![]() ![]() ![]() Maybe instead of doing the transformation in the constructor, it's a preprocessing step in all calculations? That, at least, could be done consistently. If (er,ee,e) is the local right-handed orthonormal basis associated with the spherical coordinates (r, 0, (p), then the vector spherical harmonics are. ![]() It's not clear to me how it could be done in the Awkward Array backend, which takes Vector methods as a behavior (no direct constructor). r, phi, whatever → rho, phi, whatever-but that would be a lot of edits to make each of the backends consistent, and this new code would be different in kind from the existing code, as it would perform a transformation on the spot. If students have no prior knowledge of spherical coordinates, teachers should introduce the spherical coordinate system. (The "r" is not just magnitude in a 2D plane, but magnitude in 3D.) It could be possible to add constructors based on 3D radius, which immediately convert their input to the closest cylindrical coordinate system-i.e. I've edited the README-it should never have said that we have "spherical" coordinate systems, given what that's usually taken to mean. So, it was a design choice that bought us coordinate systems for the cost of implementations. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin its polar angle measured from a fixed polar axis or zenith direction and the azimuthal angle of its orthogonal projection on a refere. Figure 4.4.1: Spherical coordinate system and associated basis vectors. If we used 3D radius in the azimuthal coordinates, the azimuthal calculations would depend on both azimuthal and longitudinal coordinates, which would prevent us from being able to share code across so many coordinate systems. The spherical system uses r, the distance measured from the origin, the angle measured from the + z axis toward the z 0 plane and, the angle measured in a plane of constant z, identical to in the cylindrical system. The interpretation of each of these coordinates can depend on the previous: the longitudinal can depend on the magnitude of the azimuthal (not z, but theta and eta do) and the temporal can depend on the magnitude of the 3D vector (not t/ energy, but tau/ mass does). The internal representation can't be a 3D radius, phi, and theta, since the coordinates are described as an azimuthal piece, a longitudinal piece, and a temporal piece. ![]()
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