English: On the left is an oriented surface and a volume. The counter-clockwise boundary of the surface and the inwards oriented surface of the volume are shown. On the right is the surface that forms the intersection of the surface with the volume, and the counter-clockwise boundary of the intersection surface is also shown. The boundary of the intersection consists of two parts: the intersection of the boundary of the original surface with the volume, and the intersection of the the inwards oriented surface of the volume with the original surface.
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