Both of the sibling comments describe quadratic Bezier curves (used often in font rendering because TrueType only supports quadratic), while graphics APIs and C

Both of the sibling comments describe quadratic Bezier curves (used often in font rendering because TrueType only supports quadratic), while graphics APIs and CFF font outlines often mandate support for cubic Beziers. Cubics are a lot more challenging to build a closed-form solution for, and also have things like self-intersection which makes it a lot more challenging. Most production renderers, sometimes even ones on the CPU, approximate cubic Bezier curves with a number of quadratic Bezier curves. This is a preprocessing step which needs to be done on the CPU. While it it could be done on the GPU, doing it in the pixel shader would be really wasteful.