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raphlinus's profile
Raph Levien
Raph Levien
Raph Levien
@raphlinus

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Raph Levien

@raphlinus

Rust. Fonts. Graphics. Quaker. Independent. he/him

Berkeley, CA
levien.com
Joined May 2009

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    Raph Levien‏ @raphlinus 23 Dec 2019
    • Report Tweet

    Recursive subdivision is not the best way to flatten quadratic Béziers to polylines. Here's a better way: https://raphlinus.github.io/graphics/curves/2019/12/23/flatten-quadbez.html … . Hopefully catnip for my followers who are really into 2D graphics and math.

    9:43 PM - 23 Dec 2019
    • 53 Retweets
    • 274 Likes
    • RodrigoThe2nd Ray Lee Nils Dillon Bailey Mark Wayland Frederik De Bleser うしお Maxim Whatevsmaker 🏳️‍🌈Douglas🏳️‍🌈
    6 replies 53 retweets 274 likes
      1. Raph Levien‏ @raphlinus 27 Dec 2019
        • Report Tweet

        I've generalized this to cubic Béziers, test page is up at https://levien.com/tmp/flatten.html …. Question for 2d graphics Twitter: what's a good journal or conference to submit to? It feels like it's met the threshold for an academic paper.

        3 replies 2 retweets 19 likes
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      2. Ali Rahimi‏ @alirahimi0 23 Dec 2019
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        Replying to @raphlinus

        my instinct is to do this by dynamic programming instead, since you know the number of segments. locate endpoint of first segment assuming subsequent ones are chosen optimally. then work backwards by DP.

        1 reply 0 retweets 0 likes
      3. Raph Levien‏ @raphlinus 23 Dec 2019
        • Report Tweet
        Replying to @alirahimi0

        Yeah, that's what was going through my head a week or so ago. But this way, you have a closed form expression that just spits out all the t values in parallel for all the segments, which is *way* better if your evaluation environment is a GPU.

        1 reply 0 retweets 1 like
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      2. Allan MacKinnon‏ @pixelio 24 Dec 2019
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        Replying to @raphlinus

        Wang’s Formula bounds how many levels of subdivision you need to achieve a specified degree of flatness. “Pyramid Algorithms” by Ron Goldman covers Wang’s formula (chap. 5.6.3). Wang’s formula is also discussed in: DEC Paris Research Laboratory report #1, May 1989. Good luck!

        2 replies 0 retweets 6 likes
      3. Raph Levien‏ @raphlinus 24 Dec 2019
        • Report Tweet
        Replying to @pixelio

        Thanks for the reference, it looks excellent. How did I not know about that before now?

        0 replies 0 retweets 0 likes
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      2. Andreas Urbán‏ @1amjau 24 Dec 2019
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        Replying to @raphlinus

        Any thoughts on doing recursive subdivision on GPU using the tessellation stage and transform feedback? Breadth first makes it quite parallel, and error can be decreased over several frames.

        2 replies 0 retweets 0 likes
      3. Raph Levien‏ @raphlinus 24 Dec 2019
        • Report Tweet
        Replying to @1amjau

        It can probably be done, but for my own GPU work I'm basically using compute exclusively. It's also the case that my algorithm produces more efficient results than recursive subdivision, which takes away most of the motivation to do that.

        0 replies 0 retweets 1 like
      4. End of conversation
      1. Nicolas Silva‏ @nicalsilva 24 Dec 2019
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        Replying to @raphlinus

        Interesting! One thing to note with these adaptative flattening techniques is that if you don't consistently flatten in the same direction (say, top to bottom) you can get unexpected cracks between adjacent paths. Easy to address in most cases but worth keeping in mind!

        0 replies 0 retweets 3 likes
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      1. DaveFile‏ @davefile 24 Dec 2019
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        Replying to @raphlinus @redblobgames

        Let's all understand this: Bézier curves are evil... 5th order curve is pure!

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