Paths MARK J. KILGARD, NVIDIA Fig. 1. Polar stroking samples: A cubic Bézier segment with a cusp rendered properly with polar stroking while uniform parametric tessellation has no cusp, both using 134 triangles; B polar stroking improves the facet angles distribution compared to uniform tessellation, both using 126 triangles; C arc length texturing; D ellipse drawn as just 2 conic segments, one external; E complex cubic Bézier path (5,031 path commands, 29,058 scalar path coordinates) with cumulative arc length texturing; F centripetal Catmull-Rom spline. Stroking and !lling are the two basic rendering operations on paths in vector graphics. The theory of !lling a path is well-understood in terms of contour integrals and winding numbers, but when path rendering standards specify stroking, they resort to the analogy of painting pixels with a brush that traces the outline of the path. This means important standards such as PDF, SVG, and PostScript lack a rigorous way to say what samples are inside or outside a stroked path. Our work !lls this gap with a principled theory of stroking. Guided by our theory, we develop a novel polar stroking method to render ACM Reference Format: Mark J. Kilgard. 2020. Polar Stroking: New Theory and Methods for Stroking Paths. ACM Trans. Graph. 39, 4, Article 145 (July 2020), 15 pages. https: //doi.org/10.1145/3386569.3392458 1 INTRODUCTION Vector graphics standards such as PDF [Adobe Systems 2008], SVG [SVG Working Group 2011], PostScript [Adobe Systems 1985], PCL 308v3 [cs.GR] 31 Oct 2020