Linear Algebra

342 Chapter Four. DeterminantsIt is not a orthogonal projection since the line from the viewer to C is notorthogonal to the image plane.The operation of central projection preserves some geometric properties, forinstance lines project to lines. However, it fails to preserve some others, forinstance equal length segments can project to segments of unequal length (ABis longer than BC, because the segment projected to AB is closer to the viewerand closer things look bigger). The study of the effects of central projections isprojective geometry.There are three cases of central projection. The first is the projection doneby a movie projector.projector P source S image IWe can think that each source point is “pushed” from the domain plane outwardto the image point in the codomain plane. The second case of projection is thatof the artist “pulling” the source back to the canvas.painter P image I source SThe two are different because in the first case S is in the middle while in thesecond case I is in the middle. One more configuration is possible, with P in themiddle. An example of this is when we use a pinhole to shine the image of asolar eclipse onto a piece of paper.source S pinhole P image I