gnuplot-info

[Gnuplot-info] plotting a knot on a torus

[Brian M. <bhm...@gm...>]

I plotted a torus, and a knot on it, using the following commands:

unset key
set parametric
set isosamples 30,30
set hidden3d
splot [-pi:pi][-pi:pi] (2 + cos(u))*cos(v), (2 + cos(u))*sin(v), sin(u),
[-pi:pi] (2 + cos(u))*cos(u), (2 + cos(u))*sin(u), sin(u)

This works beautifully.

However, if I plot a more complicated knot:

splot [-pi:pi][-pi:pi] (2 + cos(u))*cos(v), (2 + cos(u))*sin(v), sin(u),
[-pi:pi][-pi:pi] (2 + cos(3*u))*cos(2*u), (2 + cos(3*u))*sin(2*u), sin(2*u),

then the knot's curve breaks :(  It seems this has something to do with
`set hidden3d`, as if I unset that, then nothing is hidden, but the curve
is rendered normally.

What can I do to fix this problem?

I am on Windows 10, using the latest version of gnuplot, with the Qt
terminal.

Kind regards,
Brian

Re: [Gnuplot-info] plotting a knot on a torus

[Ethan A M. <eam...@gm...>]

On Thursday, 03 January 2019 20:37:49 Ethan A Merritt wrote:

There are more options you can turn on if you don't use parametric mode.
For example here is a pm3d version (rather than hidden3d) that may be
a better starting point:

set style fill  transparent solid 0.40 border
set view 53, 100, 1, 1
set isosamples 50, 50
set style data lines
set pm3d depthorder border lc "black"  lw 0.25
unset colorbox
unset key

splot sample [-pi:pi][-pi:pi] '++' using (2 + cos($1))*cos($2)\
                                        :(2 + cos($1))*sin($2):(sin($1))\
                                        :(0xffeebb) with pm3d lc rgb variable, \
             [-pi:pi] '+'  using ((2 + cos(3*$1))*cos(2*$1))\
                               : ((2 + cos(3*$1))*sin(2*$1))\
                               : (sin(2*$1)) with lines lw 4
 

Re: [Gnuplot-info] plotting a knot on a torus

[Hans-Bernhard B. <HBB...@t-...>]

Am 04.01.2019 um 05:11 schrieb Brian Merchant:
> I plotted a torus, and a knot on it, using the following commands:

> However, if I plot a more complicated knot:
> 
> splot [-pi:pi][-pi:pi] (2 + cos(u))*cos(v), (2 + cos(u))*sin(v), sin(u),
> [-pi:pi][-pi:pi] (2 + cos(3*u))*cos(2*u), (2 + cos(3*u))*sin(2*u), sin(2*u),
> 
> then the knot's curve breaks :(  

I'm convinced that that's because that knot curve is not actually _on_
the torus.  It dives into it, and therefore hidden3d is doing exactly
what you asked it to.