FillPath Union of Polygons in a Inclusive(non-XOR) Fashion

Question

I need to fill a complex region with anti-aliasing.

The region is composed of numerous rotated rectangles (as of petal of a sunflower) and a central circle.

Region does not support anti-aliasing

so I tried FillPath but areas where rectangles overlap are not filled. (XOR'ed)

        // Has alpha so FillPath-ing multiple times doesn't help
        Color color = Color.FromArgb(128, 32, 64, 255);
        Brush brush = new SolidBrush(color);
        Region region = null;
        //GraphicsPath bigPath = new GraphicsPath();
        for (int i = 0; i < nPetals; i++)
        {
            GraphicsPath pat = new GraphicsPath();
            Point p1, p2, p3, p4; // Actual code omitted
            pat.AddPolygon(new[] { p1, p2, p3, p4 });           
            //bigPath.AddPolygon(new[] { p1, p2, p3, p4 });
            if (region == null)
                region = new Region(pat);
            else region.Union(pat);
        }           
        var pathCirc = new GraphicsPath();
        pathCirc.AddEllipse(100,200,3,3);
        region.Union(path);     
        g.FillRegion(brush, region);    //Aliased
        //g.FillPath(brush, bigPath);   //XOR'ed

Is there any way to GraphicsPath.AddPolygon/AddEllipse() non-XOR way?