the difference vector.

sign_flip = (Y(2:end)-H(2:end)).*(Y(1:end-1)-H(1:end-1)); % when the curve crosses the line the difference vector will flip sign and the product of neighbouring points will be negative
X(sign_flip < 0) % gives approximate x-values for where the curve and line crossed

The 'X' values reported will be an approximation to the points of intersection. This approximation can be improved by increasing the sampling rate.