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You need to find the resulting Polygon and fill that.
<ul><li>Find center point of all Polygons (or the current 2 if you do sequientially)
<li>find all points where Polygon lines cross.
<li>For all the point you have no check if the line between the current point and the center crosses any existing line. <ul><li>yes: dismiss point. <li>no: add poin to resulting polygon</ul></ul>
This does only apply to convex polygons.