POV-Ray : Newsgroups : povray.object-collection : 3D Loop Server Time: 16 Dec 2018 22:05:00 GMT
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From: Lars Rohwedder
Subject: 3D Loop
Date: 15 May 2015 13:44:24
Message: <5555f838@news.povray.org>
Inspired by this object:

http://www.shutterstock.com/pic-94505617/stock-photo--d-infinity-shape-d-render-illustration.html

I created a simple Povray union. The resuld you can see attached.

I would like to change the whole object into a single "sphere_sweep" and
I'd like to have a closed formula that calculates the positions of all
spheres at once, with "smooth" transitions between the 3 3/4 torii, so
no cylindrical parts between them.

I tried 3 polynomials (one for each of the X, Y, Z coordinates) but it
was harder than it looked to me. :-(

Any ideas, suggestions?


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Attachments:
Download 'loop3d.pov.txt' (2 KB)
Download 'loo-opt.gif' (1936 KB)

Preview of image 'loo-opt.gif'
loo-opt.gif


 

From: Le Forgeron
Subject: Re: 3D Loop
Date: 15 May 2015 14:35:01
Message: <55560415@news.povray.org>
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA256

Le 15/05/2015 15:44, Lars Rohwedder a écrit :
> Inspired by this object:
> 
> http://www.shutterstock.com/pic-94505617/stock-photo--d-infinity-shape
- -d-render-illustration.html
>
>  I created a simple Povray union. The resuld you can see attached.
> 
> I would like to change the whole object into a single
> "sphere_sweep" and I'd like to have a closed formula that
> calculates the positions of all spheres at once, with "smooth"
> transitions between the 3 3/4 torii, so no cylindrical parts
> between them.
> 
> I tried 3 polynomials (one for each of the X, Y, Z coordinates) but
> it was harder than it looked to me. :-(
> 
> Any ideas, suggestions?
> 

search "Trefoil knot"

Beware, it's chiral, so there is a left and a right version.
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Version: GnuPG v2

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SPLkgZe4dceeciBhjh5k6Q3NawdubtH/gNaFiC9mjj7fho+Vf1Aow6E7naCUR+ab
r4SIgvFvufA5zgf8l/0Lek4kWpcckL5P6PoMaF6dwXxCLchMGxX5WMwpgQtTfyWV
EsED8/AUM+2Up4agmR0=
=BCOo
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From: Lars Rohwedder
Subject: Re: 3D Loop
Date: 15 May 2015 15:35:04
Message: <55561228$1@news.povray.org>
> search "Trefoil knot"

Nice one. It is a bit "flattened" compared to my object and the 3 "ears"
are not perpendicular to each other.

But I think I can use if for my ideas :-)

Thank you!

			Lars R.


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From: LanuHum
Subject: Re: 3D Loop
Date: 15 May 2015 16:40:00
Message: <web.55561fe6d258875a7a3e03fe0@news.povray.org>
Lars Rohwedder <rok### [at] gmxde> wrote:
> Inspired by this object:
>
>
http://www.shutterstock.com/pic-94505617/stock-photo--d-infinity-shape-d-render-illustration.html
>

>
> I would like to change the whole object into a single "sphere_sweep" and
> I'd like to have a closed formula that calculates the positions of all
> spheres at once, with "smooth" transitions between the 3 3/4 torii, so
> no cylindrical parts between them.
>

>
> Any ideas, suggestions?

Python in the Blender creates it so:

def Torus_Knot(self):
    p = self.torus_p
    q = self.torus_q
    w = self.torus_w
    res = self.torus_res
    h = self.torus_h
    u = self.torus_u
    v = self.torus_v
    rounds = self.torus_rounds

    newPoints = []
    angle = 2*rounds
    step = angle/(res-1)
    scale = h
    height = w

    for i in range(res-1):
        t = ( i*step*pi)

        x = (2 * scale + cos((q*t)/p*v)) * cos(t * u)
        y = (2 * scale + cos((q*t)/p*v)) * sin(t * u)
        z = sin(q*t/p) * height

        newPoints.extend([x,y,z,1])

    return newPoints

From the received verts cubic_spline is created


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From: LanuHum
Subject: Re: 3D Loop
Date: 15 May 2015 18:20:00
Message: <web.5556388bd258875a7a3e03fe0@news.povray.org>
Example:

