Drawing better-looking Bézier curves


257 points | by dhotson 488 days ago


  • dhotson 488 days ago

    Hello :) I'm the author of this notebook if you have any questions.

    I'm also currently working on a plugin for Adobe Illustrator based on this. Screenshot: https://i.imgur.com/tIPTjLsr.png

    • ablaba 487 days ago

      Have you seen the shadertoy implementation? https://www.shadertoy.com/view/XsX3zf He refers to the following paper. http://hhoppe.com/ravg.pdf

      • matthberg 487 days ago

        Thank you so much for the illustrator plugin work! It was the first thing I thought of after reading and the reason I clicked on it in the first place. I wish you the best with it, if you ever need beta testers or if there's a way you need help I'd love to. (I run CC 18 on a Windows 10 64bit install).

        • berendk 487 days ago

          Nice Article!

          May I ask how you made the notebook interactive? Is this based on a jupyter notebook?

        • agumonkey 488 days ago

          Great work. How hard was it to integrate it as an Illustrator plugin ?

          • dhotson 488 days ago

            Thanks! Actually it wasn't too difficult. It's all in C++ but the Adobe Illustrator SDK came with some examples that were pretty close to what I wanted already. Once I'd figured out the maths I had a prototype working in about a day.

            The one thing left that I can't figure out is how to have the curvature comb update live as you drag the Bezier control points. Currently it only updates when you mouse up.

            • amelius 488 days ago

              Does it run on multiple platforms, or only OSX?

              • dhotson 488 days ago

                It should run fine on Windows as well, but I haven't had a chance to test.

          • aoloe 486 days ago

            Would you mind creating a plugin also for Inkscape?

          • ttd 488 days ago

            If you're looking for more in-depth information on Bezier curves, I've found this document invaluable on more than one occasion, both for math and implementation suggestions: https://pomax.github.io/bezierinfo/

          • mark-r 487 days ago

            One trick I learned from a graphics editor: if you have two Bezier segments and want to make a smooth transition between them, put the two control points on either side of the center equidistant from the center and on a straight line. The curve will be tangent to that straight line at the center point, and will have the same curvature where they meet.

            • amelius 488 days ago

              I'm wondering how well one could define curves by using the physical model of a strip of material, and allowing one to change the properties (stiffness) of the material at different points along the curve, or to insert more material at a given point. Of course, there should be the usual constraints that the strip should pass through a bunch of given (x,y) coordinates, and there could be constraint that "pins" the strip to a given (x,y) coordinate.

              In a drawing program, the stiffness could be depicted by using grayscale values.

            • speps 488 days ago

              Spiro Curves are a nice alternative: http://www.levien.com/spiro/

            • ghusbands 487 days ago

              Note for Chrome users: If you've enabled Strict Site Isolation in your chrome://flags (as mitigation for Spectre), it makes all of the sliders in these observablehq notebooks not work.

              • jordigh 488 days ago

                xfig has x-splines (cross splines), and I've always wondered why they never got more popular elsewhere. Basically, they have an extra parameter at each endpoint that allows you to smoothly pick between approximation, smooth interpolation, or sharp interpolation, as odd as that may sound:


                Confusingly, there seem to be other splines called "X-splines" that appear to be completely unrelated, where the X seems to refer to the varying degree of the spline instead of just cubic.

                • egypturnash 487 days ago

                  So for what it’s worth here’s the three rules of thumb I’ve followed for about fifteen years in Illustrator:

                  1. Pull curve handles out to about 1/3 of the curve segment they control. 2. Don’t turn more than 90° between two control points. 3. Avoid S-curves between two control points.

                  Following these generally results in nice-looking curves that are easy to edit

                  A lot of “designers” these days like to present a rule of “only put your control points at 0/90/180/270° and keep your curve handles axis aligned”, which makes some degree of sense in the arena of making fonts, but results in incredibly hard to manage curves as you get further away from circles.

                  • hbosch 487 days ago

                    One great way to handle editing of complex shapes that use 90° extrema is to lean into Tunni lines[0] as a manipulation tool. Unfortunately these aren't present in Illustrator either, as far as I know, and is yet another reason why Illustrator's dominance as a bezier drawing software is less than warranted. Most font design software is better for drawing almost anything in bezier.

                    0. http://help.fontlab.com/fontlab-vi/Tunni-Lines/

                    • egypturnash 487 days ago

                      I’m gonna have to disagree with your last sentence. I’m pretty sure there isn’t any font design software out there that would let me draw an entire full-color comic page. (Which I mostly do with AI’s pencil tool - but when I need to get my hands dirty with the raw paths, I use the rules of thumbs mentioned above.)

                  • Cenk 488 days ago

                    I found Yanone’s SpeedPunk (https://yanone.de/software/speedpunk/) super useful in doing this kind of curvature work while designing typefaces.

                    • pasta 488 days ago

                      Maybe the side is down? Only white content on mobile.

                      • ldjb 488 days ago

                        It seems the page is loaded dynamically, which may cause issues.

                        There are some interactive widgets, but if you can forgo those, here is a screenshot of that page: https://screenshots.firefox.com/CoUJDgqyX5NtfC6v/beta.observ...

                        • jashkenas 487 days ago

                          The site is up, but is brand new and still in beta — what mobile OS/Browser combo are you using? We'd love to try and debug your white screen...

                          • a_e_k 487 days ago

                            Not the parent poster, but I use NoScript on desktop Firefox. Beyond whitelisting observablehq.com and observableusercontent.com I found that the content was completely missing until I also unblocked objects from fonts.gstatic.com. Could be a clue.

                            • pasta 487 days ago

                              Ah, this could be the case. I block external fonts but never had a problem because of this.

                        • virtualritz 488 days ago

                          I thought this article would explain how to do curvature based tessellation of higher order curves.

                          That way you can draw better looking curves when approximating them with (a limited number) of (straight) segments.

                          • jacobolus 488 days ago

                            You're using 'tessellation' in a weird way. Anyway, if you want to calculate optimal knot positions to approximate a curve using some fixed number of straight (or polynomial) spline segments, there are a bunch of papers about that, or I think there's a relevant chapter in De Boor's book.

                          • bagospanners 488 days ago

                            For more tasty Bézier fun: https://pomax.github.io/bezierinfo/

                            • Kiro 488 days ago

                              Are the sliders working for you?

                              • ghusbands 487 days ago

                                If you've enabled Strict Site Isolation in your Chrome flags (as mitigation for Spectre), it makes all of these observablehq notebook sliders not work. That's probably what's affecting you.

                                • Kiro 487 days ago

                                  Yeah, that's definitely it. Thank you! Very interesting.

                              • joehan 487 days ago

                                Neat! Can someone tell me why the notebook style presentation like this is gaining popularity? (e.g., jupyter notebook)