This program provides an interactive 3D visualization of perspectivity between two planes. The construction involves a fixed point O, a rotating plane Π (blue), and a fixed reference plane Π′ (red). As the blue plane rotates, the lines of intersection between the projection rays from O and each plane change dynamically. By applying rotation matrices, we can rotate Π to explore the variety of perspective projections that arise between just two planes.
The visualization demonstrates how a line in one plane corresponds to a different line in another plane. It reflects the geometric concept illustrated in Lecture 19, where the set of lines connecting O to points on a line in Π forms a plane that intersects Π′ in a line L′, which is the perspectivity image of L.
This also highlights an important property: if either plane becomes parallel to the plane defined by rays from O, no intersection line can be formed, demonstrating the limitations of the perspectivity mapping.
Provides an intuitive, visual understanding of how perspective projections depend on the relative orientation of planes and viewpoint.
Allows observation of how rotation of a plane or viewpoint affects the resulting intersection lines.
Clearly demonstrates cases where the perspectivity mapping is undefined, offering insight into degenerate configurations.
