Pentagram
You are encouraged to solve this task according to the task description, using any language you may know.
A pentagram is a star polygon, consisting of a central pentagon of which each side forms the base of an isosceles triangle. The vertex of each triangle, a point of the star, is 36 degrees.
- Task
Draw (or print) a regular pentagram, in any orientation. Use a different color (or token) for stroke and fill, and background. For the fill it should be assumed that all points inside the triangles and the pentagon are inside the pentagram.
- See also
AutoHotkey
<lang AutoHotkey>
- Include Gdip.ahk ; https://autohotkey.com/boards/viewtopic.php?f=6&t=6517
Width :=A_ScreenWidth, Height := A_ScreenHeight Gui, 1: +E0x20 +Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs Gui, 1: Show, NA hwnd1 := WinExist() OnExit, Exit
If !pToken := Gdip_Startup() { MsgBox, 48, gdiplus error!, Gdiplus failed to start. . Please ensure you have gdiplus on your system ExitApp }
hbm := CreateDIBSection(Width, Height) hdc := CreateCompatibleDC() obm := SelectObject(hdc, hbm) G := Gdip_GraphicsFromHDC(hdc) Gdip_SetSmoothingMode(G, 4) pBrush := Gdip_BrushCreateSolid(0xFF6495ED) pPen := Gdip_CreatePen(0xff000000, 3)
- ---------------------------------
LL := 165 Cx := Floor(A_ScreenWidth/2) Cy := Floor(A_ScreenHeight/2) phi := 54
- ---------------------------------
loop, 5 { theta := abs(180-144-phi) p1x := Floor(Cx + LL * Cos(phi * 0.01745329252)) p1y := Floor(Cy + LL * Sin(phi * 0.01745329252)) p2x := Floor(Cx - LL * Cos(theta * 0.01745329252)) p2y := Floor(Cy - LL * Sin(theta * 0.01745329252)) phi+= 72 Gdip_FillPolygon(G, pBrush, p1x "," p1y "|" Cx "," Cy "|" p2x "," p2y) } loop, 5 { theta := abs(180-144-phi) p1x := Floor(Cx + LL * Cos(phi * 0.01745329252)) p1y := Floor(Cy + LL * Sin(phi * 0.01745329252)) p2x := Floor(Cx - LL * Cos(theta * 0.01745329252)) p2y := Floor(Cy - LL * Sin(theta * 0.01745329252)) phi+= 72 Gdip_DrawLines(G, pPen, p1x "," p1y "|" p2x "," p2y ) ; "|" Cx "," Cy ) } UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height) Gdip_DeleteBrush(pBrush) SelectObject(hdc, obm) DeleteObject(hbm) DeleteDC(hdc) Gdip_DeleteGraphics(G) return
- ----------------------------------------------------------------------
Esc:: Exit: Gdip_Shutdown(pToken) ExitApp Return</lang>
C
Interactive program which takes the side lengths of the pentagram's core, it's arms and the colours for filling the background, drawing the figure and then filling it in. Requires the WinBGIm library.
<lang C>#include<graphics.h>
- include<stdio.h>
- include<math.h>
- define pi M_PI
int main(){
char colourNames[][14] = { "BLACK", "BLUE", "GREEN", "CYAN", "RED", "MAGENTA", "BROWN", "LIGHTGRAY", "DARKGRAY",
"LIGHTBLUE", "LIGHTGREEN", "LIGHTCYAN", "LIGHTRED", "LIGHTMAGENTA", "YELLOW", "WHITE" };
int stroke=0,fill=0,back=0,i;
double centerX = 300,centerY = 300,coreSide,armLength,pentaLength;
printf("Enter core pentagon side length : "); scanf("%lf",&coreSide);
printf("Enter pentagram arm length : "); scanf("%lf",&armLength);
printf("Available colours are :\n");
for(i=0;i<16;i++){ printf("%d. %s\t",i+1,colourNames[i]); if((i+1) % 3 == 0){ printf("\n"); } }
while(stroke==fill && fill==back){ printf("\nEnter three diffrenet options for stroke, fill and background : "); scanf("%d%d%d",&stroke,&fill,&back); }
