u is constant theta is constant
the set of lines going through a point is a sine curve in the dualspace
Given a convex object, there are two tangents to this object in a given direction . We denote in a given direction by lambda and mu their distances to the origin.
Each line whose u is between lambda and mu intersects the object.
The tangents describe two curves delimiting a strip in the dual space.
If a line is inside that strip, it intersects the object.
It's the same for two objects.
And if a line lies inside the intersection of the two strips, it intersects both objects.
this partitionning of the dual space according to its visibility is called the dual arrangement.
The faces are connected components sharing the same intersections.
They are delimited by edges, which correspond to lines tangent to one object.
They intersect at vertices that correspond to directed bitangents.
Next: The Visibility Complex