This video was captured in real-time (with minimum subsequent edition) to show a few algorithms implemented on the oriented projective plane (under extended CGAL) in action and some of the features of T²Viewer. We chose to illustrate user interaction with both models of T² for input generation (triangulation), query actions (point location), visualization of either or both models (in 3-D orbiting), smooth variation of surface transparency to show either or both ranges of T², algorithm animation (segments intersections) and the use of input tools. Furthermore, while displaying the interactive construction of the Voronoi diagram, the video illustrates the duality provided by the Oriented Projective Plane, which allows for the simultaneous construction of the order 1 (nearest neighbor) diagram and the order n-1 (farthest neighbor) diagram of points on the front range.