pentaLength = coreSide/(2 * tan(pi/5)) + sqrt(armLength*armLength - coreSide*coreSide/4);
initwindow(2*centerX,2*centerY,"Pentagram");
setcolor(stroke-1);
setfillstyle(SOLID_FILL,back-1);
bar(0,0,2*centerX,2*centerY);
floodfill(centerX,centerY,back-1);
setfillstyle(SOLID_FILL,fill-1);
for(i=0;i<5;i++){ line(centerX + coreSide*cos(i*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin(i*2*pi/5)/(2*sin(pi/5)),centerX + coreSide*cos((i+1)*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin((i+1)*2*pi/5)/(2*sin(pi/5))); line(centerX + coreSide*cos(i*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin(i*2*pi/5)/(2*sin(pi/5)),centerX + pentaLength*cos(i*2*pi/5 + pi/5),centerY + pentaLength*sin(i*2*pi/5 + pi/5)); line(centerX + coreSide*cos((i+1)*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin((i+1)*2*pi/5)/(2*sin(pi/5)),centerX + pentaLength*cos(i*2*pi/5 + pi/5),centerY + pentaLength*sin(i*2*pi/5 + pi/5));
floodfill(centerX + coreSide*cos(i*2*pi/5 + pi/10)/(2*sin(pi/5)),centerY + coreSide*sin(i*2*pi/5 + pi/10)/(2*sin(pi/5)),stroke-1); }
floodfill(centerX,centerY,stroke-1);
getch();
closegraph(); } </lang>
EasyLang
Run it <lang>floatvars xp = 10 yp = 40 linewidth 2 move xp yp while angle > -720
x = xp + cos angle * 80 y = yp + sin -angle * 80 line x y f[] &= x f[] &= y xp = x yp = y angle -= 144
. color 900 fill f[]</lang>
Go
<lang go>package main
import (
"github.com/fogleman/gg" "math"
)
func Pentagram(x, y, r float64) []gg.Point {
points := make([]gg.Point, 5)
for i := 0; i < 5; i++ {
fi := float64(i)
angle := 2*math.Pi*fi/5 - math.Pi/2
points[i] = gg.Point{x + r*math.Cos(angle), y + r*math.Sin(angle)}
}
return points
}
func main() {
points := Pentagram(320, 320, 250)
dc := gg.NewContext(640, 640)
dc.SetRGB(1, 1, 1) // White
dc.Clear()
for i := 0; i <= 5; i++ {
index := (i * 2) % 5
p := points[index]
dc.LineTo(p.X, p.Y)
}
dc.SetHexColor("#6495ED") // Cornflower Blue
dc.SetFillRule(gg.FillRuleWinding)
dc.FillPreserve()
dc.SetRGB(0, 0, 0) // Black
dc.SetLineWidth(5)
dc.Stroke()
dc.SavePNG("pentagram.png")
}</lang>
- Output:
The image produced is similar to that of the Java entry.
Haskell
This uses the Diagrams library to create an SVG drawing. Compiling, then running it like:
pentagram -w 400 -o pentagram_hs.svg
creates a 400x400 SVG file. <lang haskell>-- Extract the vertices of a pentagon, re-ordering them so that drawing lines -- from one to the next forms a pentagram. Set the line's thickness and its -- colour, as well as the fill and background colours. Make the background a -- bit larger than the pentagram.
import Diagrams.Prelude import Diagrams.Backend.SVG.CmdLine
pentagram = let [a, b, c, d, e] = trailVertices $ pentagon 1
in [a, c, e, b, d]
# fromVertices
# closeTrail
# strokeTrail
# lw ultraThick
# fc springgreen
# lc blue
# bgFrame 0.2 bisque
main = mainWith (pentagram :: Diagram B)</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Pentagra.bas" 110 OPTION ANGLE DEGREES 120 GRAPHICS HIRES 4 130 SET PALETTE BLUE,CYAN,YELLOW,BLACK 140 PLOT 640,700,ANGLE 288; 150 FOR I=1 TO 5 160 PLOT FORWARD 700,RIGHT 144; 170 NEXT 180 SET INK 3 190 SET BEAM OFF:PLOT 0,0,PAINT</lang>
J
Probably the simplest approach is:
<lang j>require'plot' plot j./2 1 o./180p_1 %~ 72*i. 6</lang>
This will give a pentagram with a blue border and a white interior.
