Please let me know the formula for the coordinate of the midpoint of 2 points in spherical coordinate system.

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rioolpijpgp · Accepted Answer

Step 1You can use the general formulas for converting between Cartesian and spherical coordinates to do this:      (                            x                                      y                                      z                      )    =      (                            r          sin          ⁡          θ          cos          ⁡          ϕ                                      r          sin          ⁡          θ          sin          ⁡          ϕ                                      r          cos          ⁡          θ                      )      ,so the midpoint between two points 1 and 2 is      1    2        (                                        x            1                    +                      x            2                                                            y            1                    +                      y            2                                                            z            1                    +                      z            2                                )    =      1    2        (                                        r            1                    sin          ⁡                      θ            1                    cos          ⁡                      ϕ            1                    +                      r            2                    sin          ⁡                      θ            2                    cos          ⁡                      ϕ            2                                                            r            1                    sin          ⁡                      θ            1                    sin          ⁡                      ϕ            1                    +                      r            2                    sin          ⁡                      θ            2                    sin          ⁡                      ϕ            2                                                            r            1                    cos          ⁡                      θ            1                    +                      r            2                    cos          ⁡                      θ            2                                )      .Then you can substitute this into the expression for the spherical coordinates in terms of the Cartesian coordinates:      (                            r                                      θ                                      ϕ                      )    =      (                                                      x              2                        +                          y              2                        +                          z              2                                                            arccos          ⁡          (          z                      /                                              x              2                        +                          y              2                        +                          z              2                                )                                      arctan          ⁡          (          y                      /                    x          )                      )      .

Please let me know the formula for the coordinate of

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