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"all" graphics software is quite the sweeping statement. One of the most common graphics languages used in every day life by everyone on a computer, is the true

"all" graphics software is quite the sweeping statement. One of the most common graphics languages used in every day life by everyone on a computer, is the truetype graphics language, used to define vector graphics for one of the two major flavours of openetype font. TTF only does quadratic curves, and is ubiquitous. There are also plenty of CNC packages that don't even give you Bezier curves at all, and I would definitely consider those graphics software. As for the book no longer being a primer: just because it's longer than a few pages, doesn't mean it's not a primer anymore =) It's currently about 100 pages, so essentially what you'd be expected to read "before the next class" in university, which is my standard for what a primer is: a primer should get you complete understanding at the fundamental level. Anything less and it's not going to prime the reader for further study. So it speaks to the subject of Bezier curves that you can have 100 pages and _still_ be just a primer on the subject. If I wanted it to be exhaustive, it'd probably be at least twice the current size (now... we might get there eventually, but not any time soon!) As such I also wouldn't consider this description a "primer" but more of a short descriptiong: it correctly describes de Casteljau's algorithm, but the drawing algorithm is not the curve type, and doesn't really work in terms of getting people to understand Bezier curves themselves (unless they're scarily good at internalising just an algorithm description and then abstracting all the implications of that algorithm without further aid =)

romwell 7y ago
Thanks again for the primer and the comment :) >"all" graphics software is quite the sweeping statement. I meant virtually all popular vector graphics programs with a GUI that let users draw curves. I am not aware of a single one that doesn't have a Bezier curve tool - even MSPaint has had it in Windows 3.11. Can't say much for CNC packages, except that Bezier curves were literally made for CNC. I'd guess that they accept CAD designs which were made with software where Bezier curves exist, but are converted to poly-lines in the output. Surely, specialized software without Bezier is out there; but that's how you draw curves in Photoshop and Illustrator :) > It's currently about 100 pages, so essentially what you'd be expected to read "before the next class" in university Ha! Spotted someone blessed with not having to teach an intro math class to 100 freshmen :D FWIW Spivak's Calculus on Manifolds is about the same size, and it's a semester-long course[1]. >twice the current size (.. but not any time soon!) ..I'll keep hitting F5 in the meantime :) -------------- On that note, a request. In the figure where you talk about curvature matching, you are effectively tracing out the Evolute[2]: the intersection points of nearby normal lines trace out the evolute in the limit (the locus of centers of curvature of the curve). I think that actually drawing the evolute would be a good addition to the text (and would improve the reader's understanding of the concept of curvature). -------------- [1]http://strangebeautiful.com/other-texts/spivak-calc-manifolds.pdf http://strangebeautiful.com/other-texts/spivak-calc-manifold... [2]https://en.wikipedia.org/wiki/Evolute https://en.wikipedia.org/wiki/Evolute
- TheRealPomax 7y ago
  Spivak doesn't use early high school maths, of course ;) mentioning the fact that there is such a thing as an "evolute" is a good point, though - could I convinve you to file an issue on the tracker so I don't forget about that? (HN threads disappear all too quickly!)

romwell 7y ago

Thanks again for the primer and the comment :) >"all" graphics software is quite the sweeping statement. I meant virtually all popular vector graphics programs with a GUI that let users draw curves. I am not aware of a single one that doesn't have a Bezier curve tool - even MSPaint has had it in Windows 3.11. Can't say much for CNC packages, except that Bezier curves were literally made for CNC. I'd guess that they accept CAD designs which were made with software where Bezier curves exist, but are converted to poly-lines in the output. Surely, specialized software without Bezier is out there; but that's how you draw curves in Photoshop and Illustrator :) > It's currently about 100 pages, so essentially what you'd be expected to read "before the next class" in university Ha! Spotted someone blessed with not having to teach an intro math class to 100 freshmen :D FWIW Spivak's Calculus on Manifolds is about the same size, and it's a semester-long course[1]. >twice the current size (.. but not any time soon!) ..I'll keep hitting F5 in the meantime :) -------------- On that note, a request. In the figure where you talk about curvature matching, you are effectively tracing out the Evolute[2]: the intersection points of nearby normal lines trace out the evolute in the limit (the locus of centers of curvature of the curve). I think that actually drawing the evolute would be a good addition to the text (and would improve the reader's understanding of the concept of curvature). -------------- [1]http://strangebeautiful.com/other-texts/spivak-calc-manifolds.pdf http://strangebeautiful.com/other-texts/spivak-calc-manifold... [2]https://en.wikipedia.org/wiki/Evolute https://en.wikipedia.org/wiki/Evolute

TheRealPomax 7y ago
Spivak doesn't use early high school maths, of course ;) mentioning the fact that there is such a thing as an "evolute" is a good point, though - could I convinve you to file an issue on the tracker so I don't forget about that? (HN threads disappear all too quickly!)