Java
<lang java>import java.awt.*; import java.awt.geom.Path2D; import javax.swing.*;
public class Pentagram extends JPanel {
final double degrees144 = Math.toRadians(144);
public Pentagram() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
}
private void drawPentagram(Graphics2D g, int len, int x, int y,
Color fill, Color stroke) {
double angle = 0;
Path2D p = new Path2D.Float();
p.moveTo(x, y);
for (int i = 0; i < 5; i++) {
int x2 = x + (int) (Math.cos(angle) * len);
int y2 = y + (int) (Math.sin(-angle) * len);
p.lineTo(x2, y2);
x = x2;
y = y2;
angle -= degrees144;
}
p.closePath();
g.setColor(fill);
g.fill(p);
g.setColor(stroke);
g.draw(p);
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
g.setStroke(new BasicStroke(5, BasicStroke.CAP_ROUND, 0));
drawPentagram(g, 500, 70, 250, new Color(0x6495ED), Color.darkGray); }
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Pentagram");
f.setResizable(false);
f.add(new Pentagram(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}</lang>
Julia
<lang julia>using Luxor
function drawpentagram(path::AbstractString, w::Integer=1000, h::Integer=1000)
Drawing(h, w, path) origin() setline(16)
# To get a different color border from the fill, draw twice, first with fill, then without.
sethue("aqua")
star(0, 0, 500, 5, 0.39, 3pi/10, :fill)
sethue("navy")
verts = star(0, 0, 500, 5, 0.5, 3pi/10, vertices=true)
poly([verts[i] for i in [1,5,9,3,7,1]], :stroke)
finish()
preview()
end
drawpentagram("data/pentagram.png")</lang>
Kotlin
<lang scala>// version 1.1.2
import java.awt.* import java.awt.geom.Path2D import javax.swing.*
class Pentagram : JPanel() {
init {
preferredSize = Dimension(640, 640)
background = Color.white
}
private fun drawPentagram(g: Graphics2D, len: Int, x: Int, y: Int,
fill: Color, stroke: Color) {
var x2 = x.toDouble()
var y2 = y.toDouble()
var angle = 0.0
val p = Path2D.Float()
p.moveTo(x2, y2)
for (i in 0..4) {
x2 += Math.cos(angle) * len
y2 += Math.sin(-angle) * len
p.lineTo(x2, y2)
angle -= Math.toRadians(144.0)
}
p.closePath()
with(g) {
color = fill
fill(p)
color = stroke
draw(p)
}
}
override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON)
g.stroke = BasicStroke(5.0f, BasicStroke.CAP_ROUND, 0)
drawPentagram(g, 500, 70, 250, Color(0x6495ED), Color.darkGray)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
with(f) {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
title = "Pentagram"
isResizable = false
add(Pentagram(), BorderLayout.CENTER)
pack()
setLocationRelativeTo(null)
isVisible = true
}
}
}</lang>
Maple
<lang maple>with(geometry): RegularStarPolygon(middle, 5/2, point(c, 0, 0), 1): v := [seq(coordinates(i), i in DefinedAs(middle))]: pentagram := plottools[rotate](plottools[polygon](v), Pi/2): plots[display](pentagram, colour = yellow, axes = none);</lang>
- Output:
Note: Plot shown below is generated using interface(plotdevice = char);
C
C C
C C
C C
C C
CC CC
C C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCC C C CCCC
CCCCC C C CCCCC
CCCC C C CCCC
CCCCC C C CCCCC
CCCC CCCC
C CCCCC CCCCC C
C CCCC CCCC C
CC CCCCC CC
C CCCCC CCCCC C
C CCCC CCCC C
C CCCCC CCCCC C
C CCCC CCCC C
CCC CCC
Mathematica
<lang mathematica> Graphics[{
EdgeForm[Directive[Thickness[0.01], RGBColor[0, 0, 1]]],(*Edge coloring*) RGBColor[0.5, 0.5, .50], (*Fill coloring*) Polygon[AnglePath[Table[6 Pi/5, 5]]]} ]
</lang>
ooRexx
<lang oorexx>/* REXX ***************************************************************
- Create a BMP file showing a pentagram
- /
