"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Alfred Knudson" <nomail@nomail> wrote:
> > How does one draw a parametric curve on a surface, for example the helyx:
> >
> >     f(t) - (cos t, sin t, t)
> >
> > on the surface of a cone x^2 + y^2 = 1?
> >
> > I can't seem to find anything about plotting cusrves on the manual.
>
> Hi Alfred
>
> The code below might give you a hint of one way to achieve this.
>...

This may be a better example for you.

You can also replace the cylinder and the spiral objects with isosurfaces.

--
Tor Olav
http://subcube.com
https://github.com/t-o-k


// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
/*

Cylinder with parametric spiral pigment

By Tor Olav Kristensen, 2024-09-29

*/
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#version 3.7;

global_settings { assumed_gamma 1.0 }

#include "functions.inc"

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#declare Tau = 2*pi;

#declare Radius = 1.5;

// Fn(s): <Radius*cos(s), Radius*sin(s), s>

#declare Helix_FnX = function(s) { Radius*cos(s) };
#declare Helix_FnY = function(s) { Radius*sin(s) };
#declare Helix_FnZ = function(s) { s };

#declare N = 1000;

#declare MinT = -2.5*Tau;
#declare MaxT = +2.5*Tau;
#declare dT = (MaxT - MinT)/N;

#declare R = 0.4;
#declare Spiral =
    union {
        #declare T_Previous = MinT;
        #declare pPrevious =
            <
                Helix_FnX(T_Previous),
                Helix_FnY(T_Previous),
                Helix_FnZ(T_Previous)
            >
        ;
        sphere { pPrevious, R }
        #for (I, 0, N - 1)
            #declare T_Next = T_Previous + dT;
            #declare pNext =
                <
                    Helix_FnX(T_Next),
                    Helix_FnY(T_Next),
                    Helix_FnZ(T_Next)
                >
            ;
            cylinder { pPrevious, pNext, R }
            sphere { pNext, R }
            #declare T_Previous = T_Next;
            #declare pPrevious = pNext;
        #end // for
    }

cylinder {
    MinT*z, MaxT*z, Radius
    pigment {
        object {
            Spiral
            color rgb <0.0, 0.3, 1.0> // Outside
            color rgb <1.0, 0.7, 0.0> // Inside
        }
    }
}

/*
object {
    Spiral
    pigment { color rgb <1.0, 1.0, 1.0> }
}
*/

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background { color rgb 0.2*<1, 1, 1> }

light_source {
    100*<+1, +3, -1>
    color rgb <1, 1, 1>
    shadowless
}

camera {
    orthographic
    location < 0, +3, -8>*2
    look_at <0, 0, 0>
}

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