Projecting a thick spherical cap onto a plane

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Consider a spherical cap of opening angle $alpha$, with some finite thickness $t$ and uniform value. I would like to project the cap onto a plane along the axis of symmetry and the auto-correlate the result. Does a closed-form expression for either the projection or the auto-correlation exist? My attempts at searching have turned up nothing except related problems in optics.




geometry circle spheres projection




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    Consider a spherical cap of opening angle $alpha$, with some finite thickness $t$ and uniform value. I would like to project the cap onto a plane along the axis of symmetry and the auto-correlate the result. Does a closed-form expression for either the projection or the auto-correlation exist? My attempts at searching have turned up nothing except related problems in optics.




    geometry circle spheres projection




    share|cite|improve this question





















      up vote
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      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Consider a spherical cap of opening angle $alpha$, with some finite thickness $t$ and uniform value. I would like to project the cap onto a plane along the axis of symmetry and the auto-correlate the result. Does a closed-form expression for either the projection or the auto-correlation exist? My attempts at searching have turned up nothing except related problems in optics.




      geometry circle spheres projection




      share|cite|improve this question











      Consider a spherical cap of opening angle $alpha$, with some finite thickness $t$ and uniform value. I would like to project the cap onto a plane along the axis of symmetry and the auto-correlate the result. Does a closed-form expression for either the projection or the auto-correlation exist? My attempts at searching have turned up nothing except related problems in optics.





      geometry circle spheres projection





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 2 at 15:44









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