// POV-Ray scene. It is created in the Blender-2.74

#version 3.7;

global_settings {
}
background {rgbt<0.05, 0.05, 0.05, 0>}

#declare Default_texture = pigment {rgb 0.8}

#declare data_Torus_Knot_orig =
union {
    sphere_sweep { cubic_spline 102,
        <2.958,-0.3775,-0.1893>,0.343,
        <3,0,0>,0.343,
        <2.958,0.3775,0.1893>,0.343,
        <2.835,0.7355,0.3717>,0.343,
        <2.638,1.056,0.5406>,0.343,
        <2.38,1.324,0.6901>,0.343,
        <2.078,1.53,0.8146>,0.343,
        <1.748,1.667,0.9096>,0.343,
        <1.41,1.735,0.9718>,0.343,
        <1.08,1.74,0.9989>,0.343,
        <0.7717,1.69,0.9898>,0.343,
        <0.4967,1.597,0.945>,0.343,
        <0.2605,1.477,0.866>,0.343,
        <0.064,1.344,0.7557>,0.343,
        <-0.09621,1.21,0.6182>,0.343,
        <-0.2276,1.088,0.4582>,0.343,
        <-0.3403,0.9833,0.2817>,0.343,
        <-0.4461,0.9001,0.09506>,0.343,
        <-0.5564,0.8363,-0.09506>,0.343,
        <-0.6814,0.7864,-0.2817>,0.343,
        <-0.8281,0.7409,-0.4582>,0.343,
        <-0.9999,0.6884,-0.6182>,0.343,
        <-1.196,0.6164,-0.7557>,0.343,
        <-1.41,0.513,-0.866>,0.343,
        <-1.632,0.3686,-0.945>,0.343,
        <-1.849,0.1766,-0.9898>,0.343,
        <-2.047,-0.06497,-0.9989>,0.343,
        <-2.208,-0.3533,-0.9718>,0.343,
        <-2.318,-0.6805,-0.9096>,0.343,
        <-2.364,-1.034,-0.8146>,0.343,
        <-2.337,-1.399,-0.6901>,0.343,
        <-2.233,-1.756,-0.5406>,0.343,
        <-2.054,-2.087,-0.3717>,0.343,
        <-1.806,-2.373,-0.1893>,0.343,
        <-1.5,-2.598,6.432e-16>,0.343,
        <-1.152,-2.75,0.1893>,0.343,
        <-0.7803,-2.822,0.3717>,0.343,
        <-0.4044,-2.812,0.5406>,0.343,
        <-0.04321,-2.723,0.6901>,0.343,
        <0.286,-2.564,0.8146>,0.343,
        <0.5695,-2.347,0.9096>,0.343,
        <0.7979,-2.089,0.9718>,0.343,
        <0.967,-1.805,0.9989>,0.343,
        <1.078,-1.513,0.9898>,0.343,
        <1.135,-1.229,0.945>,0.343,
        <1.149,-0.9642,0.866>,0.343,
        <1.132,-0.7272,0.7557>,0.343,
        <1.096,-0.5217,0.6182>,0.343,
        <1.056,-0.3467,0.4582>,0.343,
        <1.022,-0.1969,0.2817>,0.343,
        <1.003,-0.06371,0.09506>,0.343,
        <1.003,0.06371,-0.09506>,0.343,
        <1.022,0.1969,-0.2817>,0.343,
        <1.056,0.3467,-0.4582>,0.343,
        <1.096,0.5217,-0.6182>,0.343,
        <1.132,0.7272,-0.7557>,0.343,
        <1.149,0.9642,-0.866>,0.343,
        <1.135,1.229,-0.945>,0.343,
        <1.078,1.513,-0.9898>,0.343,
        <0.967,1.805,-0.9989>,0.343,
        <0.7979,2.089,-0.9718>,0.343,
        <0.5695,2.347,-0.9096>,0.343,
        <0.286,2.564,-0.8146>,0.343,
        <-0.04321,2.723,-0.6901>,0.343,
        <-0.4044,2.812,-0.5406>,0.343,
        <-0.7803,2.822,-0.3717>,0.343,
        <-1.152,2.75,-0.1893>,0.343,
        <-1.5,2.598,1.286e-15>,0.343,
        <-1.806,2.373,0.1893>,0.343,
        <-2.054,2.087,0.3717>,0.343,
        <-2.233,1.756,0.5406>,0.343,
        <-2.337,1.399,0.6901>,0.343,
        <-2.364,1.034,0.8146>,0.343,
        <-2.318,0.6805,0.9096>,0.343,
        <-2.208,0.3533,0.9718>,0.343,
        <-2.047,0.06497,0.9989>,0.343,
        <-1.849,-0.1766,0.9898>,0.343,
        <-1.632,-0.3686,0.945>,0.343,
        <-1.41,-0.513,0.866>,0.343,
        <-1.196,-0.6164,0.7557>,0.343,
        <-0.9999,-0.6884,0.6182>,0.343,
        <-0.8281,-0.7409,0.4582>,0.343,
        <-0.6814,-0.7864,0.2817>,0.343,
        <-0.5564,-0.8363,0.09506>,0.343,
        <-0.4461,-0.9001,-0.09506>,0.343,
        <-0.3403,-0.9833,-0.2817>,0.343,
        <-0.2276,-1.088,-0.4582>,0.343,
        <-0.09621,-1.21,-0.6182>,0.343,
        <0.064,-1.344,-0.7557>,0.343,
        <0.2605,-1.477,-0.866>,0.343,
        <0.4967,-1.597,-0.945>,0.343,
        <0.7717,-1.69,-0.9898>,0.343,
        <1.08,-1.74,-0.9989>,0.343,
        <1.41,-1.735,-0.9718>,0.343,
        <1.748,-1.667,-0.9096>,0.343,
        <2.078,-1.53,-0.8146>,0.343,
        <2.38,-1.324,-0.6901>,0.343,
        <2.638,-1.056,-0.5406>,0.343,
        <2.835,-0.7355,-0.3717>,0.343,
        <2.958,-0.3775,-0.1893>,0.343,
        <3,0,0>,0.343,
        <2.958,0.3775,0.1893>,0.343
    }
    texture {Default_texture}
}
object { data_Torus_Knot_orig
matrix <0.011995, -0.831861, 0.000000,  0.000000, -0.000000, -0.831948,
0.831861, 0.011995, -0.000000,  0.000000, 0.000000, 0.000000>}

