Because my mathematics is not so good, so I need spend so many years to think
these composite(I just try something I prepare for other concept).

The result yesterday is surprising me.

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Attachments:
Download 'ellipse bump function.png' (805 KB)

Preview of image 'ellipse bump function.png'

Op 26-8-2023 om 11:14 schreef And:
> I suddenly solve an important problem. About how to generate a circle associated
> pattern.
> 
> I need such a pattern for my wood-pattern generator.
> For wood heart, I don't have good function in the past. But these series opens a
> window.

I think you are doing alright with this series of experiments. 
Integrating these functions (or combination of functions) in your 
wood-pattern generator will be interesting. Have you already done this? 
I would be interested to see how that looks.

-- 
Thomas

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"And" <49341109@ntnu.edu.tw> wrote:
> I suddenly solve an important problem. About how to generate a circle associated
> pattern.
>
> I need such a pattern for my wood-pattern generator.
> For wood heart, I don't have good function in the past. But these series opens a
> window.

Hi And,

These are interesting pattern experiments, and I'm looking forward to seeing
what you come up with.

I find it interesting to see the pattern that you have here, as I didn't
understand how the effect was being generated from a circular base pattern.

I coded your pattern into a scene, and for some reason, did not get the same
result.  Perhaps you could post the full code of a working scene.

Also, if you could describe the exact type of pattern that you are looking to
make, it would be easier to help you develop something through a logical
elaboration of a base pattern function.

I started with an atan2 (x, y) function, as that will give you a radial pattern
to start with.

#version 3.8;
global_settings {assumed_gamma 1.0}
default {finish {diffuse 1}}

#include "functions.inc"

camera {
 location <0, 0, -10>
 right     x*image_width/image_height
 up y
 look_at <0, 0, 0>

}

light_source {<0,  1, -50> rgb 1.0}
sky_sphere {pigment {rgb 1}}


#declare C = function {0.5 - sqrt (x*x+y*y) + 0.1}

#declare W1 = function {f_bumps (x/C(x, y, z), y/C(x, y, z), z)}

#declare Freq = 20;
#declare Ang = function {atan2 (x, y)/(tau/Freq)}

#declare W2 = function {f_bumps (Ang (x, y, z), Ang (x, y, z), z)}

#declare Wood1 =
color_map {
 [0.00 srgb <249, 210, 173>/255]
 //[0.25 srgb <249, 210, 173>/255]

 [0.25 srgb <252, 156, 173>/255]
 //[0.50 srgb <252, 156, 173>/255]

 [0.50 srgb <206, 126,  72>/255]
 //[0.75 srgb <206, 126,  72>/255]

 [0.75 srgb <113,  51,  24>/255]
 //[1.00 srgb <113,  51,  24>/255]

}

plane {z, 0 pigment {function {W1(x, y, z)} color_map {Wood1}} }

//plane {z, 0 pigment {function {W2(x, y, z)} color_map {Wood1}} }

Attached is what I get when I try to use the functions posted here.

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Attachments:
Download 'radialfunctions.png' (108 KB)

Preview of image 'radialfunctions.png'

Le 2023-08-27 à 03:27, And a écrit :
> Because my mathematics is not so good, so I need spend so many years to think
> these composite(I just try something I prepare for other concept).
> 
> The result yesterday is surprising me.

That's not surprising for me. That's a formula for an ellipse that you 
got there for f_external_field.

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Thomas de Groot <tho### [at] degrootorg> wrote:
> I think you are doing alright with this series of experiments.
> Integrating these functions (or combination of functions) in your
> wood-pattern generator will be interesting. Have you already done this?
> I would be interested to see how that looks.
>
> --
> Thomas

Thank you... I have not integrated these function with my wood-pattern generator
yet.

In fact, I'm not sure the shape of such patterns in three dimensions. I need
researching and think more.

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"Bald Eagle" <cre### [at] netscapenet> wrote:
>
> Hi And,
>
> These are interesting pattern experiments, and I'm looking forward to seeing
> what you come up with.
>
> I find it interesting to see the pattern that you have here, as I didn't
> understand how the effect was being generated from a circular base pattern.
>
> I coded your pattern into a scene, and for some reason, did not get the same
> result.  Perhaps you could post the full code of a working scene.
>
> Also, if you could describe the exact type of pattern that you are looking to
> make, it would be easier to help you develop something through a logical
> elaboration of a base pattern function.
>
> I started with an atan2 (x, y) function, as that will give you a radial pattern
> to start with.
>
> #version 3.8;
> global_settings {assumed_gamma 1.0}
> default {finish {diffuse 1}}
>
> #include "functions.inc"
>
> camera {
>  location <0, 0, -10>
>  right     x*image_width/image_height
>  up y
>  look_at <0, 0, 0>
>
> }
>
> light_source {<0,  1, -50> rgb 1.0}
> sky_sphere {pigment {rgb 1}}
>
>
> #declare C = function {0.5 - sqrt (x*x+y*y) + 0.1}
>
> #declare W1 = function {f_bumps (x/C(x, y, z), y/C(x, y, z), z)}
>
> #declare Freq = 20;
> #declare Ang = function {atan2 (x, y)/(tau/Freq)}
>
> #declare W2 = function {f_bumps (Ang (x, y, z), Ang (x, y, z), z)}
>
> #declare Wood1 =
> color_map {
>  [0.00 srgb <249, 210, 173>/255]
>  //[0.25 srgb <249, 210, 173>/255]
>
>  [0.25 srgb <252, 156, 173>/255]
>  //[0.50 srgb <252, 156, 173>/255]
>
>  [0.50 srgb <206, 126,  72>/255]
>  //[0.75 srgb <206, 126,  72>/255]
>
>  [0.75 srgb <113,  51,  24>/255]
>  //[1.00 srgb <113,  51,  24>/255]
>
> }
>
> plane {z, 0 pigment {function {W1(x, y, z)} color_map {Wood1}} }
>
> //plane {z, 0 pigment {function {W2(x, y, z)} color_map {Wood1}} }
>
> Attached is what I get when I try to use the functions posted here.



