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In terms of computational geometry, how can you get the top-bottom wedge? We know that a line segment dualize to a left-right wedge, and I tried to expand on this idea by visualizing the top-down wedge as a left-right wedge, but was unsuccessful in doing so (largely because of the vertical line which has infinite slope).

To make my question more specific, what kind of object is needed in the primal plane so it would dualize to a top-down wedge?

Can someone nudge me in the right direction?

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In computational geometry dualization usually is being done by means of spherical reciprocation. Thus, given some line segment, which does not pass through the spherical center, then the 2 rays from the center to the ends of this segment will define the outer normals to the respective dual faces. The intersection of those 2 faces then defines the according wedge direction. So, if you want 2 faces to intersect in such a way that their wedge runs top-bottom (vertical), then the line segment ought have been horizontal.

--- rk

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