Find if point lies on line segment

Question

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

Answer 1

Find the distance of point P from both the line end points A, B. If AB = AP + PB, then P lies on the line segment AB.

AB = sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1)+(z2-z1)*(z2-z1)); AP = sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1)+(z-z1)*(z-z1)); PB = sqrt((x2-x)*(x2-x)+(y2-y)*(y2-y)+(z2-z)*(z2-z)); if(AB == AP + PB)     return true; 

Answer 2

If the point is on the line then:

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1) 

Calculate all three values, and if they are the same (to some degree of tolerance), your point is on the line.

To test if the point is in the segment, not just on the line, you can check that

x1 < x < x2, assuming x1 < x2, or y1 < y < y2, assuming y1 < y2, or z1 < z < z2, assuming z1 < z2