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For a sphere with center c and radius R, the vector form equation is (p-c).(p-c)-R^2=0

This can be algebraically manipulated into:

t = (-d.(e-c) +- sqrt((d.(e-c))^2 - (d.d)((e-c).(e-c)-R^2))) / (d.d)

How can I express t for ellipsoids? I know there's an xRadius, yRadius, and a zRadius instead of radius R