Devon - 'aspect 1' plot 0.5*_1^3%~i.7 looks perfect!
Den tirsdag den 9. februar 2021 03.12.52 CET skrev Devon McCormick
<[email protected]>:
Hauke - you are correct. A hexagon can be thought of as six equilateral
triangles.
Bo - you are correct only for an unscaled hexagon. See how "'aspect 1'
plot 0.5*_1^3%~i.7" looks.
Thanks everyone,
Devon
On Mon, Feb 8, 2021 at 8:53 AM 'Bo Jacoby' via Programming <
[email protected]> wrote:
> 'aspect 1'plot _1^3%~i.7
>
>
> Den mandag den 8. februar 2021 07.22.39 CET skrev Hauke Rehr <
> [email protected]>:
>
> The picture is Very Wrong™ (but the area formula is correct)
> The lengths of the not-horizontal lines are interchanged.
> And it looks distorted but that’s not too bad.
>
> And then it should be r =. sideOfUnitHexagon
> which is obviously due to the same confusion
> as the mislabelled lines.
>
> Just think of the hexagon cut into six triangles.
> They’ll be regular as well, so radius = side.
>
> Another way to see this is to remember you can
> construct a regular hex by taking a circle and
> repeatedly go around that circle finding
> intersections at one radius distance.
>
> Am 08.02.21 um 06:30 schrieb Devon McCormick:
> > This scales the hexagon to have unit area.
> > hexagonArea=: 3 : '3*y*(-:y)*%:3' NB. Where y is side length
> > sideOfUnitHexagon=: 0.6204032394013997
> > hexagonArea sideOfUnitHexagon
> > 1
> > ]r=. sideOfUnitHexagon*-:%:3
> > 0.537285
> > 'title Regular Hexagons Centered at Origin;type line;pensize 2; aspect
> > 0.866' plot (],.{."1) (r,1)*"(0 1) (_1^1r3)^i.6
> >
> > See
> >
> https://code.jsoftware.com/wiki/NYCJUG/2021-02-09#Corners_of_Unit_Hexagon_Centered_at_Origin
> > for a diagram illustrating why we use the square root of 3.
> >
> > On Sun, Feb 7, 2021 at 4:00 PM Hauke Rehr <[email protected]>
> wrote:
> >
> >> I wonder about that scaling factor in
> >>
> >> */ , 5e_7 > | hexCorners - 0.537285 * +. (_1^1r3)^i.6
> >>
> >> Is there anything special about it?
> >>
> >>
> >> Am 07.02.21 um 21:28 schrieb Devon McCormick:
> >>> I'm trying to draw a unit hexagon centered at the origin with the
> >>> horizontal sides parallel to the X-axis. I've come up with these
> >>> co-ordinates for the corners but when I plot them, the drawing looks a
> >>> little too wide:
> >>>
> >>> hexCorners=. _2]\,0.537285 0 0.268642 0.465302 _0.268642 0.465302
> >>> _0.537285 0 _0.268642 _0.465302 0.268642 _0.465302
> >>> 'title Regular Unit Hexagon Centered at Origin;type line;pensize 2'
> >> plot
> >>> (],{.) j./"1 hexCorners
> >>>
> >>> I can use my paint program to distort a picture of this plot until it
> >> looks
> >>> like it has a square aspect ratio (roughly, width height * 0.92 1.06)
> but
> >>> how can I plot this with the correct aspect ratio in the first place?
> >>>
> >>
> >> --
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> >>
> >
> >
>
> --
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--
Devon McCormick, CFA
Quantitative Consultant
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