How are filled paths rendered?

Question

What are the standard algorithms used in vector graphics for rendering filled paths?

I'm not only interested in the process of rendering strokes, I also would like to know how the shapes are filled - how it is determined if given point is inside or outside the path (I believe even specifying the rules of what inside and outside mean is not a straightforward thing).

Answer 1

1. find outline (perimeter as polygon)

   this I think you already have

2. triangulate (or cut to convex polygons)

   there are many approaches like:

   • clip ear
   • Delaunay

   see Wiki Polygon triangulation

3. fill convex triangles/polygons

   this is easy either use

   • gfx lib like OpenGL,DirectX,...
   • api like GDI
   • rasterize on your own like in how to rasterize convex polygons

4. style

   This stuff is more complicated then it sound like at the first hear. For:

   1. outline width pen,stroke

      convert outline to polygon by shifting it out or in. For more info see this

   2. outline style pen,stroke

      full,dash dot,dot dot,... for more info see this

   3. filling style brush

      like hatching which is most complicated from all. It involves heavy polygon tweaking similar but much harder then outline width. Some styles are simpler some extremly complicated for example for equidistant line fill simple loop + intersection + inside polygon test will do. To test polygon inside you can use hit test