get closest point to a line

Question

I\'d like to have a straight forward C# function to get a closest point (from a point P) to a line-segment, AB. An abstract function may look like this. I\'ve search through

Answer 1

Your point (X) will be a linear combination of points A and B:

X = k A + (1-k) B

For X to be actually on the line segment, the parameter k must be between 0 and 1, inclusive. You can compute k as follows:

k_raw = (P-B).(A-B)  /  (A-B).(A-B)

(where the period denotes the dot product)

Then, to make sure the point is actually on the line segment:

if k_raw < 0:
    k= 0
elif k_raw > 1:
    k= 1
else:
    k= k_raw