Re: [Bodington-developers] CSS Processing

[Sean M. <se...@sm...>]

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.