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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