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Turnery

by R. Grothmann

In this notebook, you can design a rotation object with just a few mouse clicks.

First we define a function to read the mouse clicks in a loop.

>function getpoints ...
   setplot(-1,1,-1,1); clg; xplot();
   title("Click into the half plane x>0");
   v=zeros(0,2);
   repeat
     m=mouse(); if cols(m)==1 then break; endif;
     v=v_m; 
     hold on; style("mx"); mark(m[1],m[2]); hold off;
   end;
   return v
 endfunction

Now you can try it. Click into right half plane x>0 with monotone decreasing y.

>v=getpoints()

     0.590692      0.980257 
     0.207214      0.706317 
     0.123849      0.506781 
     0.133853         0.128 
     0.287244    -0.0512448 
     0.520666     -0.223725 
     0.594027     -0.389442 
     0.520666     -0.656618 
     0.490655     -0.842627 
     0.667388     -0.910266 
     0.930821     -0.930558 

The following commands compute a natural spline, joining the points.

>v=v'; n=cols(v); x=1:n; ...
 s1=spline(x,v[1]); s2=spline(x,v[2]); ...
 t=linspace(1,n,600); ...
 y1=splineval(t,x,v[1],s1); y2=splineval(t,x,v[2],s2); ...
 hold on; plot(y1,y2); hold off:

Now generate a 3D object from these points.

>phi=linspace(0,2*pi,200)';
>X=cos(phi)*y1; Y=sin(phi)*y1; Z=y2;

And plot it.

>plot3d(X,Y,Z,hue=1,frame=0,height=30°, ...
   zoom=4,<scale,color=rgb(0.2,0,0),amb=0):

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