An area metric with support for negative values. For example, the sign of the area of a region may depend on the orientation of its boundary, i.e. whether the boundary runs clockwise or anticlockwise. This is commonly used to define holes in regions, as the negative area of a hole is automatically subtracted from the total area of the region. Signed areas are only readily applicable to two-dimensional spaces, given that in higher dimensions clockwise and anticlockwise depend on the position of the observer.