The hexagon has vertices on x axis but the flat side on y axis. the distance between opposite vertices is longer than the distance between opposite sides.
On Wed, Feb 10, 2021, 9:13 AM Ric Sherlock <[email protected]> wrote: > I enlarged the plot window, took a screenshot and then measured the > distance between _0.8 to 0.8 on the two axes using an on-screen ruler, the > Y-axis distance is about a centimetre longer than the X-axis distance. > > On Wed, Feb 10, 2021 at 1:52 PM bill lam <[email protected]> wrote: > > > I think it's ok to have different axis length, but the unit of each axis > > should have the same physical length. Is this a bug in qt output only? > Did > > you try output to pdf and then print it out on paper, and measure the > > length of each side of the hexagon using a ruler? > > > > > > On Wed, Feb 10, 2021, 7:42 AM Devon McCormick <[email protected]> > wrote: > > > > > Well, on my screen the hexagon looks too tall and the y-axis has > extremes > > > of (_0.4, 0.4) whereas the x-axis goes from _0.5 to 0.5, so it does not > > > look properly regular. > > > > > > On Tue, Feb 9, 2021 at 4:19 PM 'Bo Jacoby' via Programming < > > > [email protected]> wrote: > > > > > > > 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? > > > > > >>> > > > > > >> > > > > > >> -- > > > > > >> ---------------------- > > > > > >> mail written using NEO > > > > > >> neo-layout.org > > > > > >> > > > ---------------------------------------------------------------------- > > > > > >> For information about J forums see > > > > http://www.jsoftware.com/forums.htm > > > > > >> > > > > > > > > > > > > > > > > > > > > > > -- > > > > > ---------------------- > > > > > mail written using NEO > > > > > neo-layout.org > > > > > > > > > > > > ---------------------------------------------------------------------- > > > > > For information about J forums see > > http://www.jsoftware.com/forums.htm > > > > > > > > > > > > ---------------------------------------------------------------------- > > > > > For information about J forums see > > http://www.jsoftware.com/forums.htm > > > > > > > > > > > > > > > > > -- > > > > > > > > Devon McCormick, CFA > > > > > > > > Quantitative Consultant > > > > > ---------------------------------------------------------------------- > > > > For information about J forums see > http://www.jsoftware.com/forums.htm > > > > > > > > > ---------------------------------------------------------------------- > > > > For information about J forums see > http://www.jsoftware.com/forums.htm > > > > > > > > > > > > > -- > > > > > > Devon McCormick, CFA > > > > > > Quantitative Consultant > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
