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List:       kde-kimageshop
Subject:    Perspective Ellipse Math for SoK'22
From:       Srirupa Datta <srirupa.sps () gmail ! com>
Date:       2022-03-13 18:16:22
Message-ID: CAN9L-CEFSCNtOoBPOd1Zw8HMOmO_BFU=VC95u7ogO4QsWCW0Lg () mail ! gmail ! com
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I have a quadrilateral, whose 4 corners are known, and an inscribed ellipse
whose touching points with the quadrilateral and also known. I need to find
out the extreme points of the major axis of that ellipse.

*Method 1*
I decided to first find out the equation of the inscribed ellipse. This
<https://drive.google.com/file/d/1mMT9to50lJN1eo2SPQh3jJB_puvb-SBj/view?usp=sharing>
is what I did so far. However this approach has a challenge. I need to
solve a system of linear equations for six variables and this is *probably*
complicated. So I'm not sure if this is at all the right approach.

Also, I got stuck since I expected the solution to be a unique one.

*Method 2*
I have the transformation matrix that maps a unit square to my
quadrilateral. Is there any way I can use transformation mathematics to
solve this problem easily?

Thanks,
Srirupa

[Attachment #3 (text/html)]

<div dir="ltr">I have a quadrilateral, whose 4 corners are known, and an inscribed \
ellipse whose touching points with the quadrilateral and also known. I need to find \
out the extreme points of the major axis of that ellipse.  \
<div><br></div><div><b>Method 1</b></div><div>I decided to first find out the \
equation of the inscribed ellipse. <a \
href="https://drive.google.com/file/d/1mMT9to50lJN1eo2SPQh3jJB_puvb-SBj/view?usp=sharing">This</a> \
is what I did so far. However this approach has a challenge. I need to solve a system \
of linear equations for six variables and this is <b>probably</b> complicated. So \
I&#39;m not sure if this is at all the right approach.  \
<br></div><div><br></div><div>Also, I got stuck since I expected the solution to be a \
unique one.  </div><div><br></div><div><b>Method 2</b></div><div>I have the \
transformation matrix that maps a unit square to my quadrilateral. Is there any way I \
can use transformation mathematics to solve this problem easily?  \
</div><div><br></div><div>Thanks,</div><div>Srirupa</div><div><br></div><div><br></div></div>




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