Geometry in spherical coordinate

[Asuralm]

Hi all:

I am wondering if there is any book or course note about the geometry in spherical coordinate. Not just the superficial definition and the convertion with Euclidean coordinate. But something like how a line is defined in spherical coordinate in 3D space, how a plane is defined, how to calculate the distance between a 3D point and a plane both in spherical coordinates. Also, the geometry calculus in spherical coordinates.

Is anyone aware of such things please?

Thanks

 

[HallsofIvy]

I don't understand what you are asking. A line or plane is defined without regard to coordinates. Do you mean the general equations of line or plane?

 

[Asuralm]

I don't understand what you are asking. A line or plane is defined without regard to coordinates. Do you mean the general equations of line or plane?

I mean what's they expression of plane and line in the spherical coordinates. For example, the line is defined as something like $${\bf v} = {\bf v}_0 + t\cdot {\bf n}$$. But here $${\bf v} = (v_x, v_y, v_z)$$, i.e. cartesian coordinate. How can a plane and line be expressed in the spherical coordinate form, i.e. $$(\rho, \theta, \phi)$$