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I have a flat elliptical plane and I'm trying to figure out how to represent it based on its direction. So I basically need to calculate its pitch, yaw, and roll.

I have a camera at $C$, and a point at $P$. $P$ has a normal (or direction) of $N$. $N$ is also = $P$'s local Up vector.

I believe that Roll is the hard value to calculate here and I'm not sure I have enough information—if not, what additional information would I need and for what equation? Thanks.

EDIT:

I'm talking video game programming here, so objects can have any kind of transformation or rotation. The normal is the vector direction at which the plane is facing. The plane's 'Up' value is the direction Up would be if the plane had no transformation or rotation. IE. if this plane had no rotation on it, it would be facing directly upwards $(0, 1, 0)$. The Pitch Yaw and Roll being the rotation in each individual axis that would achieve the objects currently location. I believe there may be a problem finding roll because $N = P.Up$ but thought there may be a solution along the lines of the dot product of the cross of $N$ before and after transformation?

Description of normal Description of pitch yaw roll
(source: fiu.edu)

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    $\begingroup$ What is this $N$? What is a local Up vector? While I'm at it, how do you define pitch, yaw, and roll? Can you draw a picture? $\endgroup$ – dfeuer Feb 1 '14 at 1:02
  • $\begingroup$ Updated my question $\endgroup$ – jProg2015 Feb 1 '14 at 1:27

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