Which of those is correct for your purpose depends on what that purpose is. If you parametrise the circumference of such a circle #C_n# around point #p_n#, with starting point #q_n# on the circumference, by function #f_n:\to\mathbb=0.2# then that shape will be roughly elliptical with the major axis pointing towards the North Pole, so when viewed from the chosen vantage point it could well look roughly circular as shown. Why are you using a Jacobian? It looks like what you are aiming to do is plot the y and z coordinates of points in three circles of radius 0.2, centred at each of the the three points.
Then the ellipses of transformation are obtained by multiplying J by a vector of coordinate ( dθ, dΦ) that satisfies the equation of a circle of a radius smaller than 1 (0.2 in this example) so I can see the footprints in all direction. \sin(\theta)\sin(\phi) & \cos(\theta)\sin(\phi) & \sin(\theta)\cos(\phi) \\Īssociated with the following transformation from spherical to cartesian (with a unit radius): I used this formula for the Jacobian of the transformation from Spherical to Cartesian coordinates for the unit-sphere: The original image is taken from a viewpoint in the X-axis, using the present coordinate space and X-, Y-,Z- axis of the left-hand side figure. While I expected the shape of the blue and red ellipse as they are here, I do not understand why the green one is not the 90-degrees-rotated red circle. On the right-hand side, we have my ellipses of transformation, which I interpret as the footprint onto the input space (the original image coordinates ) from small angle differences in the input space.
It shows (left) the spherical grid with a unit-sphere, with the three points p1, p2, p3 that I consider.
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