Am 14.05.2016 um 19:06 schrieb Le_Forgeron:
> Le 09/05/2016 18:40, Le_Forgeron a écrit :
>> I'm just dreaming of the
>> rocket on the cover (and inside) the "Destination moon" of Tintin (by Hergé).
> 
> 4 lemon, 3 discs, 3 spheres, a bit of cut and voilà.

I love it!

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Am 12.05.2016 um 20:06 schrieb LanuHum:

> But, in the Blender the lemon is unprofitable to be used.
> Any this form is created by lathe.

You can't create this exact shape with lathe. All you can get is an
approximation.

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Am 2016-05-08 20:43, also sprach clipka:
> Am 08.05.2016 um 21:33 schrieb Le_Forgeron:

> Not happy at all with the term "lemon" here, because it only fits the
> special case R1=R2=0 (which btw is already covered by the torus in 3.7.1)
>
> The term "ogive" would at least be technically fitting for cases where
> only one of R1 and R2 is zero; the term "barrel", too, would be fitting
> for more cases than "lemon".
>

I don't like lemon either; it seems too specific (although I don't know 
why).  I prefer barrel.  Just my humble opinion.


-- 
dik

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clipka <ano### [at] anonymousorg> wrote:
> Am 12.05.2016 um 20:06 schrieb LanuHum:
>
> > But, in the Blender the lemon is unprofitable to be used.
> > Any this form is created by lathe.
>
> You can't create this exact shape with lathe.

I won't argue. Accuracy of computation of Bezier curves has enough for creation
of a body of the car.

But, as the exact form of a lemon allows to place on its surface objects for
csg.

Task:
To place five spheres so that centers of spheres lay on a lemon surface.
difference{
lemon{}
sphere{??}
sphere{??}
sphere{??}
sphere{??}
sphere{??}
}

Look attachment

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Attachments:
Download 'lemon.jpg' (119 KB)

Preview of image 'lemon.jpg'

Am 18.05.2016 um 20:25 schrieb LanuHum:
> clipka <ano### [at] anonymousorg> wrote:
>> Am 12.05.2016 um 20:06 schrieb LanuHum:
>>
>>> But, in the Blender the lemon is unprofitable to be used.
>>> Any this form is created by lathe.
>>
>> You can't create this exact shape with lathe.
> 
> I won't argue. Accuracy of computation of Bezier curves has enough for creation
> of a body of the car.

I doubt the designers of car bodies use Bezier splines -- their weapon
of choice are NURBS (non-uniform rational B-splines); AFAIK those do
have the capacity to precisely represent circular arcs.

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clipka <ano### [at] anonymousorg> wrote:

>
> I doubt the designers of car bodies use Bezier splines -- their weapon
> of choice are NURBS (non-uniform rational B-splines); AFAIK those do
> have the capacity to precisely represent circular arcs.

https://en.wikipedia.org/wiki/B%C3%A9zier_curve


ity to graphics was not realized for


> Renault. The study of these curves was however first developed in 1959 by
> mathematician Paul de Casteljau using de Casteljau's algorithm, a numerically

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Am 19.05.2016 um 16:10 schrieb LanuHum:
> clipka <ano### [at] anonymousorg> wrote:
> 
>>
>> I doubt the designers of car bodies use Bezier splines -- their weapon
>> of choice are NURBS (non-uniform rational B-splines); AFAIK those do
>> have the capacity to precisely represent circular arcs.
> 
> https://en.wikipedia.org/wiki/B%C3%A9zier_curve
> 
[quote from Wikipedia, not clipka]

>> known since 1912, but its applicability to graphics was not realized for


>> Renault. The study of these curves was however first developed in 1959 by
>> mathematician Paul de Casteljau using de Casteljau's algorithm, a numerically


Yes, the /invention/ of Bezier curves was driven by the French
automotive industry.

But as the article also notes, that was around _1960_.

Car body quality requirements have increased quite a lot since then.

Note how the "Applications" section in that article lists computer
graphics, animation and fonts, but /not/ [contemporary] automotive design.

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clipka <ano### [at] anonymousorg> wrote:

>
> Yes, the /invention/ of Bezier curves was driven by the French
> automotive industry.
>
> But as the article also notes, that was around _1960_.
>
> Car body quality requirements have increased quite a lot since then.
>
> Note how the "Applications" section in that article lists computer
> graphics, animation and fonts, but /not/ [contemporary] automotive design.