pentagram='pentagram.bmp' 'erase' pentagram s='424d4600000000000000360000002800000038000000280000000100180000000000'X s=s'1000000000000000000000000000000000000000'x Say 'sl='length(s) z.0=0 white='ffffff'x red ='00ff00'x green='ff0000'x blue ='0000ff'x rd6=copies(rd,6) m=133 m=80 n=80 hor=m*8 /* 56 */ ver=n*8 /* 40 */ Say 'hor='hor Say 'ver='ver Say 'sl='length(s) s=overlay(lend(hor),s,19,4) s=overlay(lend(ver),s,23,4) Say 'sl='length(s) z.=copies('ffffff'x,3192%3) z.=copies('ffffff'x,8*m) z.0=648 s72 =RxCalcsin(72,,'D') c72 =RxCalccos(72,,'D') s144=RxCalcsin(144,,'D') c144=RxCalccos(144,,'D') xm=300 ym=300 r=200 p.0x.1=xm p.0y.1=ym+r p.0x.2=format(xm+r*s72,3,0) p.0y.2=format(ym+r*c72,3,0) p.0x.3=format(xm+r*s144,3,0) p.0y.3=format(ym+r*c144,3,0) p.0x.4=format(xm-r*s144,3,0) p.0y.4=p.0y.3 p.0x.5=format(xm-r*s72,3,0) p.0y.5=p.0y.2 Do i=1 To 5
Say p.0x.i p.0y.i End
Call line p.0x.1,p.0y.1,p.0x.3,p.0y.3 Call line p.0x.1,p.0y.1,p.0x.4,p.0y.4 Call line p.0x.2,p.0y.2,p.0x.4,p.0y.4 Call line p.0x.2,p.0y.2,p.0x.5,p.0y.5 Call line p.0x.3,p.0y.3,p.0x.5,p.0y.5
Do i=1 To z.0
s=s||z.i End
Call lineout pentagram,s Call lineout pentagram Exit
lend: Return reverse(d2c(arg(1),4))
line: Procedure Expose z. red green blue Parse Arg x0, y0, x1, y1 Say 'line' x0 y0 x1 y1 dx = abs(x1-x0) dy = abs(y1-y0) if x0 < x1 then sx = 1
else sx = -1
if y0 < y1 then sy = 1
else sy = -1
err = dx-dy
Do Forever
xxx=x0*3+2 Do yy=y0-1 To y0+1 z.yy=overlay(copies(blue,5),z.yy,xxx) End if x0 = x1 & y0 = y1 Then Leave e2 = 2*err if e2 > -dy then do err = err - dy x0 = x0 + sx end if e2 < dx then do err = err + dx y0 = y0 + sy end end
Return
- requires RxMath Library</lang>
Perl
<lang perl>use SVG;
my $tau = 2 * 4*atan2(1, 1); my $dim = 200; my $sides = 5;
for $v (0, 2, 4, 1, 3, 0) {
push @vx, 0.9 * $dim * cos($tau * $v / $sides); push @vy, 0.9 * $dim * sin($tau * $v / $sides);
}
my $svg= SVG->new( width => 2*$dim, height => 2*$dim);
my $points = $svg->get_path(
x => \@vx, y => \@vy, -type => 'polyline',
);
$svg->rect (
width => "100%",
height => "100%",
style => {
'fill' => 'bisque'
}
);
$svg->polyline (
%$points,
style => {
'fill' => 'seashell',
'stroke' => 'blue',
'stroke-width' => 3,
},
transform => "translate($dim,$dim) rotate(-18)"
);
open $fh, '>', 'pentagram.svg'; print $fh $svg->xmlify(-namespace=>'svg'); close $fh;</lang> Pentagram (offsite image)
Perl 6
Generate an SVG file to STDOUT. Redirect to a file to capture and display it. <lang perl6>use SVG;
constant $dim = 200; constant $sides = 5;
my @vertices = map { 0.9 * $dim * cis($_ * τ / $sides) }, ^$sides;
my @points = map |*.reals.fmt("%0.3f"),
flat @vertices[0, 2 ... *], @vertices[1, 3 ... *], @vertices[0];
say SVG.serialize(
svg => [
:width($dim*2), :height($dim*2),
:rect[:width<100%>, :height<100%>, :style<fill:bisque;>],
:polyline[ :points(@points.join: ','),
:style("stroke:blue; stroke-width:3; fill:seashell;"),
:transform("translate($dim,$dim) rotate(-90)")
],
],
);</lang> See Pentagram (offsite svg image)
Ever wondered what a regular 7 sided star looks like? Change $sides to 7 and re-run. See Heptagram
Phix
Resizable and optionally rotating gui (desktop) version <lang Phix>-- demo\rosetta\Pentagram.exw include pGUI.e
Ihandle dlg, canvas, timer cdCanvas cddbuffer, cdcanvas
integer rot = 0 enum FILL,BORDER constant colours = {CD_BLUE,CD_RED},
modes = {CD_FILL,CD_CLOSED_LINES}
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE"),
cx = floor(w/2),
cy = floor(h/2),
r = floor(min(cx,cy)*0.9)
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
cdCanvasSetFillMode(cddbuffer, CD_WINDING)
cdCanvasSetLineWidth(cddbuffer, round(radius/100)+1)
for mode=FILL to BORDER do
cdCanvasSetForeground(cddbuffer,colours[mode])
cdCanvasBegin(cddbuffer,modes[mode])
for a=90 to 666 by 144 do
atom ra = (a+rot)*CD_DEG2RAD,
x = r*cos(ra)+cx,
y = r*sin(ra)+cy
cdCanvasVertex(cddbuffer, x, y)
end for
cdCanvasEnd(cddbuffer)
end for
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, CD_WHITE) cdCanvasSetForeground(cddbuffer, CD_GRAY) return IUP_DEFAULT
end function
function timer_cb(Ihandle /*ih*/)
rot = mod(rot+359,360) IupRedraw(canvas) return IUP_IGNORE
