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  2. Stereographic projection - Wikipedia

    en.wikipedia.org/wiki/Stereographic_projection

    Stereographic projection is conformal, meaning that it preserves the angles at which curves cross each other (see figures). On the other hand, stereographic projection does not preserve area; in general, the area of a region of the sphere does not equal the area of its projection onto the plane. The area element is given in (X, Y) coordinates by

  3. Planisphaerium - Wikipedia

    en.wikipedia.org/wiki/Planisphaerium

    The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.

  4. 3-sphere - Wikipedia

    en.wikipedia.org/wiki/3-sphere

    Stereographic projection of a 3-sphere (again removing the north pole) maps to three-space in the same manner. (Notice that, since stereographic projection is conformal, round spheres are sent to round spheres or to planes.) A somewhat different way to think of the one-point compactification is via the exponential map. Returning to our picture ...

  5. Pole figure - Wikipedia

    en.wikipedia.org/wiki/Pole_figure

    It is possible to choose any projection plane parallel to the equator (except the South pole): the figures will be proportional (property of similar triangles). It is usual to place the projection plane at the North pole. Definition The pole figure is the stereographic projection of the poles used to represent the orientation of an object in space.

  6. Stereographic map projection - Wikipedia

    en.wikipedia.org/wiki/Stereographic_map_projection

    The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity. Like the orthographic projection and gnomonic projection, the stereographic projection is an azimuthal projection, and when on a sphere, also a perspective projection.

  7. Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Inversive_geometry

    Stereographic projection as an inversion of a sphere. A stereographic projection usually projects a sphere from a point (north pole) of the sphere onto the tangent plane at the opposite point (south pole). This mapping can be performed by an inversion of the sphere onto its tangent plane.

  8. Gudermannian function - Wikipedia

    en.wikipedia.org/wiki/Gudermannian_function

    Twice the area of the purple triangle is the stereographic projection s = tan ⁠ 1 / 2 ⁠ ϕ = tanh ⁠ 1 / 2 ⁠ ψ. The blue point has coordinates (cosh ψ, sinh ψ). The red point has coordinates (cos ϕ, sin ϕ). The purple point has coordinates (0, s). Graph of the Gudermannian function. Graph of the inverse Gudermannian function.

  9. Gall stereographic projection - Wikipedia

    en.wikipedia.org/wiki/Gall_stereographic_projection

    Gall stereographic projection of the world. 15° graticule. Gall stereographic projection with 1,000 km indicatrices of distortion. The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection.