(Follow-up of this question.)

Given a sequence of cubic Bézier curves, how can I modify them minimally to make them join in a C2-continuous way?

Input:

  • curve P with control points P0, P1, P2, P3
  • curve Q with control points Q0, Q1, Q2, Q3
  • if it helps, you can assume that they are already C1 continuous.

Constraints:

  • C0 continuity: P3 = Q0
  • C1 continuity: P2 - P3 = Q0 - Q1
  • C2 continuity: P1 - 2*P2 + P3 = Q0 - 2*Q1 + Q2
  • modified curves as close as possible to original curves P and Q
math graphics bezier continuous
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