Re: [Bodington-developers] CSS Processing

[Jon M. <jo...@te...>]

I must bow to your superior mathologicity.

Many thanks for taking on this work package, good luck.....

Jon

Sean Mehan wrote:

> Yes, all fine Jon, BUT what about compliance with the critical and  
> well known Hausdorff's Metric Top, you know:
>
> Let (S,d) be a metric space, and let X be the collection of all  
> nonempty bounded closed subsets of S. Let f:S * X -> R+ be defined by  
> f(s,B) = inf _(b in B) d(s,b), and let g: X * X -> R+ be given by g 
> (A,B) = sup_(a in A) f(a,B), and let delta(A,B) = max {g(A,B),g 
> (B,A)}. You must concern yourself with (X, delta)! Your method  
> clearly fails here! Pah!
>
> And for anyone wanting to quibble with my counterexample, yes, I  
> know, but I couldn't write the vector cross product adequately in  
> this crap test format, so had to resort to *.
>
> -s
>
>
> On 6 Apr 2006, at 18:59, Jon Maber wrote:
>
>> Nearly all user colour preference work will operate in Hue- 
>> Saturation-Value space, not Red-Green-Blue space. However, the  
>> standard Java HSV colour space (which Bodington currently uses) is  
>> not very good so I've devised a better method. (Probably reinvented  
>> but it only took a couple of days work.) The standard HSV space is  
>> cylindrical where H is the perpendicular distance from the axis to  
>> the colour point, H is the angle of that line from the red plane  and 
>> V is the distance up the cylinder.  All of the bottom face is  black. 
>> (which means that if V=0 then the colour is black regardless  of the 
>> values of H or S) However, the top face has white only at  the center 
>> and has bright rainbow colours around the edge.  This  means that if 
>> V is non-zero, V and H are kept constant and S is  varied then not 
>> only does the perceived saturation change but the  brightness does 
>> too. The method used to map the cube rgb space onto  the cylinder is 
>> also dodgy since for certain values of H changing S  distorts the 
>> perceived hue.
>>
>> My method also maps to a cylinder but the top face of the cylinder  
>> is completely white.  This means that V==100% always produces white  
>> no matter what the value of H or S. It also means that if H and V  
>> are kept constant and S is varied, the perceived brightness and hue  
>> keep constant. This is acheived by two rotations of the rgb cube so  
>> that the white to black vector lines up with the z axis. Then the  
>> shape is distorted so that vectors which run from the z axis to the  
>> cube surface and which lie parallel to the x,y plane are stretched  
>> uniformly to unit length.  The resulting cylinder is squashed down  
>> the z axis to unit length.
>
>
>