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Get Technical

I intend to discuss the equations and explain essential derivations (or proofs) but for now, I am going to simply dump the relevant equations here.

Equations based on cartesian and cylindrical coordinates​

Equation 1

Diagram for deriving cartesian coordinates​

Equation 2

Superellipse radius​

Equation 3

Superellipse angle based on cylindrical coordinates​

Equations based on spherical coordinates​

Equation 1

Diagram for deriving spherical coordinates​

Equation 9

Sphere rho​

Equation 7

Superellipsoid rho​

Equation 8

Superellipsoid rho, featuring expanded exponents​

Equation 6

Sphere x,y,z​

Equation 1

Superellipsoid x,y,z featuring expanded exponents​

Equation 4

Superellipsoid angle Phi based on spherical coordinates​

Equation 5

Superellipse angle Theta based on spherical coordinates​