Geometry in spherical coordinate

  • Thread starter Asuralm
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  • #1
Asuralm
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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
 

Answers and Replies

  • #2
HallsofIvy
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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?
 
  • #3
Asuralm
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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 [tex]{\bf v} = {\bf v}_0 + t\cdot {\bf n}[/tex]. But here [tex]{\bf v} = (v_x, v_y, v_z)[/tex], i.e. cartesian coordinate. How can a plane and line be expressed in the spherical coordinate form, i.e. [tex](\rho, \theta, \phi)[/tex]
 

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