Hello
I have a set of parametric equations defining a 3D surface, in this
example a "klein bottle", as a non-orientable surface. DFW file attached.
k:=4(1-cos(u)/2)
For u=0-pi
x=6cos(u)(1+sin(u))+kcos(u)cos(v)
y=16sin(u)(1+sin(u))+ksin(u)cos(u)
z=ksin(v)
For u=pi-2pi
x=6cos(u)(1+sin(u))+kcos(u)cos(v)
y=16sin(u)
z=ksin(v)
v= -pi to pi
What I would like to do is create a demonstration plot that shows normals
to the surface (say at the mesh nodes for z=0, panels=20), to illustrate
the nature of the "one-sided" surface i.e. no volume in this case. I am
not too sure how to proceed on this other than setting a plane to z=0 as a
starting point.
Ideally I am looking to do a cutaway view. In the above case setting v=-pi
to 0 for illustration.
This is quite a complicated modelling task as not only do I need to
determine the normals to the surface at a given z value, but also to make
the normal vectors a small enough length to be instructive. Hopefully
someone can provide some guidance on this issue as I would be looking to
apply the technique to other surfaces.
The DFW file is in version 5 format, but works fine in version 6. Any
advice about how to proceed will be welcome.
Thanks
Lester
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