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Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

R_m(x,y) = (J_m^'(x)Y_m^'(y)-J_m^'(y)Y_m^'(x))/(J_m(x)Y_m^'(y)-J_m^'(y)Y_m(x)) (1) S_m(x,y) = (J_m^'(x)Y_m(y)-J_m(y)Y_m^'(x))/(J_m(x)Y_m(y)-J_m(y)Y_m(x)). (2)

Let lambda be the longitude, lambda_0 the reference longitude, phi the latitude, phi_0 the reference latitude, and phi_1 and phi_2 the standard parallels. Then the ...

The solid cut from a horizontal cylinder of length L and radius R by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

A set of curvilinear coordinates defined by x = (asinhv)/(coshv-cosu) (1) y = (asinu)/(coshv-cosu) (2) z = z, (3) where u in [0,2pi), v in (-infty,infty), and z in ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

A nonconformal, equal-area projection which is a special case of the Bonne projection where one of the poles is taken as the standard parallel. Because of its heart shape, ...

The Mollweide projection is a map projection also called the elliptical projection or homolographic equal-area projection. The forward transformation is x = ...