Functional Differential Geometry
The points on the plane can also be specified with polar coordinates and the points on the sphere are specified both by Riemann coordinates and the traditional colatitude and longitude .
(show-expression ((compose (chart S2-spherical) (point S2-Riemann) (chart R2-rect) (point R2-polar)) (up 'rho 'theta)))
1. The code
(up 'rho 'theta)
represents the polar coordinates of a point.
2. The function
generates an abstract point from a point in
3. The function
rect coordinates given an abstract point on the plane
(show-expression ((compose (chart R2-rect) (point R2-polar)) (up 'rho 'theta)))
(point S2-Riemann)gives the point on the sphere given rectangular coordinates on the plane.
In other words, the function
generates an abstract point-on-the-sphere (
S2) from a point-on-the-plane (
rect coordinates. In other words,
Perform an analogous computation to get the polar coordinates of the point on the plane corresponding to a point on the sphere given by its colatitude and longitude.
(show-expression ((compose (chart R2-polar) (point R2-rect) (chart S2-Riemann) (point S2-spherical)) (up 'phi 'lambda)))
— Me@2023-04-22 10:42:50 PM
2023.04.25 Tuesday (c) All rights reserved by ACHK
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