[R] 3D pie

[(Ted Harding)]

On 19-Apr-06 Peter Ehlers wrote:
> This discussion of 3-d pie charts comes at an opportune time. I have
> just formulated a new theory of graphical information transfer which
> is particularly simple in the case of 3-d pie charts.
> 
> Let theta denote the angle between the normal to the pie cylinder and
> the pie-eyed line (connecting eye and centre of pie). Then the
> information transmitted from pie to viewer is
> 
>    K * (pi/2 - theta)^3
> 
> for theta in [0, pi/2]. The normalizing constant may be written in
> the obvious manner as
> 
>    K = 8 * I_0 / pi^3.
> 
> I conjecture that I_0 is not large, but I'm still waiting to hear
> from Microsoft regarding my application for funding to allow me to
> conduct extensive testing.

I think I can confirm your conjecture. With theta = 0, you have in
effect a 2-D pie, and then, according to my calculations, if you take

  I_0 = 3.14159265358979...

the information you get is 1 pie.

Ted.

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Date: 20-Apr-06                                       Time: 09:10:01
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