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On 12.Jun.13.Wed 02:08 (UTC), Nomen Nescio wrote:
> I have seen two different types of cartesian coordinates: > > x = a * cos(theta) > y = b * sin(theta) > and > x' = a * sin(theta) > y' = b * cos(theta) > or > x' = b * cos(theta) > y' = a * sin(theta) > > What is the difference between x,y and x',y', in terms of > names (identities?) and their basic meanings? > I believe x and y are known as the "parametric equation of > ellipse", but what about x' and y'?
I don?t know what the formal name is, but basically x' and y' define the ?parametric equation of the ellipse surface? or, extending it to three axes??X', Y', Z'??by adding a longitude, the ?parametric equation of the ellipsoid surface?.
? is the geographical/geodetic longitude;
a_x, a_y are the equatorial radii of their respective axis: a(?) = ((a*cos(?))^2 + (a*sin(?))^2)^.5;
Where ? is the geographical/geodetic latitude and M is the (conjugate) meridional radius of curvature,