I subdivide a cubic Bézier curve at a given t value using de Casteljau’s algorithm, which yields two cubic Bézier curves. Afterwards I “scale” the second curve (proportionally).
I’d like to reconnect or approximate the two curves to/with a single curve in a third step. Is that possible?
This illustrates what I’m intending to do.
I guess reversing de Casteljau’s algorithm won’t work because I don’t have one of the intermediate points.
If there are multiple approaches, I’d favor a simpler (faster to compute) strategy.
Thanks in advance.
Update:
Maybe this figure makes it more clear; it shows all the points I have:
The original cubic Bézier curve is defined by the points $ p_{0}, p_{1}, p_{2}, p_{3} $.
It is divided at a given $ t $ (timing) value using de Casteljau’s algorithm, which yields the points $ q_{1}, r_{2}, i_{1}, q_{2}, r_{1}, k $ where $ k $ is the division point.
The two subcurves are defined by the control points $ p_{0}, q_{1}, q_{2}, k $ and $ k, r_{1}, r_{2}, p_{3} $, respectively.
The scaled second subcurve is defined by the points $ k, {r}' _{1}, {r}' _{2}, {r}' _{3} $
Scaling is applied as follows: $ {p}' = k + (p - k) \cdot factor $ for $ r_{1}, r_{2}, p_{3} $