Rune wrote:

>>Thus, a trick would be to "go round byond the end point".
>>I.e to use a additional control point that is identical with
>>the second point on the curve.
>>
> 
> I thought this was exactly what I had done in my example code?
> I didn't understand you. I would appreciate if you could look at my example
> code and show me how to change it to get a smooth connection.

Sorry, Rune, indeed I was in hurry and overlooked, that you had added
an additional point at the start. So this was my fault.

In cases where it has to bee *realy* smooth, one additional point 
often is not sufficient. I found myself using sometimes three or four.

Some weeks ago, I had to create lots of closed splies, so I wrote a
short macro, see below enclosed in your example.

Hermann



#macro nat_closed(o)
   #if (o<=0)
     #error "number of additional control points needs be >0\n"
   #end
   #declare u_nr=0;
   #declare o_nr=0;
   #declare firstPts=array[o+1];
   #declare firstVec=array[o+1];
   #declare lastPts =array[o];
   #declare lastVec =array[o];
   #declare over=o;
   spline { cubic_spline
#end
#macro CP(pt,V)
   pt, V,
   #if (u_nr<over+1)
     #declare firstPts[u_nr]=pt;
     #declare firstVec[u_nr]=V;
   #end
     #declare lastPts[o_nr]=pt;
     #declare lastVec[o_nr]=V;
   #declare u_nr=u_nr+1;
   #declare o_nr=mod(o_nr+1,over);
#end
#macro join_it(join_at)
   #if (u_nr<over+1)
     #error concat("only ",str(u_nr-1,0,0)," additional control points 
possible with this data\n")
   #end
   #local i=0;
   #while(i<over+1)
     join_at+firstPts[i]-firstPts[0], firstVec[i],
     #local i=i+1;
   #end
   #local i=0;
   #while(i<over)
     firstPts[0]+lastPts[i]-join_at, lastVec[i],
     #local i=i+1;
   #end
   }// end generated spline declaration
#end



camera {location 4*y look_at 0 translate z}
light_source {1000*y, color 1}
plane {y, 0 pigment {checker color rgb 1.0, color rgb 0.9}}


#declare Spline = nat_closed(3)   // <--- No of additional control pts
    CP( 0, < 0,0,0>) // P3 red joining point
    CP( 1, < 1,0,0>) // P4
    CP( 2, < 2,0,2>) // P5

    CP( 8, <-2,0,2>) // P1
    CP( 9, <-1,0,0>) // P2
join_it(10)


#declare C = 0;
#while (C<=200)
    #declare V = C/20;
    sphere {Spline(V), 0.02 pigment {color <1,0,0>}}
    #declare C = C+1;
#end
#declare C = 0;
#declare Cm = 400;
#while (C<=Cm)
    #declare V = C/Cm;
    #declare T0 = mod((C-1)/40+5,10);
    #declare T1 = mod( C   /40+5,10);
    #declare T2 = mod((C+1)/40+5,10);
    sphere {
       <-2+4*C/Cm
          0,
          1+100*vlength(
             +(Spline(T1)-Spline(T0))
             -(Spline(T2)-Spline(T1))
          )
       >
         0.02
       pigment {color <0,0,1>}}
    #declare C = C+1;
#end

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