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On Jun 13, 2:08 am, 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,