Mathematical Experiment 1

Construct this surface whose boundary consists of two linking circles:

> x:=cos(s);
> y:=sin(s);
> z:=0;
> x1:=x+t*2/Pi;
> y1:=y;
> z1:=z;
> x2:=x1;
> x2 := cos(s)+2*t/Pi;
> y2:=cos(t)*y1-sin(t)*z1;
> z2:=sin(t)*y1+cos(t)*z1;
> plot3d([x2,y2,z2],s=0..2*Pi,t=0..Pi/2,scaling=constrained);

Construct a VRML file of the above surface.

> h2:=plot3d([x2,y2,z2],s=0..2*Pi,t=0..Pi/2,scaling=constrained):
> with(plottools):
> vrml(h2,"z:/usr1/data/disk3/exp02/1/s0.wrl",background_color=white);

Make sure that you understand the settings: scaling=constrained, background_color=white.

Make sure that Pi is different from pi.

The lighting scheme may be changed with the setting lightmodel=1ight1 or lightmodel=1ight2 or lightmodel=1ight3 or lightmodel=1ight4.

To increase the accuracy of the surface, add the setting grid = [50,50].

Modify the above equations to construct these surfaces