Le 16/05/2017 à 13:41, Bald Eagle a écrit :
> I didn't have as much time as I would have liked to explore this,
> but after fiddling with the Dupin cyclide in both isosurface (implicit) and
> parametric form, I found the parameters to be highly unintuitive, the desired
> shape very difficult to achieve and control, and the constraints on the
> parameters too complex to be easily implemented.
> 
> I hadn't gotten around to unraveling the implicit equation to fit the syntax for
> a polynomial.

I asked the other Internets about that, they had a round tuit left so I
got a nice answer.

> It is, however, SLLLLllllllllllooooooooooowwwwwwww.

It is not slow with a polynomial.

True Duplin Cyclide !


#version 3.7;
global_settings{ assumed_gamma 1.0}
#default { finish { ambient 0.2 diffuse 0.8 } }

#declare HEIGHT=9;
camera { orthographic
location <00,00,30>
up HEIGHT*y
right HEIGHT*image_width/image_height*x
look_at 0
rotate clock*x*90
}

light_source { <20,30,40>,1 }
#declare TC=texture { pigment { color srgb <1,1,1> } };
sphere { 0, 1 texture { TC }}

#declare A=3;
#declare B=A*0.98;
#declare C=sqrt(A*A-B*B);
#declare D=1.3*C;
#declare T=texture { pigment { color srgb <1,0.75,0.5> } };
polynomial{
4,
/* expand  (x^2+y^2+z^2+b^2-d^2)^2-4*(a*x-c*d)^2-4*b^2*y^2=0 */
/* -4 a^2 x^2 + 2 b^2 x^2 - 2 d^2 x^2
  + 8 a c d x
  + b^4 - 2 b^2 d^2 - 4 c^2 d^2 + d^4
  - 2 b^2 y^2 - 2 d^2 y^2
  + 2 b^2 z^2 - 2 d^2 z^2
  + 2 x^2 y^2
  + 2 x^2 z^2
  + 2 y^2 z^2
  + x^4
  + y^4
  + z^4
  = 0
*/
xyz(2,0,0):(-4*A*A)+(2*B*B)-(2*D*D),
xyz(1,0,0):8*A*C*D,
xyz(0,0,0):(B*B*B*B)-(2*B*B*D*D)-(4*C*C*D*D)+(D*D*D*D),
xyz(0,2,0):(-2*B*B)-(2*D*D),
xyz(0,0,2):(2*B*B)-(2*D*D),
xyz(2,2,0):2,
xyz(2,0,2):2,
xyz(0,2,2):2,
xyz(4,0,0):1,
xyz(0,4,0):1,
xyz(0,0,4):1

texture { T }}

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