In the past few years Ingo, Tor Olav and others have played around with 
include files supporting complex numbers for sound and images. Attached 
is an image using a few of 30 plus inbuilt complex functions added to 
the povr fork. Mostly just wrapping the complex functions coming with 
C++11, but sometimes using function names more in line with the existing 
complex includes and POV-Ray's function naming.

In povr, to work with the existing function vm, packing two 32 bit 
floats into a double space as the complex value and all complex function 
code runs at single float accuracy.

The render takes advantage of povr's big jitter and v3.8's ability to 
write png files at a reduced bit depth; I used +fn4 to get the file size 
down to something reasonable. Given the detail the image doesn't 
compress well.

Bill P.

//---
...
#include "functions.inc"
#include "cfunctions.inc"
#declare Fn00 = function { f_hash(y,Seed00,0.0005,0) }
#declare Pigm00 = pigment {
     function {
         Fn00(
             cf_real(cf_pow(cf_cmplx(abs(x),y),cf_cmplx(4.4,0))),
             cf_imag(cf_pow(cf_cmplx(abs(x),y),cf_cmplx(4.4,0))),
             z)
     }
     color_map {
     ...
     }
...
//---

cf_abs, cf_acos, cf_acosh, cf_add, cf_asin, cf_asinh, cf_atan,
cf_atanh, cf_cmplx, cf_conj, cf_cos, cf_cosh, cf_div, cf_exp,
cf_imag, cf_inv, cf_ln, cf_log, cf_mul, cf_neg, cf_norm, cf_phase,
cf_polar, cf_pow, cf_proj, cf_real, cf_sin, cf_sinh, cf_sqr,
cf_sqrt, cf_sub, cf_tan, cf_tanh

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Attachments:
Download 'kaboom.png' (230 KB)

Preview of image 'kaboom.png'

I like the image itself, it's a very artistic-looking render. Like a painting.

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On 3/9/23 20:51, Kenneth wrote:
> I like the image itself, it's a very artistic-looking render. Like a painting.
> 

Thanks. :-)

I'll attach another I liked while playing. Same set up with complex 
functions, but much lower power exponents. Plus adding in some spiral 
action in the middle.

Another bit I stumbled across working with cf_pow() 'warping' is the 
effective change in scaling from the origin outward makes it pretty easy 
to set up images which change from a near constant color away from the 
origin to something where the f_hash()-ing is clear.

In other words, when the changes in region due the f_hash(), and/or 
higher cf_pow exponents, are happening at >>1 per pixel we end up with 
kind of an aggregate color. As we move to the origin things spread out 
and and we get a fade-in effect. FWIW, I guess, but neat. Hints at a 
possible general technique with on top of f_hash() for fading in or out 
of near constant colors.

Bill P.

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Attachments:
Download 'kaboomkeep3.jpg' (498 KB)

Preview of image 'kaboomkeep3.jpg'

Op 10-3-2023 om 11:08 schreef William F Pokorny:
> On 3/9/23 20:51, Kenneth wrote:
>> I like the image itself, it's a very artistic-looking render. Like a 
>> painting.
>>
> 
> Thanks. :-)
> 
> I'll attach another I liked while playing. Same set up with complex 
> functions, but much lower power exponents. Plus adding in some spiral 
> action in the middle.
> 
> Another bit I stumbled across working with cf_pow() 'warping' is the 
> effective change in scaling from the origin outward makes it pretty easy 
> to set up images which change from a near constant color away from the 
> origin to something where the f_hash()-ing is clear.
> 
> In other words, when the changes in region due the f_hash(), and/or 
> higher cf_pow exponents, are happening at >>1 per pixel we end up with 
> kind of an aggregate color. As we move to the origin things spread out 
> and and we get a fade-in effect. FWIW, I guess, but neat. Hints at a 
> possible general technique with on top of f_hash() for fading in or out 
> of near constant colors.
> 
> Bill P.
> 

Ooh! This one is nice! Going to download it: could be useful for 
something ;-)

-- 
Thomas

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On 3/10/23 07:11, Thomas de Groot wrote:
> Ooh! This one is nice! Going to download it: could be useful for 
> something 😉

:-) How about a POV-Ray, user ink blot test image?

"That Looks like an ink blot test," is what I thought on getting the 
result - and I'm never letting you all know I see in there! ;-)

Here again a complex function 'warp' acting on a small portion of a 
photograph; where I also used those undocumented / hidden, image_map, 
repeat and offset options.

Bill P.

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Attachments:
Download 'povrayinkblottest.jpg' (409 KB)

Preview of image 'povrayinkblottest.jpg'

Op 11-3-2023 om 10:17 schreef William F Pokorny:
> On 3/10/23 07:11, Thomas de Groot wrote:
>> Ooh! This one is nice! Going to download it: could be useful for 
>> something 😉
> 
> :-) How about a POV-Ray, user ink blot test image?
> 
> "That Looks like an ink blot test," is what I thought on getting the 
> result - and I'm never letting you all know I see in there! ;-)
> 
LOL! I wont either! ;-)

> Here again a complex function 'warp' acting on a small portion of a 
> photograph; where I also used those undocumented / hidden, image_map, 
> repeat and offset options.
> 
> 
Fascinating stuff indeed.

-- 
Thomas

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William F Pokorny <ano### [at] anonymousorg> wrote:
>
> :-) How about a POV-Ray, user ink blot test image?
>

That is really interesting and fabulous! I can imagine all sorts of
different-looking and visually unexpected results from using this technique.

One possible use would be for texturing the walls in a room-- like wall paper.
Or for creating designs for floor rugs and carpets.

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On 10/03/2023 00:39, William F Pokorny wrote:
> In the past few years Ingo, Tor Olav and others have played around with 
> include files supporting complex numbers for sound and images. Attached 
> is an image using a few of 30 plus inbuilt complex functions added to 
> the povr fork. Mostly just wrapping the complex functions coming with 
> C++11, but sometimes using function names more in line with the existing 
> complex includes and POV-Ray's function naming.
> 
> In povr, to work with the existing function vm, packing two 32 bit 
> floats into a double space as the complex value and all complex function 
> code runs at single float accuracy.
> 
> 

Sorry to re-open this old discussion. I didn't know this pov4 group exist :(


Anyway, i too have worked a lot in the world of complex numbers. I
started to write a macro library that implements complex functions using
povray "function".

And so: is "cfunctions.inc" just an encapsulation of C functions ?
Does v4 include a new data type like c = <re,im> with the possibility to
access c.re and c.im ?

I'm attaching my "complex_functions.inc" just in case ... I continue to
develop it or I wait for v4 ?

last thing : where can I find "cfunctions.inc" ?






-- 
Kurtz le pirate
Compagnie de la Banquise

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Attachments:
Download 'complex_functions.inc.txt' (34 KB)

hi,

kurtz le pirate <kur### [at] gmailcom> wrote:
> ...
> last thing : where can I find "cfunctions.inc" ?

installs as part of 'povr' branch (published in p.b.programming)


regards, jr.

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On 28/04/2023 16:10, jr wrote:
> hi,
> 
> kurtz le pirate <kur### [at] gmailcom> wrote:
>> ...
>> last thing : where can I find "cfunctions.inc" ?
> 
> installs as part of 'povr' branch (published in p.b.programming)
> 
> 
> regards, jr.
> 

Find. Thank jr

But as I suspected, the functions are just calls to internal functions.
so I will continue my work






-- 
Kurtz le pirate
Compagnie de la Banquise

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