[R] 3D pie

[Stuart Leask]

> 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.

Unless you cut it into quarters, in which case you have that rare situation 
where pie by two equals pie by four!!!!...
... sorry ....

Stuart



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