<< CSPlotter.m

Connecting two points in the radial structure

conormalleft[x_, y_, z_] = {y/2, -x/2, 1};

ga[
        rd_]:= ArcTan[ conormalleft[rd, 0, 
            0][[3]], -conormalleft[rd, 0, 
              0][[2]]]

Plot[ga[t], {t, 0.01, 40}]

z0 = 
        1.5;

    AB = Graphics3D[{Line[{{0, 0, 0}, {0, 0, z0}}]}]

    platesize = 0.10;

rad = 0.4055119;

    γ = ga[rad];

    speed = rad Tan[γ];

    

    startangle = 0.0;

    astop = z0/speed + startangle;

    

    A0  =  
        Table[contactelement[{x, 0, 0}, conormalleft[x, 0, 0], 
            platesize], {x, 0, rad, platesize}];

    A1 = 
        Table[contactelement[{rad  Cos[α], rad  Sin[α], 
              speed α}, 
            conormalleft[rad Cos[α], rad Sin[α], 
              speed α ], platesize], {α, 0, astop,  
            platesize Cos[γ]/rad}];

    A2 = 
        Table[contactelement[{rr Cos[astop], rr Sin[astop], speed astop}, 
            conormalleft[rr Cos[astop], rr Sin[astop], speed  astop], 
            platesize], {rr, 0, rad, platesize}];

    

     Show[A0, A1, A2, AB, Boxed -> False]

rad = 0.9;

    γ = ga[rad];

    speed = rad Tan[γ];

    startangle = 0.2;

    astop = z0/speed + startangle;

    

    B0 = 
        Table[contactelement[{rr Cos[startangle], rr Sin[startangle], 0}, 
            conormalleft[rr Cos[startangle], rr Sin[startangle], 0], 
            platesize], {rr, 0, rad, platesize}];

    B1 = 
        Table[contactelement[{rad Cos[α], rad Sin[α], 
              speed (α - startangle)}, 
            conormalleft[rad Cos[α], rad Sin[α], 
              speed (α - startangle)], platesize], {α, 
            startangle, astop, 
            platesize Cos[γ]/rad}];

    B2 = 
        Table[contactelement[{rr Cos[astop], rr Sin[astop], 
              speed (astop - startangle)}, 
            conormalleft[rr Cos[astop], rr Sin[astop], speed astop], 
            platesize], {rr, 0, rad, platesize}];

    

    Show[A0, A1, A2, B0, B1, B2, Boxed -> False]

(*#1-- - 
        Outer sprial (almost no rotation)*) 
rad = 1.6;

    γ = ga[rad];

    speed = rad Tan[γ];

    startangle = 0.4;

    astop = z0/speed + startangle;

    

    C0 = 
        Table[contactelement[{rr Cos[startangle], rr Sin[startangle], 0}, 
            conormalleft[rr Cos[startangle], rr Sin[startangle], 0], 
            platesize], {rr, 0, rad, platesize}];

    C1 = 
        Table[contactelement[{rad Cos[α], rad Sin[α], 
              speed (α - startangle)}, 
            conormalleft[rad Cos[α], rad Sin[α], 
              speed (α - startangle)], platesize], {α, 
            startangle, astop, 
            platesize Cos[γ]/rad}];

    C2 = 
        Table[contactelement[{rr Cos[astop], rr Sin[astop], 
              speed (astop - startangle)}, 
            conormalleft[rr Cos[astop], rr Sin[astop], speed astop], 
            platesize], {rr, 0, rad, platesize}];

    Show[A0, A1, A2, B0, B1, B2, C0, C1, C2, 
      Boxed -> False]

AB = 
      Graphics3D[{Line[{{0, 0, 0}, {0, 0, z0}}]}]
cout  = 
      Show[AB, A0, A1, A2, B0, B1, B2, C0, C1, C2, 
        Boxed -> False]

Export["connect.eps", cout];
Export["connect.png", cout];
Export["connect.pdf", cout];