Editing Point in polygon (section)

=== SVG ===
Similar methods are used in [[Scalable Vector Graphics|SVG]] for defining a way of filling with color various shapes (such as path, polyline, polygon, text etc.).<ref>{{Cite web|title=Painting: Filling, Stroking, Colors and Paint Servers – SVG Tiny 1.2|url=https://www.w3.org/TR/2008/REC-SVGTiny12-20081222/painting.html#FillProperties|access-date=2021-07-24|website=www.w3.org}}</ref> The algorithm of filling is influenced by 'fill-rule' attribute. The value may be either {{Code|nonzero}} or {{Code|evenodd}}. For example, in a [[pentagram]], there is a central "hole" (visible background) with {{Code|evenodd}}, and none with {{Code|nonzero}} attribute.<ref>{{Cite web|title=Painting: Filling, Stroking, Colors and Paint Servers – SVG Tiny 1.2|url=https://www.w3.org/TR/2008/REC-SVGTiny12-20081222/painting.html#FillProperties|access-date=2021-07-24|website=www.w3.org}}</ref>

For [[simple polygons]], the algorithms will give the same result. However, for [[complex polygons]], the algorithms may give different results for points in the regions where the polygon intersects itself, where the polygon does not have a clearly defined inside and outside. One solution using the even-odd rule is to transform (complex) polygons into simpler ones that are even-odd-equivalent before the intersection check.<ref>{{cite conference |author=Michael Galetzka, Patrick Glauner |year=2017 |title=A Simple and Correct Even-Odd Algorithm for the Point-in-Polygon Problem for Complex Polygons |conference=Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications ([[VISIGRAPP]] 2017), Volume 1: GRAPP }}</ref> This, however, is computationally expensive. It is less expensive to use the fast non-zero winding number algorithm, which gives the correct result even when the polygon overlaps itself.