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OK, so it turns out I don't understand cylindrical warp after all.
A few years ago, I introduced cylindrical textures to CoffeeMug in the 
object collection.  Looking back to see how I could adapt the code to 
work with cylinders or cones oriented in different directions, I 
realized that I had never specified any orientation for the coffee mug! 
I went back to RTFM to see how it would be done.
The orientation keyword would seem to do the trick, but the doc says 
that the default is <0, 0, 1>.  My coffee mug is vertically oriented, 
and my code works without changing the default.
I whipped up a test scene to investigate the orientation keyword.  I 
used Parse_String() to make sure that the SDL for each test case exactly 
matched the annotation text.  In these scenes, p_Test is defined as 
pigment { square scale 1/8 }.
True to the docs, orientation z matches the default, not orientation y. 
And somehow, orientation z corresponds to a cylinder with axis y.  I do 
not understand why this is; and more importantly, I have no clue how to 
get a cylindrical warp to match a cylinder of arbitrary orientation. 
How does it work?
Also, I am bemused by the cylinder illustration, which somehow works 
with a vertical cylinder and orientation y, and I am befuddled the 
spiral at the top; but since the example uses a non-default dist_exp 
(whose explanation soars way above my head), I don't know if it's relevant.
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Attachments: 
Download 'test_cylindrical_warp1.jpg' (37 KB)
Download 'test_cylindrical_warp2.jpg' (46 KB)
Download 'test_cylindrical_warp3.jpg' (39 KB)
Download 'test_cylindrical_warp4.jpg' (48 KB)
 
  
Preview of image 'test_cylindrical_warp1.jpg'
   
Preview of image 'test_cylindrical_warp2.jpg'
   
Preview of image 'test_cylindrical_warp3.jpg'
   
Preview of image 'test_cylindrical_warp4.jpg'
   
   
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Cousin Ricky <ric### [at] yahoo com> wrote:
> OK, so it turns out I don't understand cylindrical warp after all.
Heh, I went through this no so long ago.
http://news.povray.org/povray.bugreports/thread/%3Cweb.5c01b8a81374e197765e06870%40news.povray.org%3E/
I can't imagine having to conceive of the warp, code it, and make it work with
all of the rest of what's going on in POV-Ray without breaking.   :O
Maybe the discussion and my code at the end of the thread will help you puzzle a
bit more of this out.  :)
 
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On 2019-05-04 12:49 AM (-4), Cousin Ricky wrote:
> OK, so it turns out I don't understand cylindrical warp after all.
> 
> [snip]
> 
> True to the docs, orientation z matches the default, not orientation y. 
> And somehow, orientation z corresponds to a cylinder with axis y.  I do 
> not understand why this is; and more importantly, I have no clue how to 
> get a cylindrical warp to match a cylinder of arbitrary orientation. How 
> does it work?
> 
> Also, I am bemused by the cylinder illustration, which somehow works 
> with a vertical cylinder and orientation y, and I am befuddled the 
> spiral at the top; but since the example uses a non-default dist_exp 
> (whose explanation soars way above my head), I don't know if it's relevant.
I rendered some permutations of the example in the reference manual, and 
two things are clear.  Most obviously, I should leave dist_exp alone. 
The other is that all orientations work with a vertical cylinder. 
Extrapolating, it looks to me that the cylindrical warp always assumes a 
vertical structure, and that I should start with that assumption in 
defining the texture, then reorient it to match the object.
 
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Attachments: 
Download 'cylindrical_warp_ref.jpg' (478 KB)
 
  
Preview of image 'cylindrical_warp_ref.jpg'
   
   
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