============================================= Spherical to Cartesian Coordinates Conversion ============================================= In spherical coordinates, a point in space is described by three values: the radial distance of that point from the origin, the inclination angle from the positive z-axis, and the azimuth angle from the positive x-axis and the intersection between the plane passing through the point and the origin perpendicular to the z-axis. The spherical coordinates are usually represented as `(r, theta, phi)`, where: - `r` is the radial distance, - `theta` is the inclination angle (ranging from 0 to pi), and - `phi` is the azimuth angle (ranging from 0 to 2pi). The conversion from spherical to Cartesian coordinates is given by the following equations: - `x = r * cos(theta)` - `y = r * sin(theta) * cos(phi)` - `z = r * sin(theta) * sin(phi)` For example, if we have a point in spherical coordinates as `(1, pi/2, 0)`, the conversion to Cartesian coordinates would be: - `x = r * cos(pi/2) = 0` - `y = r * sin(pi/2) * cos(0) = 1` - `z = r * sin(pi/2) * sin(0) = 0` So the Cartesian coordinates for this point would be `(0, 1, 0)`. It's important to note that in a 2D space (or when `r` and `theta` are defined, but `phi` is not), the conversion simplifies to: - `x = r * cos(theta)` - `y = r * sin(theta)` The `spherical_to_cartesian` function implements these conversions. For the multi-dimension case see the article here `N-sphere `__.