spheroidal collineation - definitie. Wat is spheroidal collineation
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Wat (wie) is spheroidal collineation - definitie

A BIJECTION FROM ONE PROJECTIVE SPACE TO ANOTHER THAT PRESERVES COLLINEARITY
Collineation group; Automorphic collineation; Colineation group

Collineation         
·noun The act of aiming at, or directing in a line with, a fixed object.
Collineation         
In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself.
Oblate spheroidal coordinates         
  • Figure 2: Plot of the oblate spheroidal coordinates μ and ν in the ''x''-''z'' plane, where φ is zero and ''a'' equals one. The curves of constant ''μ'' form red ellipses, whereas those of constant ''ν'' form cyan half-hyperbolae in this plane. The ''z''-axis runs vertically and separates the foci; the coordinates ''z'' and ν always have the same sign. The surfaces of constant μ and ν in three dimensions are obtained by rotation about the ''z''-axis, and are the red and blue surfaces, respectively, in Figure 1.
  • Figure 3: Coordinate isosurfaces for a point P (shown as a black sphere) in the alternative oblate spheroidal coordinates (σ, τ, φ). As before, the oblate spheroid corresponding to σ is shown in red, and φ measures the azimuthal angle between the green and yellow half-planes. However, the surface of constant τ is a full one-sheet hyperboloid, shown in blue. This produces a two-fold degeneracy, shown by the two black spheres located at (''x'', ''y'', ±''z'').
THREE-DIMENSIONAL ORTHOGONAL COORDINATE SYSTEM
Oblate spheroidal harmonics; Oblate spheroidal coordinate system
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e.

Wikipedia

Collineation

In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a group, called the collineation group.