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South Pole of the Rotated Sphere, and coordinates of the centres of the haloes on
the upright sphere.
Sharon Liu.
2023/08/09.
North pole x: -sin(45)*sin(45).
North pole y: cos(45).
The south pole, on the xy projection, is the mirror image, of the north pole.
South pole x: 0.5 .
South pole y: -cos(45).
Radial circle x: sin(theta).
Radial circle y: cos(theta).
r_sphere = 1.
Upright sphere: x coordinates are 0.
DU45, y: cos(45).
DE, y: 0.
DD45, y: cos(135).
Next steps.
Length of the upright axis, is 2.
Length of the rotated sphere axis, is sqrt(1^2 + (2*cos(45))^2). (Used pythagoras.)

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20230809 South Pole of the Rotated Sphere.docx

  • 1. South Pole of the Rotated Sphere, and coordinates of the centres of the haloes on the upright sphere. Sharon Liu. 2023/08/09. North pole x: -sin(45)*sin(45). North pole y: cos(45). The south pole, on the xy projection, is the mirror image, of the north pole. South pole x: 0.5 . South pole y: -cos(45). Radial circle x: sin(theta). Radial circle y: cos(theta). r_sphere = 1.
  • 2. Upright sphere: x coordinates are 0. DU45, y: cos(45). DE, y: 0. DD45, y: cos(135). Next steps. Length of the upright axis, is 2. Length of the rotated sphere axis, is sqrt(1^2 + (2*cos(45))^2). (Used pythagoras.)