Evenodd

Evenodd, or the even-odd rule, is a rule used to determine which regions of a closed path are considered inside a shape for fill operations in vector graphics and computational geometry. It is especially relevant for paths that self-intersect or contain holes.

The rule is simple: for any point, project a ray to infinity and count how many times the ray crosses the path. If the count is odd, the point is inside; if even, the point is outside. This parity-based approach yields intuitive results for complex shapes, since overlapping segments toggle the inside/outside status each time they are crossed.

The even-odd rule is commonly contrasted with the nonzero winding rule. The nonzero rule uses the orientation of crossings (the winding number) to determine inside status, which can produce different results for the same path.

In practice, many graphics systems and formats use the even-odd rule as one of two fill modes. SVG uses the even-odd fill-rule and the nonzero fill-rule as available options; PDF and other formats support both rules as well. Artists and programmers leverage the even-odd rule to create shapes with holes and to render self-intersecting outlines predictably.

Limitations include potential unintuitive results for highly self-intersecting paths and the need to choose a rule consistently across a project. Related concepts include the winding number and boolean operations on polygons.