Mathematics and Art
2. Mathematical tools for artists
A much more important issue is the realism with which artists can draw on a flat piece of paper what they perceive when they look out at their 3-dimensional world. If one looks at attempts at scene representation in Egyptian and Mesopotamian art, one sees that phenomena that are associated with the human vision system are not always respected. We are all familiar with the fact that objects that are far away from us appear smaller than they actually are and that lines which are parallel appear to converge in the distance. These features, which are a standard part of the way that 3-dimensional objects are now usually represented on a planar surface, were not fully understood before the Renaissance. It is common to refer to artists as using "perspective" (or "linear perspective") to increase the realism of their representations. The issues and ideas involved in understanding perspective are quite subtle and evolved over a long time.
A', B', and C' show where the vertices are moved by "parallel" projection and A'', B'', and C'' show where the vertices are moved by "conical" projection.
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