How do you inflate a Bezier cuves? That is, move each point a constant distance from its current position. Circles are easy, just increase or decrease the radius accordingly. But Beziers, come on, a quadratic Bezier is a parabola, if you just increase the scale of a the parabola, you’ll end up with the endpoints being skinnier than the vertex. But, couldn’t you just stretch the envelope wider/narrower and be done with it? Okay, okay… well I guess that’s a pretty good approximation. Just be careful about very sharp quadratic Beziers, ideally I’d recommend subdividing this down into something close to linear then using the mentioned approximation technique.
Now, cubic Beziers are not so easy. I’d say in general with Beziers, with the exception of lines, there is not an exact solution to inflating a Bezier, only approximate ones. For cubic Beziers, if you are just rendering, yeah you can subdivide into approximate quadratic Beziers and then use the mentioned approximate inflation technique.
For rendering thick geometric strokes, often times converting the stroke into a path and then scan-filling the region is the best technique. Otherwise, repeatedly plotting circles along each point is another easy way, though this means you can’t control the joint and cap style. Oh, and I didn’t mention METAFONT-style pens, but that’s not in the PostScript, PDF, and SVG and standards. METAFONT-style pents are technically polyline approximations of an ellipse, polylines are another simple way to inflate Bezier curves. Within the threshold of two polyline angles, you simply offset the Bezier curve by the corresponding distance of a polyline point from its center. This is exact to the geometry of the polyline and the Bezier.
But, what if you don’t just want to render, but want to generate some clean data directly for artist use? Like the Inkscape command to convert a stroke into a path? Well, I’ll say this, follow in the footsteps of the Inkscape source code. Just like Inkscape, after computing your approximation, you then simplify the path as much as possible, while still remaining within your target margin of error.