¶ Projective Transformation (3)
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Index Entry
Projective Transformation:
"I use three fundamental reference lines instead of two. When only two lines cross, infinity is involved since one or two lines are open-ended and have no finitely contained areas. If three lines overlap one another they make a triangle. Thus, a finite area is inherently contained. I do not have to break open the data transferred from the sphere to the plane by triangles.
"There is, however, what we call spherical excess in the topological transformation of the spherical data to the flat surface. Spherical excess is the only source of distortion. . . Spherical excess refers to the amount by which the sum of the spherical triangle’s angles exceed 180°. Spherical excess for a large spherical triangle is very much larger than for a small spherical triangle. For instance, on a spherical tetrahedron each of the angles is 120 degrees, so that the total of the three angles of each of the spherical tetrahedron’s four triangles is 360 degrees; 360 degrees minus 180 degrees leaves an excess of 180 degrees. In a spherical octahedron obtained by bisecting the edges of a spherical tetrahedron and interconnecting the three great circles, each of them angles will be 90 degrees, or
¶ Citations
- RBF, Univ. of Rhode Island, 26 Aug. '66, p. 197.
