1. Apparently a quadratic can't be substituted by a cubic where both cubic controls are set equal to the single quadratic one, or one cubic control is set equal to a node and the other is set equal to the quadratic control. Only the 2/3 formula will work. See attached images. (http://processingjs.nihongoresources.com/bezierinfo/)
So I did some more digging:
1. Apparently a quadratic can't be substituted by a cubic where both cubic controls are set equal to the single quadratic one, or one cubic control is set equal to a node and the other is set equal to the quadratic control. Only the 2/3 formula will work. See attached images. (http:// processingjs. nihongoresource s.com/bezierinf o/)
2. FWIW I submitted some simple patches for Cairo to support quadratics: http:// lists.cairograp hics.org/ archives/ cairo/2012- August/ 023397. html