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: enter image description here

  • $\begingroup$ You need two more constraints, such as the curvature at each end, or two points on the curve. $\endgroup$ May 26 '20 at 14:05
  • $\begingroup$ How would you define the curvature of the two points exactly ? What does that mean ? $\endgroup$
    – WDUK
    May 26 '20 at 19:16
  • $\begingroup$ Formally, curvature is the rate of change of the tangent angle with respect to arc length; less formally, the reciprocal of the radius of the best-fitting circle at that point. $\endgroup$ May 27 '20 at 4:47

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.


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