nanosvg | Simple stupid SVG parser | Animation library

The algorithm is the one described in the SVG fill-rule definition. Start from a point and draw one arbitrary ray to infinity (well, a line that ends outside the area you need to consider) and count the path crossings with one of the two methods nonzero and evenodd described.

Determining the count of crossings: Don't try to do this for subpaths in one go, but consider each path segment individually. The majority will have a count of zero, which is fine. This library has for example a function for computing the intersection points between a cubic Bezier and a line. Look at the source code, it is well documented. (Although it is not very clear which stance the author takes on copyright.)

Determining the path direction: You only have to determine whether the starting and end point of the segment are left or right of your ray.

• If both are on the same side, count one left-to-right and one right-to-left. (nonzero rule: 0, evenodd rule: +2)
• If the start point is left and the end point is right, either count one left-to-right (+1), or, for a cubic Bezier with three crossings, count two left-to-right and one right-to-left. (nonzero rule: +1, evenodd rule: +3)
• If the start point is right and the end point is left, for one crossing (nonzero rule: -1, evenodd rule: +1) or for three crossings (nonzero rule: -1, evenodd rule: +3)
• If the ray crosses a subpath just at a segment point, you have to avoid counting the crossing twice. The best way to avoid errors is to handle the two segments as if they were one, subtract one from the added count of crossings, and determine the side only for the overall start/end points.

In the end, for nonzero, a point is inside if the final count total is not zero. For evenodd, it is inside if the final count total is odd.