light_source {
    <4.08,5.9,5.1>
    color rgb<1, 1, 1>
}

camera {
    location  <0, 0, 0>
    look_at  <0, 0, -1>
    right <-1.7777777777777777, 0, 0>
    up <0, 1, 0>
    angle  49.134343
    rotate  <-27.098163, 46.688390, -0.903519>
    translate <7.481132, 5.343666, 6.507640>
}


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From: Lars Rohwedder
Subject: Re: 3D Loop
Date: 19 May 2015 09:55:55
Message: <555b08ab@news.povray.org>
Am 15.05.2015 um 20:18 schrieb LanuHum:
> Example:
> 
> // POV-Ray scene. It is created in the Blender-2.74
> 
> []

Nice one. But there are quite sharp curves at the transition between the
straight and the curved parts of the loop (marked read on the attached
image)

>
>   right <-1.7777777777777777, 0, 0>
>   up <0, 1, 0>

Oh, when will 16:9 aspect ratio will be the default in Povray? ;-)

L.


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Attachments:
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from-newsgroup.jpg


 

From: LanuHum
Subject: Re: 3D Loop
Date: 19 May 2015 17:10:00
Message: <web.555b6e08d258875a7a3e03fe0@news.povray.org>
Lars Rohwedder <rok### [at] gmxde> wrote:
> Am 15.05.2015 um 20:18 schrieb LanuHum:
> > Example:
> >
> > // POV-Ray scene. It is created in the Blender-2.74
> >
> > []
>
> Nice one. But there are quite sharp curves at the transition between the
> straight and the curved parts of the loop (marked read on the attached
> image)
>
> >
> >   right <-1.7777777777777777, 0, 0>
> >   up <0, 1, 0>
>
> Oh, when will 16:9 aspect ratio will be the default in Povray? ;-)
>
> L.

