Dual ParaboloidMath Cheat Sheet

s = rx / (1-rz)

t = ry / (1-rz)

How to map (rx,ry,rz) unit vector to

(s,t) texture coordinate in [-1,1] range

s = - rx / (rz + 1)

t = - ry / (rz + 1)

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Reverse mapping: (s,t) to (rx,ry,rz)

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rx = 2 s / (s2 + t2 + 1)

ry = 2 t / (s2 + t2 + 1)

rz = (-1 + s2 + t2) / (s2 + t2 + 1)

rx = - 2 s / (s2 + t2 + 1)

ry = - 2 t / (s2 + t2 + 1)

rz = - (-1 + s2 + t2) / (s2 + t2 + 1)

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