To make the NY3D display work, we need to interleave the left and right images on the display and also to create a corresponding set of opaque/clear stripes on the optical shutter. But how do we figure out where the stripes should go? The key is to keep drawing crossed lines: 
The two eye positions:
L = (L_{x},L_{y}) Shutter location: y=1 y=0 
Also, try clicking between the two black lines.

Fractional distance of shutter from display screen to p:
p_{y}^{1} = (1  0) / (p_{y}  0)Location on shutter between (x,0) and p:
f_{p}(x) = p_{x} p_{y}^{1} + x (1  p_{y}^{1})Location on display screen between (x,1) and p :
f_{p}^{1}(x) = (x  p_{x} p_{y}^{1})_{/}(1  p_{y}^{1})
Line 1:
(x_{n} ,0)
>
(x_{n},1)
>
R
Line 2:
(x_{n+1},0)
<
(x_{n},1)
<
L
x_{n+1} = f_{L}^{1}(f_{R}(x_{n}))which expands out to:
(R_{x} R_{y}^{1} + x (1R_{y}^{1})  L_{x} L_{y}^{1})_{/}(1L_{y}^{1})Express this as a linear equation in x_{n}:
x_{n+1} = A x_{n} + B
A = x (1  R_{y}^{1})_{/}(1  L_{y}^{1})Sequence of display stripe locations:
B = (R_{x} R_{y}^{1}  L_{x} L_{y}^{1})_{/}(1  L_{y}^{1})
x_{0} = 0
x_{1} = B
x_{2} = AB + B
x_{3} = A^{2}B + AB + B
:
:
x_{n} = B (A^{n1} + ... + A + 1)
Assume the two eye positions are: p = (p_{x},p_{y}) and q = (q_{x},q_{y}), that the display screen is on the line y=0, and that the shutter is on the line y=1.
Given a location (x,0) on the display screen, we find the lineofsight location f_{p}(x) on the shutter that lies between display screen location (x,0) and eye position p by linear interpolation:
f_{p}(x) = p_{x} p_{y}^{1} + x (1  p_{y}^{1})Given a location (x,1) on the shutter, we can find the corresponding lineofsight location on the display screen by inverting the above equation:
f_{p}^{1}(x) = (x  p_{x} p_{y}^{1})_{/}(1  p_{y}^{1})Therefore, given a location x_{n} on the display screen that is visible through a clear stripe on the shutter from both p and q, the next such location is given first by finding the location on the shutter f_{p}(x_{n}) in the lineofsight from p, and then finding the corresponding location on the display screen which is in the lineofsight from q:
x_{n+1} = f_{q}^{1}(f_{p}(x_{n}))which expands out to:
(p_{x} p_{y}^{1} + x (1  p_{y}^{1})  q_{x} q_{y}^{1})_{/}(1  q_{y}^{1})This can be expressed as a linear equation x_{n+1} = A x_{n} + B, where:
A = x (1  p_{y}^{1})_{/}(1  q_{y}^{1})The nth location in the sequence of stripe locations on the display screen can be calculated by iterating x_{n+1} = A x_{n} + B:
B = (p_{x} p_{y}^{1}  q_{x} q_{y}^{1})_{/}(1  q_{y}^{1})
x_{0} = 0 x_{1} = B x_{2} = AB + B x_{3} = A^{2}B + AB + Bx_{n} = B (A^{n1} + ... + A + 1)