Originally Posted by

**HallsofIvy** It looks to me like you want the **curvature** to be continuous through the three curves. That means you want specific values for the function at A and B, specific values for the derivative (so there is no "corner") at those points, and specific values for the second derivative (so the curvature is continuous). That is that you have six conditions. You could fit a **fifth degree** polynomial, of the form $\displaystyle ax^5+ bx^4+ cx^3+ dx^2+ ex+ f$ which has 6 coefficients to determine.