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pcwalton's profile
Patrick Walton
Patrick Walton
Patrick Walton
@pcwalton

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Patrick Walton

@pcwalton

Research engineer at Mozilla

San Francisco, CA
pcwalton.github.io
Joined November 2009

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    1. Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @warrenm @BlurSpline @mrdoob

      Ah. That’s O(n^2) and won’t handle self-intersecting paths, which are extremely common in the real world :(

      2 replies 0 retweets 0 likes
    2. Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @pcwalton @warrenm and

      Not trying to troll you, BTW; it’s impressive work. Just trying to save you a year’s worth of dead-ends that I had to go through. There’s only one practical solution for tessellation of resolution independent paths that I know of, and it’s what Pathfinder uses.

      1 reply 0 retweets 1 like
    3. Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @pcwalton @warrenm and

      You will need to rework the whole thing for SVG spec compliance when you get to implementing fill rules. The spec mandates that you handle winding vs. even-odd properly. Probably best to do it sooner rather than later, IMO.

      1 reply 0 retweets 0 likes
    4. Mr.doob‏ @mrdoob 5 Apr 2018
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      Replying to @pcwalton @warrenm @BlurSpline

      Yeah. I already found some svgs that earcut can't handle. SVG is like COLLADA, we won't support it fully, but we'll have decent support with performant and maintainable code. Enjoying the luxury of not being a browser 😇

      2 replies 0 retweets 1 like
    5. Mr.doob‏ @mrdoob 5 Apr 2018
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      Replying to @mrdoob @pcwalton and

      Really appreciate sharing your findings by the way. I have the same urge when I see someone starting a open source library 🤓

      1 reply 0 retweets 1 like
    6. Graphics Noob‏ @BlurSpline 5 Apr 2018
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      Replying to @mrdoob @pcwalton @warrenm

      Sorry noob qn for @pcwalton - what's the complexity for pathfinder and does it avoid polygon triangulation?

      1 reply 0 retweets 0 likes
    7. Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @BlurSpline @mrdoob @warrenm

      It’s O(k * n * log n) where n is the number of vertices and k is the maximum number of simultaneous active edges (usually a low number). Same complexity as a CPU renderer. It creates trapezoidal meshes that preserve curves (so the mesh is resolution independent).

      1 reply 0 retweets 0 likes
    8. Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @pcwalton @BlurSpline and

      In the case of a monotone path, Pathfinder’s tessellation is O(n log n), whereas ear clipping is O(n^2).

      1 reply 0 retweets 0 likes
    9. Graphics Noob‏ @BlurSpline 5 Apr 2018
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      Replying to @pcwalton @mrdoob @warrenm

      Would if replace Ear Clipping with Constrained Delaunay Triangulation, would the complexity be reduce O(n log n)? Anyways when I get some time, I'll try to check out Pathfinder's code.

      1 reply 0 retweets 0 likes
    10. Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @BlurSpline @mrdoob @warrenm

      Delaunay triangulation is even worse—it’s O(n^3). The paper Pathfinder is based on is Lorenzetto et al, “A Fast Trapezoidation Technique for Planar Polygons”: https://pdfs.semanticscholar.org/b590/6dd5a48ad8927ea9fadd5110f791f569116e.pdf …

      2 replies 0 retweets 1 like
      Patrick Walton‏ @pcwalton 5 Apr 2018
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      Replying to @pcwalton @BlurSpline and

      Pathfinder could be O(n log n) by storing the active edge list as a red-black tree as in the paper, I think, but it’s not worth it in practice because of constant factor overhead…

      5:14 PM - 5 Apr 2018 from South Beach, San Francisco
      1 reply 0 retweets 0 likes
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        2. Graphics Noob‏ @BlurSpline 5 Apr 2018
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          Replying to @pcwalton @mrdoob @warrenm

          Thanks for the link - I couldn't find much description on Pathfinder when I googled it just now (I did however find your blog post https://pcwalton.github.io/2017/02/14/pathfinder.html …).

          1 reply 0 retweets 0 likes
        3. Ahli.Li‏ @AhliLi3 8 Apr 2018
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          Replying to @BlurSpline @pcwalton and

          Transforming to a 3d+ function generated line allows a surface projection normal (for triangulation or procedural shading) and other qualities like material transparency or bump roughnes or color to be calculated by the function, 2d+3d curve hulls and extrusion can approach nurbs

          2 replies 0 retweets 1 like
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