Re[2]: [cgmo-webcgm] Drawing model (take 2)

[Benoit Bezaire <benoit@itedo.com>]

BTW, I forgot to mention (again), that the examples are using a 'argb'
notation instead of 'rgba'.

Any way, it doesn't seem to be the source of your question. As I said
in this version of the wording "all color values use premultiplied
alpha".

So fully transparent red is not (0,1,0,0) it is (0,0,0,0). That should
work.

-- 
Regards,
 Benoit   mailto:benoit@itedo.com

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Thursday, April 20, 2006, 10:36:40 AM, you wrote:

> [...1 of 2...]

> I'll write more about Benoit's questions in next message.  But for now, a
> technical nit...

> I wonder if there's a bug in the equations?

>>[...]
>>WebCGM uses a painters model of rendering. Colors are applied in
>>successive operations to the output device. When an area overlaps a
>>previously colored area the new color partially or completely obscures
>>the old. When the color is not completely opaque the result on the
>>output device is defined by the following (mathematical) rules for
>>compositing (all color values use premultiplied alpha):
>>
>>Pr, Pg, Pb    - Primitive color value
>>Pa            - Primitive alpha value
>>Cr, Cg, Cb    - Canvas color value (before blending)
>>Ca            - Canvas alpha value (before blending)
>>Cr', Cg', Cb' - Canvas color value (after blending)
>>Ca'           - Canvas alpha value (after blending)
>>Ca' = 1 - (1 - Pa) * (1 - Ca)

> Are the following equations correct?  If primitive is fully transparent
> red, for example (0, 1, 0, 0), then it should not affect the canvas, 
> right?  I.e., intuitively Cr'=Cr.  But the equation gives,

> Cr' = Cr + Pr

> Similarly, the equation gives intuitively wrong result for Pa=1 (fully
> opaque).  So I think the equation actually needs to be:

> Cr' = (1 - Pa)*Cr + Pa*Pr

> Thoughts?

> -Lofton.

>>Cr' = (1 - Pa) * Cr + Pr
>>Cg' = (1 - Pa) * Cg + Pg
>>Cb' = (1 - Pa) * Cb + Pb
>>
>>Example #1:
>>Primitive is semi transparent red: (Pa, Pr, Pg, Pb) = (0.5,0.5,0,0)
>>Canvas is opaque black: (Ca, Cr, Cg, Cb) = (1,0,0,0)
>>Ca' = 1 - (1 - 0.5) * (1 - 1) = 1
>>Cr' = (1 - 0.5) * 0 + 0.5 = 0.5
>>Cg' = (1 - 0.5) * 0 + 0 = 0
>>Cb' = (1 - 0.5) * 0 + 0 = 0
>>The result is an opaque dark red (1,0.5,0,0).
>>
>>Example #2:
>>Primitive is opaque red: (Pa, Pr, Pg, Pb) = (1,1,0,0)
>>Canvas is semi transparent black: (Ca, Cr, Cg, Cb) = (0.5,0,0,0)
>>Ca' = 1 - (1 - 1) * (1 - 0.5) = 1
>>Cr' = (1 - 1) * 0 + 1 = 1
>>Cg' = (1 - 1) * 0 + 0 = 0
>>Cb' = (1 - 1) * 0 + 0 = 0
>>The result is an opaque red (1,1,0,0).
>>
>>Example #3:
>>Primitive is semi transparent red: (Pa, Pr, Pg, Pb) = (0.5,0.5,0,0)
>>Canvas is semi transparent black: (Ca, Cr, Cg, Cb) = (0.5,0,0,0)
>>Ca' = 1 - (1 - 0.5) * (1 - 0.5) = 0.75
>>Cr' = (1 - 0.5) * 0 + 0.5 = 0.5
>>Cg' = (1 - 0.5) * 0 + 0 = 0
>>Cb' = (1 - 0.5) * 0 + 0 = 0
>>The result is a transparent dark red (0.75,0.5,0,0).