#version 3.7;

global_settings {
}
background {rgbt<0.00971, 0.271, 0.985, 0>}

#declare Default_texture = pigment {rgb 0.8}

#declare data_Torus_Knot_001_orig =
union {
    sphere_sweep { cubic_spline 83,
        <0.1889,-3.04,-0.7471>,0.565,
        <-0.1152,-2.87,-0.842>,0.565,
        <-0.3964,-2.646,-0.8663>,0.565,
        <-0.6436,-2.379,-0.8232>,0.565,
        <-0.8529,-2.076,-0.7224>,0.565,
        <-1.026,-1.743,-0.5749>,0.565,
        <-1.164,-1.381,-0.3898>,0.565,
        <-1.267,-0.9939,-0.1751>,0.565,
        <-1.332,-0.5868,0.06163>,0.565,
        <-1.353,-0.1668,0.3122>,0.565,
        <-1.326,0.2574,0.5671>,0.565,
        <-1.246,0.6765,0.8154>,0.565,
        <-1.11,1.083,1.045>,0.565,
        <-0.9191,1.468,1.241>,0.565,
        <-0.6758,1.828,1.387>,0.565,
        <-0.3872,2.154,1.47>,0.565,
        <-0.06428,2.436,1.479>,0.565,
        <0.2778,2.662,1.413>,0.565,
        <0.6228,2.823,1.277>,0.565,
        <0.9578,2.916,1.086>,0.565,
        <1.274,2.943,0.854>,0.565,
        <1.566,2.907,0.5949>,0.565,
        <1.83,2.812,0.3217>,0.565,
        <2.06,2.661,0.04721>,0.565,
        <2.253,2.456,-0.2153>,0.565,
        <2.402,2.202,-0.4518>,0.565,
        <2.502,1.903,-0.6472>,0.565,
        <2.546,1.569,-0.7864>,0.565,
        <2.532,1.217,-0.858>,0.565,
        <2.46,0.8624,-0.859>,0.565,
        <2.335,0.5193,-0.7955>,0.565,
        <2.162,0.1922,-0.6779>,0.565,
        <1.945,-0.1188,-0.5169>,0.565,
        <1.687,-0.4137,-0.3212>,0.565,
        <1.391,-0.6896,-0.09828>,0.565,
        <1.06,-0.9399,0.1441>,0.565,
        <0.6969,-1.156,0.3972>,0.565,
        <0.3079,-1.329,0.6512>,0.565,
        <-0.1013,-1.452,0.8947>,0.565,
        <-0.5249,-1.518,1.114>,0.565,
        <-0.9566,-1.526,1.296>,0.565,
        <-1.389,-1.476,1.423>,0.565,
        <-1.81,-1.372,1.482>,0.565,
        <-2.205,-1.217,1.465>,0.565,
        <-2.554,-1.021,1.374>,0.565,
        <-2.846,-0.7931,1.219>,0.565,
        <-3.072,-0.5433,1.013>,0.565,
        <-3.231,-0.2789,0.77>,0.565,
        <-3.325,-0.005833,0.5048>,0.565,
        <-3.352,0.2704,0.2297>,0.565,
        <-3.315,0.5444,-0.0423>,0.565,
        <-3.212,0.8102,-0.2978>,0.565,
        <-3.045,1.061,-0.5223>,0.565,
        <-2.816,1.288,-0.7005>,0.565,
        <-2.532,1.48,-0.8181>,0.565,
        <-2.208,1.628,-0.8661>,0.565,
        <-1.858,1.726,-0.8446>,0.565,
        <-1.495,1.772,-0.7617>,0.565,
        <-1.122,1.77,-0.6286>,0.565,
        <-0.7421,1.723,-0.4552>,0.565,
        <-0.3564,1.633,-0.2495>,0.565,
        <0.02999,1.501,-0.01925>,0.565,
        <0.4091,1.324,0.2277>,0.565,
        <0.7709,1.103,0.4823>,0.565,
        <1.105,0.8383,0.7341>,0.565,
        <1.403,0.5314,0.9713>,0.565,
        <1.657,0.1851,1.18>,0.565,
        <1.863,-0.1956,1.345>,0.565,
        <2.019,-0.6024,1.45>,0.565,
        <2.12,-1.022,1.485>,0.565,
        <2.164,-1.437,1.443>,0.565,
        <2.15,-1.828,1.329>,0.565,
        <2.081,-2.18,1.155>,0.565,
        <1.962,-2.485,0.9351>,0.565,
        <1.798,-2.737,0.6835>,0.565,
        <1.596,-2.937,0.4135>,0.565,
        <1.36,-3.08,0.138>,0.565,
        <1.095,-3.165,-0.13>,0.565,
        <0.8061,-3.188,-0.3768>,0.565,
        <0.5008,-3.147,-0.5876>,0.565,
        <0.1889,-3.04,-0.7471>,0.565,
        <-0.1152,-2.87,-0.842>,0.565,
        <-0.3964,-2.646,-0.8663>,0.565
    }
    texture {Default_texture}
}
object { data_Torus_Knot_001_orig
matrix <0.877638, -0.479323, 0.000000,  0.000000, -0.000000, -1.000000,
0.479323, 0.877638, -0.000000,  0.000000, 0.000000, 0.000000>}
light_source {
    <4.08,5.9,-1.01>
    color rgb<1, 1, 1>
}

