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Stroking and filling are the two basic rendering operations on paths invector graphics. The theory of filling a path is well-understood in terms ofcontour integrals and winding numbers, but when path rendering standardsspecify stroking, they resort to the analogy of painting pixels with a brushthat traces the outline of the path. This means important standards such asPDF, SVG, and PostScript lack a rigorous way to say what samples are inside oroutside a stroked path. Our work fills this gap with a principled theory ofstroking.  Guided by our theory, we develop a novel polar stroking method to renderstroked paths robustly with an intuitive way to bound the tessellation errorwithout needing recursion. Because polar stroking guarantees small uniformsteps in tangent angle, it provides an efficient way to accumulate arc lengthalong a path for texturing or dashing. While this paper focuses on developingthe theory of our polar stroking method, we have successfully implemented ourmethods on modern programmable GPUs.

Polar Stroking: New Theory and Methods for Stroking Paths