algorithm - merging two SKShapeNode polygons into one -

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i have multiple polygons (skshapenodes) on sprite kit layer. of them non-selfintersecting polygons. know:

1) if introduce new one, intersect of previous ones:

does sknode's: "func intersectsnode(_ node: sknode) -> bool" provide means this? how can iterate on node tree check against existing skshapenodes?

2) area of intersection:

if new polygon intersects , existing one, need calculate area of intersection (e.g. area in red in picture below). propose simple algirithm this?

3) merge both of polygons new skshapenode polygon , remove 2 prior polygons sknode tree.

so after introducing new polygon intersects existing polygon b, remove both of existing polygons , b sprite kit's node tree , introduce new polygon c path merge paths of polygon , b (in orange in picture below)

i'm relatively new sprite kit , graphics programming , not comfertable euclidean geometrics either. suggestions on approaches how proceed in these tasks appreciated!!!

enter image description here


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