Modeling the Pinhole Camera

• A pinhole camera is a box, with photographic paper at one end and a pinhole in the other end.
• Light travels from the outside world and strikes the photographic paper, creating an image.
• from each point, only a single ray of light can travel through the pinhole and strike the image.
• Assume the origin is at the pinhole, with the xy plane the front of the camera.
• 
• Can we model what is going on here?
• If we project the entire system into the xy plane we get the following picture.
• 
• These are similar triangles, so

  	 y' -d            y(-d)       y
  	 - = -   so  y' = ----- = - -----
  	 y   z             z         z/d
  	 

• The same is true for x (x' = -x/(z/d))
• So, given a point in space, we can compute the place it will show up on the final image
• This is called a projection and takes objects from 3-space to 2-space.
• Notice, we can't view everything in-front of the camera.
• 
• We can compute the angle of visibility since again, we have two similar triangles.
• Angle a (which is 1/2 of the angle of viewing) is described by opposite(h/2) and adjacent(d)
• This is the tangent (tan (a) = 1/2 h / d = h/2d)
• so the viewing angle is 2 tan^-1 (h/2d)
• We can do the same thing for the angle for x, if the width of the back of the camera is not the same as the height.
• Notice we have a "viewing pyramid" with the tip at the pinhole
• And we can view objects at infinity.
• Notice, this silly camera takes an upside down picture!

• I have written some c++/openGL code to model this camera.
  • The source code
  • My Makefile