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if c=' ' then
IupSetInt(timer,"RUN",not IupGetInt(timer,"RUN"))
end if
return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "640x640")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Pentagram")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
timer = IupTimer(Icallback("timer_cb"), 80, active:=false)
IupMainLoop()
IupClose()
end procedure
main()</lang> And a quick svg version
<lang Phix>constant HDR = """ <?xml version="1.0" standalone="no" ?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd"> <svg height="%d" width="%d" style="" xmlns="http://www.w3.org/2000/svg"> <rect height="100%%" width="100%%" style="fill:black;" /> """ constant LINE = """ <polyline points="%s" style="fill:blue; stroke:white; stroke-width:3;" transform="translate(%d, %d) rotate(-18)" /> """
function pentagram(integer dim=200, sides=5)
sequence v = repeat(0,sides)
for i=1 to sides do
atom theta = PI*2*(i-1)/5,
x = cos(theta)*dim,
y = sin(theta)*dim
v[i] = {sprintf("%.3f",x),
sprintf("%.3f",y)}
end for
v = append(v,v[1])
sequence q = {}
for i=1 to length(v) by 2 do
q &= v[i]
end for
for i=2 to length(v) by 2 do
q &= v[i]
end for
string res = sprintf(HDR,dim*2)
res &= sprintf(LINE,{join(q),dim,dim})
res &= "</svg>\n"
return res
end function
puts(1,pentagram())</lang> Output identical to sidef
PostScript
<lang postscript>%!PS-Adobe-3.0 EPSF %%BoundingBox: 0 0 200 600
/n 5 def % 5-star; can be set to other odd numbers
/s { gsave } def /r { grestore } def /g { .7 setgray } def /t { 100 exch translate } def /p { 180 90 n div sub rotate 0 0 moveto n { 0 160 rlineto 180 180 n div sub rotate } repeat closepath } def
s 570 t p s g eofill r stroke r % even-odd fill s 370 t p s g fill r stroke r % non-zero fill s 170 t p s 2 setlinewidth stroke r g fill r % non-zero, but hide inner strokes
%%EOF</lang>
The following isn't exactly what the task asks for, but it's kind of fun if you have a PS interpreter that progressively updates. The program draws a lot of stars, so it's extremely likely that some of them are pentagrams... <lang postscript>%!PS-Adobe-3.0 EPSF %%BoundingBox: 0 0 400 400
% randomly choose from 5- to 35-stars /maxpoint 35 def /minpoint 5 def /maxradius 30 def
/rnd1 { rand 16#80000000 div } def /rnd { rnd1 mul} def /rndi { 2 index sub rnd1 mul 1 index div cvi mul add} def /line { rotate 0 rlineto } def
/star { gsave /n minpoint 2 maxpoint rndi def /r maxradius rnd def /a 180 180 n div sub def /b 360 a n mul sub n div def
400 rnd 400 rnd translate 360 rnd rotate 0 0 moveto n { r a line r b line } repeat closepath rnd1 rnd1 rnd1 3 { 2 index 1 exch sub } repeat gsave setrgbcolor fill grestore setrgbcolor stroke grestore } def
0 setlinewidth 2000 {star} repeat showpage %%EOF</lang>
Python
<lang python>import turtle
turtle.bgcolor("green") t = turtle.Turtle() t.color("red", "blue") t.begin_fill() for i in range(0, 5):
t.forward(200) t.right(144)
t.end_fill()</lang>
R
Very simple approach, <lang R>p <- cbind(x = c(0, 1, 2,-0.5 , 2.5 ,0),
y = c(0, 1, 0,0.6, 0.6,0))
plot(p) lines(p)</lang>
Using circle equation
A better more accurate approach utilising equation of a circle using polar coordinates.[1] 5 points are required to draw a pentagram. a circle with centre coordinates x=10 and y=10 with radius 10 was chosen for this example. In order to find 5 equal points circle needs to be divided by 5 i.e 360/5 = 72 each point on the circumference is 72 degrees apart, 5 points on the circles circumference are calculated and than plotted and line drawn in-between to produce pentagram <lang rsplus>#Circle equation
- x = r*cos(angle) + centre_x
- y = r*sin(angle) + centre_y
- centre points
centre_x = 10 centre_y = 10
- radius
r = 10
deg2rad <- function(d){
return((d*pi)/180)
