Even–odd rule

The even–odd rule is an algorithm implemented in vector-based graphic software, like the PostScript language and Scalable Vector Graphics (SVG), which determines how a graphical shape with more than one closed outline will be filled. Unlike the nonzero-rule algorithm, this algorithm will alternatively color and leave uncolored shapes defined by nested closed paths irrespective of their winding.

The SVG defines the even–odd rule by saying:

The rule can be seen in effect in many vector graphic programs (such as Freehand or Illustrator), where a crossing of an outline with itself causes shapes to fill in strange ways.

On a simple curve, the even–odd rule reduces to a decision algorithm for the point in polygon problem.

The SVG computer vector graphics standard may be configured to use the even–odd rule when drawing polygons, though it uses the non-zero rule by default.

Implementation

Below is a partial example implementation in Python, by using a ray to the right of the point being checked:

See also

• Jordan curve theorem
• Complex polygon
• Tessellation
• TrueType

References

External links

• Definition of fill rules in SVG