Very beautiful image.
I use
    camera{
    location <0, 0, 10.4>
    look_at <0.0, 0.0, 0.0>
    right -x*image_width/image_height
    sky <0,0,1>
    angle 48
    }

as my camera.

I must read your reply more. But it is mid-night here. See you tomorrow.

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"Bald Eagle" <cre### [at] netscapenet> wrote:
>
>
> I coded your pattern into a scene, and for some reason, did not get the same
> result.  Perhaps you could post the full code of a working scene.
>
I feel it is similar with your pattern and mine. I post another image I rendered
today. The output of mine is "f_freq_control_test".

> Also, if you could describe the exact type of pattern that you are looking to
> make, it would be easier to help you develop something through a logical
> elaboration of a base pattern function.
>

I'm looking for patterns which have random characteristic(like bump), but I need
apply it to associate 0~360 degree(angular), because that is a not completed yet
challenge for me.

Some other topic of different feature is what my concern, too. For example,
proximity pattern which I saw on POV-Ray newsgroup sometimes is another one.

I want to find several methods to combine them (bump, angular bump, streaks,...
with proximity pattern,...) to form a more complex pattern.



--------------------------------------
In fact, I know your W2 function have a seam... I have tried your (W2) method
when I started coding the macro for my wood generator program last year. So I
exchange it by a array value - function that time.

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Attachments:
Download 'bump horizontal slice _diagram1.png' (338 KB)

Preview of image 'bump horizontal slice _diagram1.png'

Alain Martel <kua### [at] videotronca> wrote:

> > Because my mathematics is not so good, so I need spend so many years to think
> > these composite(I just try something I prepare for other concept).
> >
> > The result yesterday is surprising me.
>
> That's not surprising for me. That's a formula for an ellipse that you
> got there for f_external_field.

I know, it is not strange of its appearance. I surly know (x/a)^2 + (y/b)^2 = 1
is the equation of ellipse. I just thinking about these trying of the
combination of it and f_bump. I was not so familiar with these combinations in
the past.

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"And" <49341109@ntnu.edu.tw> wrote:

> I'm looking for patterns which have random characteristic(like bump), but I need
> apply it to associate 0~360 degree(angular), because that is a not completed yet
> challenge for me.

OK, I ran a few more experiments and came up with the attached.

#declare Rad = function {sqrt (x*x+y*y)}
#declare S = 0.5;
#declare W5 = function {Ang (x, y, z) * sin (Rad(x,y,z)*tau/RadFreq)*f_noise3d
(x/S, y/S, z)}

I hope that's more like what you want.

> In fact, I know your W2 function have a seam... I have tried your (W2) method
> when I started coding the macro for my wood generator program last year. So I
> exchange it by a array value - function that time.

Yeah - I've noticed a radial asymmetry and a seam as well - I'll try to think
about a way to not have any discontinuities.

- BE

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Attachments:
Download 'radialfunctions.png' (199 KB)

Preview of image 'radialfunctions.png'

"Bald Eagle" <cre### [at] netscapenet> wrote:
> "And" <49341109@ntnu.edu.tw> wrote:
>
> > I'm looking for patterns which have random characteristic(like bump), but I need
> > apply it to associate 0~360 degree(angular), because that is a not completed yet
> > challenge for me.
>
> OK, I ran a few more experiments and came up with the attached.
>
> #declare Rad = function {sqrt (x*x+y*y)}
> #declare S = 0.5;
> #declare W5 = function {Ang (x, y, z) * sin (Rad(x,y,z)*tau/RadFreq)*f_noise3d
> (x/S, y/S, z)}
>
> I hope that's more like what you want.
>
> > In fact, I know your W2 function have a seam... I have tried your (W2) method
> > when I started coding the macro for my wood generator program last year. So I
> > exchange it by a array value - function that time.
>
> Yeah - I've noticed a radial asymmetry and a seam as well - I'll try to think
> about a way to not have any discontinuities.
>
> - BE

I'm thinking and trying yours. In fact, that is interesting, too. But the seam
is still there. I have known that if you angular direct, (your Ang(x,y) ), you
unavoidable get the seam, or you mirror the pattern, but if so, you will produce
a symmetric pattern, not a randomize pattern.

I have found (just this thread I post) some combination to generate
angular-association or radial-association pattern to naturally avoid the seam,
they just don't have that seam. If you notice? I divide the (x, y) by its vector
length (your Rad(x,y,z) here) to f_bumps input, or just input a function which
used your Rad(x,y,0) to z. It is simple, I just never noticed the method before.

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