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Edit : This question is better to be ignored until the following related question will be discussed enough.

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I know "almost identical " is not mathematics. But if you have good mathematical words , please answer to my question. I learned (here StackExchange)I can compute an ellipse arc for my 2 end points and tangents at them. But I also learned there are possibly many other ellipse arcs of the condition. Then let me ask you whether these ellipse arcs are almost identical or not?

Thank you in advance.

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You should wait till we discuss everything through instead of saying that "we are all saying right things and none of us is wrong". We're humans, we're not perfect, we might say wrong things. I don't think this question deserves to be answered right away. –  Patrick Da Silva Feb 16 '12 at 7:37
Yes, I wait. But I just wanted to make sure that your algorithm is suitable for my particular purpose . –  seven_swodniw Feb 16 '12 at 7:48
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My algorithm described in the previous answer characterizes an ellipse by its center two non-parallel tangents at two generic points on the boundary of the ellipse (generic points means the underlying vectors are linearly independent relatively to the center of the ellipse). Given those, "almost identical" means "they are the same set of points on the plane". If your tangents are parallel, you lose unicity ; the second parallel only gives information you already had with the first one, hence you need "new" information. That is because if you have a point on an ellipse and you know the tangent there, then the point at the opposite of the ellipse (going through the center with a straight line) has the exact same tangent. If you don't specify the center you will end up with different ellipses depending on where you choose to put this center.

Hope that helps,

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