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Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...
Light scattering from a multilayered sphere based on the algorithm by W Yang. [17] Very robust and stable, slower than Toon and Ackerman. Evaluate integral parameters and angular patterns, near-field and power flow streamlines plotting. Has a compilation option to use Boost.Multiprecision for higher accuracy.
Mie Scattering from a sphere. x is the wave number times the sphere's radius and m is the refractive index of the sphere divided by the refractive index of the medium. In electromagnetism , the Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution , the Lorenz–Mie–Debye solution or Mie scattering ) describes the ...
Because in a continuous function, the function for a sphere is the function for a circle with the radius dependent on z (or whatever the third variable is), it stands to reason that the algorithm for a discrete sphere would also rely on the midpoint circle algorithm. But when looking at a sphere, the integer radius of some adjacent circles is ...
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
Equirectangular projection of the world; the standard parallel is the equator (plate carrée projection). Equirectangular projection with Tissot's indicatrix of deformation and with the standard parallels lying on the equator True-colour satellite image of Earth in equirectangular projection Height map of planet Earth at 2km per pixel, including oceanic bathymetry information, normalized as 8 ...
Stereographic projection of complex numbers and onto the points and of the Riemann sphere - connect () with A or B by a line and determine the intersection with the sphere. In mathematics , the Riemann sphere , named after Bernhard Riemann , [ 1 ] is a model of the extended complex plane (also called the closed complex plane ): the complex ...