Find the cubic bezier control points from end points and tangents

Question

If i have 2 end points and two unit vectors as tangents at the two end points is it possible to find the cubic bezier curve control points that make the curve ? Is there one solution or many solutions ?

Visual of what i am trying to find:

Answer 1

There are infinitely many solutions. At the start of the curve, the given point and unit vector define a line. You can place the curve’s second control point anywhere along this line. The same reasoning applies at the end of the curve.