Makes an elliptical or circular selection

So this is still elliptical shapes.

Ellipse Draw an ellipse

And the question is, is sigma circular, which would be like this, or elongated, which would be like this or like this?

Ellipse

An ellipse

Ellipse Shape

A cyan ellipse

Cyan Ellipse

The orbit around Sirius is elliptical.

About a billion miles away, here's what happens to Earth's orbit it becomes elliptical instead of circular.

Ellipse Shape

Draws ellipses and circles

Superquadrics

Elliptical Selection

elliptical dab ratio

Let me do an ellipse in another color.

And in fact, what's even the relationship.

Now, another super interesting, and perhaps the most interesting property of an ellipse, is that if you take any point on the an ellipse, and measure the distance from that point to two special points which we, for the sake of this discussion, and not just for the sake of this discussion, for pretty much forever, we will call the focuses, or the foci, of this ellipse.

So that's the origin right there.

Elliptic Gradient

Change ellipse

Close ellipse

And if I tilted it the other way, the ellipse would squeeze the other way.

So here's an example of a contour figure, shown on the right, where the axis are theta zero and theta one.

So, just to make sure you understand what I'm saying.

Select Ellipsoid Model

So, this is very, very tall and skinny ellipses, or these very tall skinny ovals, can form the contours of the cause function J of theta.

Superquadric ellipsoid

Superquadric Ellipsoid

superquadric ellipsoid

This is our x axis and this is our y axis.

This magenta distance minus this light blue distance.

So you go up 2, then you go down 2.

It'll be perfectly round.

Galaxies seem to fit all over this particular family of profiles.

Filled ellipse Draw a filled ellipse

Even in our immediate neighbor Andromeda

There's no way that you could this is the exact center point the ellipse.

Well, that's the same thing as g plus h.

And there are thousands of galaxies in this cluster.

Filled Ellipse

But this is a general sense.

In the last video, we learned a little bit about the circle.

And the way I drew this, we have kind of a short and fat ellipse you can also have kind of a tall and skinny ellipse.