3.6. Ellipses
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## 3.6. Ellipses #

Within pgSphere, ellipses are defined as :

> If the center of any spherical ellipse is the North Pole, the perpendicular projection into the `x`-`y`-plane gives an ellipse as in two-dimensional space.

Use cases are:

- cluster or nebula on the sky sphere where the `height' is lower than the `width'

- to describe a position error

An ellipse always has:

- a major radius `rad_1`

- a minor radius `rad_2`

- a center `center`

- a position angle `pos` (inclination)

Hence, the input syntax is:

    < { rad_1, rad_2 }, center, pos >

### Note

- The radii `rad_1` and `rad_2` have to be less than 90°.

- If `rad_1` is less than `rad_2` , the values will be swapped.

- The position angle `pos` is defined within pgSphere as a counterclockwise rotation around the ellipse center and is zero, if the ellipse is “parallel to the equator”

Example 3.9. Input of a spherical ellipse

An ellipse has a center at 20° longitude and 0° latitude. The minor radius is part of the equator. The major radius is 10°, the minor radius is 5°.

    sql> SELECT sellipse '< { 10d, 5d } , ( 20d, 0d ), 90d >';

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