Linear Algebra, 2020a

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Topic
Projective Geometry
There are geometries other than the familiar Euclidean one. One such geometry
arose when artists observed that what a viewer sees is not necessarily what is
there. As an example, here is Leonardo da Vinci’s The Last Supper.
Look at where the ceiling meets the left and right walls. In the room those lines
are parallel but da Vinci has painted lines that, if extended, would intersect.
The intersection is the vanishing point. This aspect of perspective is familiar
as an image of railroad tracks that appear to converge at the horizon.
Da Vinci has adopted a model of how we see. Imagine a person viewing a
room. From the person’s eye, in every direction, carry a ray outward until it
intersects something, such as a point on the line where the wall meets the ceiling.
This first intersection point is what the person sees in that direction. Overall
what the person sees is the collection of three-dimensional intersection points
projected to a common two dimensional image.