Convert a quadratic bezier to a cubic one

问题:

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

回答1:

From http://fontforge.sourceforge.net/bezier.html:

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.