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Polygon intersection

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Hi, I know there are a lot of tutorials online about this topic, but I haven't found what I am looking for yet.. I have to arbitrary polygons, the first one can move in every direction, the second doesn't change its position. The first one has the task to clip the second polygon, this means it cuts the intersection parts of the second polygon away. Hence it changes its appearence and becomes smaller. Now the big problem is that the first polygon can move everywhere. This means with every translation of this polygon, the intersection parts of the second polygon have to be calculated and those intersection parts have to be cutted. I know this is not an easy task, but my only idea was to ask here in this forum.

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