camera {
    location  <0, 0, 0>
    look_at  <0, 0, -1>
    right <-1.7777777777777777, 0, 0>
    up <0, 1, 0>
    angle  49.134343
    rotate  <-27.098163, 46.688390, -0.903519>
    translate <7.481132, 5.343666, 6.507640>
}


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From: And
Subject: Re: 3D Loop
Date: 22 May 2015 06:55:01
Message: <web.555ed213d258875a449d5c170@news.povray.org>
Lars Rohwedder <rok### [at] gmxde> wrote:
>
> Oh, when will 16:9 aspect ratio will be the default in Povray? ;-)
>
> L.

camera {
    location  <-1.4, 1.0 ,1.4>
    right     16/9*x       // 16:9
    look_at   <0.0 , 0.0 , 0.5>
}


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From: Lars Rohwedder
Subject: Re: 3D Loop
Date: 24 May 2015 20:08:10
Message: <55622faa@news.povray.org>
Am 22.05.2015 um 08:52 schrieb And:
> Lars Rohwedder <rok### [at] gmxde> wrote:
>>
>> Oh, when will 16:9 aspect ratio will be the default in Povray? ;-)
>>
>> L.
> 
> camera {
>     location  <-1.4, 1.0 ,1.4>
>     right     16/9*x       // 16:9
>     look_at   <0.0 , 0.0 , 0.5>
> }

What do you want to do me with that snippet?

I do know how to adjust the camera to render 16:9 images in Povray.

That was _not_ my question. I asked when 16:9 will become the _default_
in Povray so such scaling of the right vector becomes unnecessary. oO

Lars R.


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From: Le Forgeron
Subject: Re: 3D Loop
Date: 25 May 2015 06:49:44
Message: <5562c608$1@news.povray.org>
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA256

Le 24/05/2015 22:08, Lars Rohwedder a écrit :
> Am 22.05.2015 um 08:52 schrieb And:
>> Lars Rohwedder <rok### [at] gmxde> wrote:
>>> 
>>> Oh, when will 16:9 aspect ratio will be the default in Povray?
>>> ;-)
>>> 
>>> L.
>> 
>> camera { location  <-1.4, 1.0 ,1.4> right     16/9*x       //
>> 16:9 look_at   <0.0 , 0.0 , 0.5> }
> 
> What do you want to do me with that snippet?
> 
> I do know how to adjust the camera to render 16:9 images in
> Povray.
> 
> That was _not_ my question. I asked when 16:9 will become the
> _default_ in Povray so such scaling of the right vector becomes
> unnecessary. oO
> 
> Lars R.
> 
Unnecessary for you... my screen are 1920x1200, I would need 16:10.

Changing the default right vector (even to something like
image_width:image_height ratio, assuming square pixel everywhere)
would only have one sure effect: break every historical scenes.
Without providing 100% satisfaction to all users. Better not move.

And guess what: 4K screens are coming... and there is at least 5
different resolution under the name 4K, none with exactly the same ratio
.

So far:

 * 4096 x 2160 ( 256:135) [DCI native]
 * 3840 x 2160 ( 16:9 ) [UHD-1]
 * 5120 x 2160 ( 21:9 ) [UWT]
 * 5120 x 3200 ( 16:10 ) [WHXGA]
 * 4096 x 1716 ( 2.39: 1 ) [DCI cinemascope cropped]
 * 3996 x 2160 ( 1.85: 1 ) [DCI flat cropped]
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