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Spherical projection

  • Map 3D point (X,Y,Z) onto sphere

Y

Z X

(xˆ, yˆ, zˆ) =

1 X2 +Y2 + Z2

( X ,Y , Z )

  • Convert to spherical coordinates

(sinθ cosφ,sinφ,cosθ cosφ) = (xˆ, yˆ, zˆ)

  • Convert to spherical image coordinates

φ

unwrapped sphere

spherical image

Inverse Spherical projection

(x,y,z)

Y

(sin cos ,cos cos ,sin )

Z X

  • cos

  • sin

  • cos

cos

Full-view Panorama

+

+

+

+

Spherical Projection

Y

X

3D rotation

  • Rotate image before placing

on unrolled sphere

(x,y,z)

Y

(sin cos ,cos cos ,sin )

Z X

p=Rp

  • cos

  • sin

  • cos

cos

_ _ _ _

Polar Projection

  • Extreme “bending” in ultra-wide fields of view

10

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