A professor built eight drawing apps because 2D graphics libraries can't draw variable-width curves
Variable-width Bézier curves (2025)
Luther Tychonievich wanted to do live board work on a graphics tablet but found no 2D graphics API offers Bézier curves with a pen-width coordinate, so he wrote his own boardwork application—eight times over. He compares three pressure-to-width models, explains why circular offsets beat linear ones against stylus jitter, and walks through the Bézier math (de Casteljau splitting, hodographs, squaring polynomials) needed to render smooth variable-width strokes.
Throughout this development experience I've been continually frustrated by the lack of an important primitive in 2D graphics libraries: Bézier curves with a pen width coordinate.
- WillAdams
In case the author reads this:
>The stroke boundary algorithm could be extended to 3D by generating a ring (instead of a pair) of stroke boundary points at each sample point. I do not know of compelling uses for such a 3D element.
That would actually be an excellent way to describe a V-carving toolpath for a CNC router.
- AlphaCerium
It's a breath of fresh air to see an article that so clearly and carefully explains a concept amongst the sea of llm-prose.
- xigoi
Why is there not a single picture in an article about Bézier curves?