c++ - Convert a quadratic bezier to a cubic one

Question

What is the algorithm to convert a quadratic bezier (with 3 points) to a cubic one (with 4 points)?

question from:https://stackoverflow.com/questions/3162645/convert-a-quadratic-bezier-to-a-cubic-one

Answer 1

From https://fontforge.org/docs/techref/bezier.html#converting-truetype-to-postscript:

Any quadratic spline can be expressed as a cubic (where the cubic term is zero). The end points of the cubic will be the same as the quadratic's.

CP₀ = QP₀
CP₃ = QP₂

The two control points for the cubic are:

CP₁ = QP₀ + 2/3 *(QP₁-QP₀)
CP₂ = QP₂ + 2/3 *(QP₁-QP₂)

...There is a slight error introduced due to rounding, but it is unlikely to be noticeable.