} #Converts Degrees to radians X_coord <- function(r=10,centre_x=10,angle) #Finds Xcoordinate on the circumference {
return(r*cos(deg2rad(angle)) + centre_x)
} Y_coord <- function(r=10,centre_y=10,angle) #Finds Ycoordinate on the circumference {
return(r*sin(deg2rad(angle)) + centre_x)
}
- series of angles after dividing the circle in to 5
angles <- list() for(i in 1:5) {
angles[i] <- 72*i
} angles <- unlist(angles) #flattening the list
for(i in seq_along(angles)){
print(i)
print(angles[i])
if(i == 1)
{
coordinates <-
cbind(c(
x = X_coord(angle = angles[i]),
y = Y_coord(angle = angles[i]))
)
}
else{
coordinates <- cbind(coordinates,cbind(c(
x = X_coord(angle = angles[i]),
y = Y_coord(angle = angles[i]))))
}
} plot(xlim = c(0,30), ylim = c(0,30),x = coordinates[1,], y=coordinates[2,])
polygon(x = coordinates[1,c(1,3,5,2,4,1)],
y=coordinates[2,c(1,3,5,2,4,1)],
col = "#1b98e0",
border = "red",
lwd = 5)</lang>
Racket
<lang racket>#lang racket (require 2htdp/image)
(overlay
(star-polygon 100 5 2 "outline" (make-pen "blue" 4 "solid" "round" "round")) (star-polygon 100 5 2 "solid" "cyan"))</lang>
REXX
<lang rexx>/* REXX ***************************************************************
- Create a BMP file showing a pentagram
- /
Parse Version v If pos('Regina',v)>0 Then
pentagram='pentagrama.bmp'
Else
pentagram='pentagramx.bmp'
'erase' pentagram s='424d4600000000000000360000002800000038000000280000000100180000000000'X||,
'1000000000000000000000000000000000000000'x
Say 'sl='length(s) z.0=0 white='ffffff'x red ='00ff00'x green='ff0000'x blue ='0000ff'x rd6=copies(rd,6) m=133 m=80 n=80 hor=m*8 /* 56 */ ver=n*8 /* 40 */ Say 'hor='hor Say 'ver='ver Say 'sl='length(s) s=overlay(lend(hor),s,19,4) s=overlay(lend(ver),s,23,4) Say 'sl='length(s) z.=copies('ffffff'x,3192%3) z.=copies('ffffff'x,8*m) z.0=648 pi_5=2*3.14159/5 s72 =sin(pi_5 ) c72 =cos(pi_5 ) s144=sin(pi_5*2) c144=cos(pi_5*2) xm=300 ym=300 r=200 p.0x.1=xm p.0y.1=ym+r
p.0x.2=format(xm+r*s72,3,0) p.0y.2=format(ym+r*c72,3,0) p.0x.3=format(xm+r*s144,3,0) p.0y.3=format(ym+r*c144,3,0) p.0x.4=format(xm-r*s144,3,0) p.0y.4=p.0y.3 p.0x.5=format(xm-r*s72,3,0) p.0y.5=p.0y.2 Do i=1 To 5
Say p.0x.i p.0y.i End
Call line p.0x.1,p.0y.1,p.0x.3,p.0y.3 Call line p.0x.1,p.0y.1,p.0x.4,p.0y.4 Call line p.0x.2,p.0y.2,p.0x.4,p.0y.4 Call line p.0x.2,p.0y.2,p.0x.5,p.0y.5 Call line p.0x.3,p.0y.3,p.0x.5,p.0y.5
Do i=1 To z.0
s=s||z.i End
Call lineout pentagram,s Call lineout pentagram Exit
lend: Return reverse(d2c(arg(1),4))
line: Procedure Expose z. red green blue Parse Arg x0, y0, x1, y1 Say 'line' x0 y0 x1 y1 dx = abs(x1-x0) dy = abs(y1-y0) if x0 < x1 then sx = 1
else sx = -1
if y0 < y1 then sy = 1
else sy = -1
err = dx-dy
Do Forever
xxx=x0*3+2 Do yy=y0-1 To y0+1 z.yy=overlay(copies(blue,5),z.yy,xxx) End if x0 = x1 & y0 = y1 Then Leave e2 = 2*err if e2 > -dy then do err = err - dy x0 = x0 + sx end if e2 < dx then do err = err + dx y0 = y0 + sy end end
Return
sin: Procedure /* REXX ****************************************************************
- Return sin(x<,p>) -- with the specified precision
- /
Parse Arg x,prec If prec= Then prec=9 Numeric Digits (2*prec) Numeric Fuzz 3 pi=3.14159 Do While x>pi x=x-pi End Do While x<-pi x=x+pi End o=x u=1 r=x Do i=3 By 2 ra=r o=-o*x*x u=u*i*(i-1) r=r+(o/u) If r=ra Then Leave End Numeric Digits prec Return r+0
cos: Procedure /* REXX ****************************************************************
- Return cos(x) -- with specified precision
- /
Parse Arg x,prec If prec= Then prec=9 Numeric Digits (2*prec) Numeric Fuzz 3 o=1 u=1 r=1 Do i=1 By 2 ra=r o=-o*x*x u=u*i*(i+1) r=r+(o/u) If r=ra Then Leave End Numeric Digits prec Return r+0
sqrt: Procedure /* REXX ***************************************************************
- EXEC to calculate the square root of a = 2 with high precision
- /
