# Ellipse's Visual Fidelity after Rotation, Transportation, Scaling

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Hi, guys, My question is simple. One x,y axis based ellipse is given. After rotation, transportation and scaling to this ellipse, the shape is still ellipse? If it's true, how to prove it? Thanks, Ed.

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By default equation of a circle x^2+y^2 = a^2
when you apply two constants then the circle will appear an ellipse.
when you change the position of a whole geometry by applying a scale factor then the shape will change and its no more the original shape.By removing the scale factor go will gain the original shape hence there is no requirement of proof.

For example scale = 2.5 times original size.

reverse this and you get an original shape.
original size/2.5 = scale

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Quote:
 Original post by coolhelixAfter rotation, transportation and scaling to this ellipse, the shape is still ellipse?
Yes.

Quote:
 If it's true, how to prove it?

Using the definition of an ellipse. Show that, given that a set of points all obey the equation of an ellipse, the transformed set of points also obey such an equation (with different constants). It's not a simple proof, but it is a straightforward one.

Quote:
 Original post by SaurabhTornewhen you change the position of a whole geometry by applying a scale factor then the shape will change and its no more the original shape.By removing the scale factor go will gain the original shape hence there is no requirement of proof.
lol wut?

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Scaling in XYZ direction would not be the same. Matrix would be

| 1.5f, 0, 0 |
| 0, 2.5f, 0 |
| 0, 0, 3.0f |

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