We distracted, but the task remained unresolved.
Task:
To place five spheres so that centers of spheres lay on a lemon surface.
difference{
lemon{}
sphere{??}
sphere{??}
sphere{??}
sphere{??}
sphere{??}
}

http://news.povray.org/povray.binaries.images/attachment/%3Cweb.573cb381370a969c7a3e03fe0%40news.povray.org%3E/lemon.jp
g

WRITTEN_FOR="LANUHUM"
use_bezier_lathe = False
use_lemon = True
#macro Calculate_points_coords_lemon_surface(number_x,number_y,number_z)
//bla-bla-bla...
replace, please, //bla-bla-bla... with the working source code
If it isn't in documentation, then I don't know how to the rocket to attach
wings
:))))))

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On 05/19/2016 11:46 AM, LanuHum wrote:
> clipka <ano### [at] anonymousorg> wrote:
>
>>
>> Yes, the /invention/ of Bezier curves was driven by the French
>> automotive industry.
>>
>> But as the article also notes, that was around _1960_.
>>
>> Car body quality requirements have increased quite a lot since then.
>>
>> Note how the "Applications" section in that article lists computer
>> graphics, animation and fonts, but /not/ [contemporary] automotive design.
>
> We distracted, but the task remained unresolved.
> Task:
> To place five spheres so that centers of spheres lay on a lemon surface.
> difference{
> lemon{}
> sphere{??}
> sphere{??}
> sphere{??}
> sphere{??}
> sphere{??}
> }
>
>
http://news.povray.org/povray.binaries.images/attachment/%3Cweb.573cb381370a969c7a3e03fe0%40news.povray.org%3E/lemon.jp
> g
>
> WRITTEN_FOR="LANUHUM"
> use_bezier_lathe = False
> use_lemon = True
> #macro Calculate_points_coords_lemon_surface(number_x,number_y,number_z)
> //bla-bla-bla...
> replace, please, //bla-bla-bla... with the working source code
> If it isn't in documentation, then I don't know how to the rocket to attach
> wings
> :))))))
>
>
>
>
>

The code below uses the new spindle torus & not the lemon, but is 
something like this what you are after?

#declare Torus00=torus { 0.25, 0.5 intersection scale <1,2,1> }
#declare Norm=<0,0,0>;
difference {
     object { Torus00 }
     sphere { trace(Torus00, <1,0,0>,    <-1,0,0>, Norm) , 0.15 }
     sphere { trace(Torus00, <1,0.5,0>,  <-1,0,0>, Norm) , 0.15 }
     sphere { trace(Torus00, <1,-0.5,0>, <-1,0,0>, Norm) , 0.15 }
     pigment { color Niagara }
}

Bill P.

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Le 19/05/2016 17:46, LanuHum a écrit :
> clipka <ano### [at] anonymousorg> wrote:
> 
>>
>> Yes, the /invention/ of Bezier curves was driven by the French
>> automotive industry.
>>
>> But as the article also notes, that was around _1960_.
>>
>> Car body quality requirements have increased quite a lot since then.
>>
>> Note how the "Applications" section in that article lists computer
>> graphics, animation and fonts, but /not/ [contemporary] automotive design.
> 
> We distracted, but the task remained unresolved.
> Task:
> To place five spheres so that centers of spheres lay on a lemon surface.
> difference{
> lemon{}
> sphere{??}
> sphere{??}
> sphere{??}
> sphere{??}
> sphere{??}
> }

For lemon { 0, 0, H*y, 0, R }

The 2D circle (of radius R) of the lemon is centred at <-V, H/2>, with
V^2 = R^2 - ((H^2)/4)

easily solved as V = sqrt( R^2 - ((H^2)/4) ).

Assuming you want the spheres in the z=0,x+ demi plane, you just have to satisfy for 
< A, B, C> as the centre:

C = 0

R^2 = (B-(H/2))^2 + (A+V)^2

0 <= B <= H

As I'm tired of equations solving, I let it to wolframalpha solver :

A is sqrt(-2 B^2+2 B H-H^2+4 R^2+sqrt(H^2-4 R^2) sqrt(4 B^2-4 B H+H^2-4 R^2))/sqrt(2)


Have a nice sleep.

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