bezier

It would be interesting to know how to compute the calligraphic stroke outline in terms of bezier curves from a given bezier curve.

For instance quadratic bezier curves, arcs, a shorthand syntax for successive horizontal/vertical lines in a subpath.

Things like Bezier curves are defined mathematically, so you can represent the way a tiger looks in a, albeit large, mathematical equation!

The hardest part was figuring out how to convert ellipse sections and AutoCAD bulge arcs (line + bulge factor) to quadratic bezier curves.

Quadratic bezier curves, unlike cubic ones, do actually map really well onto GPUs (given their basis on triangles) quite unlike what you've said here.

Or do you need the precise bezier-curves for the stroke outline?

Genuinly curious: I thought you can't represent ellipses with bezier curves, at least accurately...

It might be somewhat less efficient for the very simplest images, but doing raster layers in code and including things like bezier handling seems perversely complex.

From a copyright standpoint in the US, you can copy the glyph outlines of fonts (usually some form of bezier curve or in some cases bitmap) without violating copyright.

I'm writing a demo (one shader for two triangles) that does 2d distance field rendering, and I'm using quadratic bezier curves for a large part of it.

Once you start doing layers and blending and so on, you're just asking for misalignment errors, surprises when your bezier paths turn out to generate little unwanted loops and so on...

Ideas for next version: allow control points of the bezier curve to be moved; generate a javascript function (for those of us who want to run the animation from within javascript completely).

Perhaps quadratic bezier curves aren't as mathematically pure (cannot represent circles "perfectly") -- but they are artistically beautiful and, in my mind, just as useful as pixels are (in real-time applications).

The easiest way is to draw a spline or a bezier curve, along one axis, then apply a "lathing" function, which duplicates the spline, rotating about the axis, and then connecting the splines at each control point on the spline/curve.

Bezier paths manipulations, linear transforms, linear algebra, etc.