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I asked similar question on stackoverflow but still no answers.https://stackoverflow.com/questions/25185329/image-rotation-with-the-gyro-data-math I assume it is more math than programming problem.

I have an abstract world view sphere. And I have a camera view 2d coordinate plane P(X,Y) which is a view projection from the center of the sphere C to its bounds . Angular dimensions of the view projection are known (vertical and horizontal field of view - FoV_v, FoV_h). I have a point on that plane - PoI (point of interest) with known 2d coordinates on the plane pX, pY. Let's name its sphere projected counterpart PoI_s.

Now I rotate my 2d plane around the center of the sphere. I have the rotation matrix M or the quaternion Q of this rotation (provided by phone gyro data).

The point PoI_n is the point on the rotated plane Pr where it is crossed by the line from the C to the PoI_s.

The question is how can I found new PoI_n coordinates pXn, pYn in the new plane 2d coordinate system (X,Y)n?

here is the picture

Could you help me please?

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  • $\begingroup$ "Now I rotate my 2d plane around the center of the sphere." So this could be any rotation, possibly carrying the plane to be parallel with the line segment in your picture? Or maybe you mean something other than "around the center of the sphere."? It is pretty ambiguous what you mean: please try to reexpress what you really mean $\endgroup$ – rschwieb Aug 8 '14 at 11:49
  • $\begingroup$ @rschwieb It can be rotation in any direction. Let's say we have a line segment which is perpendicular to the plain from the point C to the plain. So the only condition is that this line segment length will be constant in all occasions (that's why I said that it is the rotation around center of the sphere). And yes, you are right, plane may become parallel to the original projection line and thus pXn and pYn become infinity so there is no mandatory "values". $\endgroup$ – gleb.kudr Aug 8 '14 at 14:08
  • $\begingroup$ OK, thanks for clarification: just making sure I understand what you meant to ask. $\endgroup$ – rschwieb Aug 8 '14 at 14:29

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