Find if point lays on line segment

Question

I have line segment defined by two points A(x1,y1,z1) and B(x2,y2,z2) and point p(x,y,z). How can I check if the point lays on the line segment?

Answer 1

Your segment is best defined by parametric equation

for all points on your segment, following equation holds: x = x1 + (x2 - x1) * p y = y1 + (y2 - y1) * p z = z1 + (z2 - z1) * p

Where p is a number in [0;1]

So, if there is a p such that your point coordinates satisfy those 3 equations, your point is on this line. And it p is between 0 and 1 - it is also on line segment