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An ellipse has 2D geometry and an ellipsoid has 3D geometry. An ellipse represents the intersection of a plane surface and an ellipsoid. Both have shape (eccentricity) and size (axis). A standard ellipsoid has a circular midsection. Assume the general equation of a doubly rotated ellipsoid may be written as; s2/a2 + t2/b2 + u2/c2 = 1 Where; a,b,c represent eliptic properties (shape and size) s,t,u represent spatial planes; s = (x-h)CACB + (y-j)SACB + (z-k)SB t = (y-j)CA - (x-h)SAu = (z-k)CB - (y-j)SASB - (x-h)CASB x,y,z are Cartesian co-ordinatesh,j,k are Cartesian displacementsA,B are angles of rotation;CA = Cos(A) and SA = Sin(A)CB = Cos(B) and SB = Sin(B) A radial dimension (r) is; r2 = s2 + t2 + u2 = x2 + y2 + z2 The conditions for a standard ellipsoid are; a = b , or a = c , or b = c Are the planes properly defined?Does the foregoing represent a doubly rotated ellipsoid?