Surface normal

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The relationship between the normal (x,y,z) in Euclidean space and the normal (,) in polar coordinate.

• x=sincos
• y=sinsin
• z=cos

• =arccos(z)
• =atan2(y, x)

Where the following conditions hold.

• 0<
• 0<2
• sqrt(x²+y²+z²)=1
• is the angle between z axis and the normal
• is the direction from positive z axis to the normal
• is the angle between x axis and the vector where the normal is projected to xy plane
• is the direction from positive x axis to positive y axis
• atan2(y,x) is a function which calculates arctan(y/x)
  • It is the same for atan2() in ANSI C
  • If x==0 then atan2 returns 0
  • atan2 returns the value between - to
  • So, add 2 if atan2 returns a negative value

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