Parse Arg x,prec If prec<9 Then prec=9 prec1=2*prec eps=10**(-prec1) k = 1 Numeric Digits 3 r0= x r = 1 Do i=1 By 1 Until r=r0 | (abs(r*r-x)<eps) r0 = r r = (r + x/r) / 2 k = min(prec1,2*k) Numeric Digits (k + 5) End Numeric Digits prec Return r+0</lang>
Ring
<lang ring>
- Project : Pentagram
load "guilib.ring"
paint = null
new qapp
{
win1 = new qwidget() {
setwindowtitle("Pentagram")
setgeometry(100,100,500,600)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(5)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
nn = 165
cx = 800
cy = 600
phi = 54
color = new qcolor()
color.setrgb(0, 0, 255,255)
mybrush = new qbrush() {setstyle(1) setcolor(color)}
setbrush(mybrush)
for n = 1 to 5
theta = fabs(180-144-phi)
p1x = floor(cx + nn * cos(phi * 0.01745329252)) p1y = floor(cy + nn * sin(phi * 0.01745329252)) p2x = floor(cx - nn * cos(theta * 0.01745329252)) p2y = floor(cy - nn * sin(theta * 0.01745329252)) phi+= 72 drawpolygon([[p1x,p1y],[cx,cy],[p2x,p2y]],0)
next
endpaint()
}
label1 { setpicture(p1) show() }
return
</lang> Output:
https://www.dropbox.com/s/znbcsoatlc00n4w/Pentagram.jpg?dl=0
Scala
Java Swing Interoperability
<lang Scala>import java.awt._ import java.awt.geom.Path2D
import javax.swing._
object Pentagram extends App {
SwingUtilities.invokeLater(() =>
new JFrame("Pentagram") {
class Pentagram extends JPanel {
setPreferredSize(new Dimension(640, 640))
setBackground(Color.white)
final private val degrees144 = Math.toRadians(144)
override def paintComponent(gg: Graphics): Unit = {
val g = gg.asInstanceOf[Graphics2D]
def drawPentagram(g: Graphics2D, x: Int, y: Int, fill: Color): Unit = {
var (_x, _y, angle) = (x, y, 0.0)
val p = new Path2D.Float
p.moveTo(_x, _y)
for (i <- 0 until 5) {
val (x2, y2) = (_x + (Math.cos(angle) * 500).toInt, _y + (Math.sin(-angle) * 500).toInt)
p.lineTo(x2, y2)
_x = x2
_y = y2
angle -= degrees144
}
p.closePath()
g.setColor(fill)
g.fill(p)
g.setColor(Color.darkGray)
g.draw(p)
}
super.paintComponent(gg)
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.setStroke(new BasicStroke(5, BasicStroke.CAP_ROUND, BasicStroke.JOIN_MITER))
drawPentagram(g, 70, 250, new Color(0x6495ED))
}
}
add(new Pentagram, BorderLayout.CENTER)
pack()
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
}
)
}</lang>
Sidef
Generates a SVG image to STDOUT. <lang ruby>func pentagram(dim=200, sides=5) {
var pentagram = <<-EOT <?xml version="1.0" standalone="no" ?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd"> <svg height="#{dim*2}" width="#{dim*2}" style="" xmlns="http://www.w3.org/2000/svg"> <rect height="100%" width="100%" style="fill:black;" /> EOT
func cis(x) {
cos(x) + sin(x).i
}
func pline(q) {
<<-EOT
<polyline points="#{[q..., q[0], q[1]].map{|n| '%0.3f' % n }.join(' ')}"
style="fill:blue; stroke:white; stroke-width:3;"
transform="translate(#{dim}, #{dim}) rotate(-18)" />
EOT
}
var v = sides.range.map {|k| 0.9 * dim * cis(k * Num.tau / sides) }
pentagram += pline([v[range(0, v.end, 2)], v[range(1, v.end, 2)]].map{.reals})
pentagram += '</svg>'
return pentagram
}
say pentagram()</lang>
- Output:
<?xml version="1.0" standalone="no" ?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd"> <svg height="400" width="400" style="" xmlns="http://www.w3.org/2000/svg"> <rect height="100%" width="100%" style="fill:black;" /> <polyline points="180.000 0.000 -145.623 105.801 55.623 -171.190 55.623 171.190 -145.623 -105.801 180.000 0.000" style="fill:blue; stroke:white; stroke-width:3;" transform="translate(200, 200) rotate(-18)" /> </svg>
SPL
<lang spl>mx,my = #.scrsize() xc = mx/2 yc = my/2 mr = #.min(mx,my)/3
- .angle(#.degrees)
- .drawcolor(1,0,0)
- .drawsize(10)
> r, mr..0,-1
#.drawline(xc,yc-r,xc,yc-r) > a, 54..630,144 #.drawline(r*#.cos(a)+xc,r*#.sin(a)+yc) < #.drawcolor(1,1,0) #.drawsize(1)
<</lang>
Tcl
This implementation draws a simple pentagram on a Canvas widget.
