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

You could check if the point lies between the two planes defined by point1 and point2 and the line direction:

///  Returns the closest point from @a point to this line on this line.
vector3 
line3d ::closest_point (const vector3  & point) const
{
    return this -> point () + direction () * dot (point - this -> point (), direction ());
}

///  Returns true if @a point lies between point1 and point2.
template 
bool
line_segment3 ::is_between (const vector3  & point) const
{
    const auto closest = line () .closest_point (point);
    return abs ((closest - point0 ()) + (closest - point1 ())) <= abs (point0 () - point1 ());
}