What does a Log Gradient look like. Maybe if you post an example on the web and tell us the link, some folks can chime in with how to accomplish it.
Peace,
Tony
I was wondering if he meant a sine wave?
Could mean anything I suppose – I used Log curves in math and science to create a linear curve for calibration of equipment/standards, etc. That is to say, that my experience was that using log was a way to create something linear. So, I’m just as stumped.
A log gradient is a log gradient and not a sine wave.
For example in x-direction x=0 to x=1:
luminance =Ln (1+x) / Ln(2)
This delivers luminance=0 for x=0 and luminance=1 for x=1 and between we have a function which looks like
luminance = x^0.5 or so.
"Ln" is the logarithmus naturalis (based on the Euler number e).
Sorry for bothering the folks with mathematics – it cannot be done by PhS accurately.
Best regards –Gernot Hoffmann
Thanks for the lesson Gernot 🙂
But what does he want to do with such a gradient? Is he trying to achieve, for instance, a black -> white gradient in a log gradient fashion?
Yes, as Gernot mentioned, a log function is very different than a linear one. A linear function–or gradient for this matter–is a straight line. So the gradient transistions from say black to white evenly. However a log gradient would go from black to white much differently. I’ll try to illustrate…forgive the crude manner…
Let’s say you want a gradient from black to white going from A to B spatially. Now let’s say that the colors from black to white are represented by the numbers 1-10, 1 being black and 10 being white.
A linear gradient would look somewhat like the following…
A………………………………………..B
1…2…3…4…5…6…7…8…9…10
Giving a nice even transition from black to white. However a log gradient would look somewhat like the following:
A…………………………………………B
123.4..5…6….7…..8……9…….10
Where the rate of transistion is much faster at point A and the rate of transitin gets slower as you approach point B.
Hope this helps explain…
* *EDIT: My A B thing didn’t work with spaces so I put periods in there to keep the correct spacing. Sorry
Grass Hopper,
I regret if my post should sound like a "lesson".
Occasionally some questions are written in mathematical terms. Then I feel obliged to respond similarly.
Best regards –Gernot Hoffmann
Gradients made with the gradient tool are not exactly linear but are a bit more gradual at both ends.
Chris Cox "SQUARE gradiant tool- where is it??????" 1/25/03 4:24pm </cgi-bin/webx?13/21>
However they are not exactly logarithmic either. I would think applying a curve would be the answer, though the exact curve is beyond me.
John – UNLESS you change the smoothness to zero, then they are linear.
Gernot,
I regret if my post should sound like a "lesson". Please, no need to apologize! I really do learn some things from your mathematics, although I will confess many times it is over my head! 😉 I am a firm believer in the notion that there is *always* more to learn 🙂 I am also pleased that you share your knowledge with us.
kind regards,
grasshopper
Thanks, then I can continue:
Rob,
a gradient from black to white is modified by Curves,
bottom left black, top right white, by a banana upwards
deformation:
x……..255*x……….Ln(x+1)/Ln(2)……..255*Ln(x+1)/Ln( 2)
0.0……….0………….0.0……………………….0
0.25….. 64………….0.322………………….82
0.50….128………….0.585………………..149
0.75….191………….0.807………………..206
1.0……255………….1.0……………………255
The value in column 2 is the input, the value in column 4 is the output for the modified curve.
One should be aware that the indicated values for the
straight line curve (without modification) are already Gamma- pre-distorted: in the middle of the gradient pattern we find c = 255*(0.5)^(1/2.2) = 255*0.5^0.4545 = 186 instead of 127.5 .
It would me more accurate to calculate the new values in this order (log in linear light space):
Given input x
y=(x/255)^2.2
z=Ln(y+1)/Ln(2)
output=255*z^(0.4545)
Best regards –Gernot Hoffmann
Out of curiosity, I opened up my old Power Basic and plugged in Gernot’s formulas:
open logtest.amp for output as #1
for x=0 to 255
y=(x/255)^2.2
z=log(y+1)/log(2)
o=int(255*z^(0.4545))
print #1,chr$(o);
next i
close #1
The resulting file, logtest.amp, was just a tad away from being linear. Not sure if thats the way its suppossed to be, or if I messed something up.
See for yourself: logtest.amp <
http://www.playfiddlelearn.com/stuff/logtest.amp> – right click save as
It’s one channel, so either in an alpha or in a greyscale.
How about this?
In 0 / Out 0
In 214 / Out 177
In 232 / Out 197
In 280 / Out 236
In 255 / Out 255
Stroker,
So is using the AMP file the only way to get this to work? From the replies I’ve gotten, I assume there is no easy tool/setting already in photoshop that allows this type of gradient. I’m interested in your amp file method though and I think that i’ll give it a try. Hope it works.
Any other suggestions/hints are still VERY welcome! Thanks.
BTW..I’m actually kind of surprised that this type of gradient isn’t a more common thing…
Rob – most users need visually designed gradients or simple linear gradients.
We haven’t had any demand for logarithmic gradients except from programmers who already knew how to generate them on their own….