<lang Tcl> package require Tk 8.6 ;# lmap is new in Tcl/Tk 8.6
set pi [expr 4*atan(1)]
pack [canvas .c] -expand yes -fill both ;# create the canvas
update ;# draw everything so the dimensions are accurate
set w [winfo width .c] ;# calculate appropriate dimensions set h [winfo height .c] set r [expr {min($w,$h) * 0.45}]
set points [lmap n {0 1 2 3 4 5} {
set n [expr {$n * 2}]
set y [expr {sin($pi * 2 * $n / 5) * $r + $h / 2}]
set x [expr {cos($pi * 2 * $n / 5) * $r + $w / 2}]
list $x $y
}] set points [concat {*}$points] ;# flatten the list
puts [.c create line $points]
- a fun reader exercise is to make the shape respond to mouse events,
- or animate it!
</lang>
VBA
<lang vb>Sub pentagram()
With ActiveSheet.Shapes.AddShape(msoShape5pointStar, 10, 10, 400, 400)
.Fill.ForeColor.RGB = RGB(255, 0, 0)
.Line.Weight = 3
.Line.ForeColor.RGB = RGB(0, 0, 255)
End With
End Sub</lang>
zkl
Generate an SVG file to STDOUT. Redirect to a file to capture and display it. <lang zkl>const DIM=200, SIDES=5, A=360/SIDES, R=DIM.toFloat(); vs:=[0.0..360-A,A].apply("toRad"); // angles of vertices
- <<<
0'|<?xml version="1.0" standalone="no" ?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd"> <svg height="%d" width="%d" style="" xmlns="http://www.w3.org/2000/svg"> <rect height="100%" width="100%" style="fill:bisque;" />|
- <<<
.fmt(DIM*2, DIM*2).println();
var vertices=vs.pump(List,fcn(a){ R.toRectangular(a) }); //( (x,y), (x,y)... SIDES.pump(String,pline).println(); // the line pairs that draw the pentagram
fcn pline(n){ a:=(n + 2)%SIDES; // (n,a) are the endpoints of the right leg
pts:=String("\"", ("% 0.3f,% 0.3f "*2), "\" "); // two points
vs:='wrap(){ T(n,a).pump(List,vertices.get).flatten() }; //(x,y, x,y)
String(
(0'|<polyline points=| + pts).fmt(vs().xplode()),
0'|style="fill:seashell; stroke:blue; stroke-width:3;" |,
0'|transform="translate(%d,%d) rotate(-18)"|.fmt(DIM,DIM),
" />\n"
);
} println("</svg>");</lang>
- Output:
$ zkl bbb > pentagram.svg $ cat pentagram.svg <?xml version="1.0" standalone="no" ?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd"> <svg height="400" width="400" style="" xmlns="http://www.w3.org/2000/svg"> <rect height="100%" width="100%" style="fill:bisque;" /> <polyline points=" 200.000, 0.000 -161.803, 117.557 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" /> <polyline points=" 61.803, 190.211 -161.803,-117.557 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" /> <polyline points="-161.803, 117.557 61.803,-190.211 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" /> <polyline points="-161.803,-117.557 200.000, 0.000 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" /> <polyline points=" 61.803,-190.211 61.803, 190.211 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" /> </svg>
Until local image uploading is re-enabled, see this image.
