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
Action!
INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit
DEFINE REALPTR="CARD"
TYPE PointR=[REALPTR x,y]
INT ARRAY SinTab=[
0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
147 150 154 158 161 165 168 171 175 178 181 184 187 190
193 196 199 202 204 207 210 212 215 217 219 222 224 226
228 230 232 234 236 237 239 241 242 243 245 246 247 248
249 250 251 252 253 254 254 255 255 255 256 256 256 256]
INT FUNC Sin(INT a)
WHILE a<0 DO a==+360 OD
WHILE a>360 DO a==-360 OD
IF a<=90 THEN
RETURN (SinTab(a))
ELSEIF a<=180 THEN
RETURN (SinTab(180-a))
ELSEIF a<=270 THEN
RETURN (-SinTab(a-180))
ELSE
RETURN (-SinTab(360-a))
FI
RETURN (0)
INT FUNC Cos(INT a)
RETURN (Sin(a-90))
PROC Det(REAL POINTER x1,y1,x2,y2,res)
REAL tmp1,tmp2
RealMult(x1,y2,tmp1)
RealMult(y1,x2,tmp2)
RealSub(tmp1,tmp2,res)
RETURN
BYTE FUNC IsZero(REAL POINTER a)
CHAR ARRAY s(10)
StrR(a,s)
IF s(0)=1 AND s(1)='0 THEN
RETURN (1)
FI
RETURN (0)
BYTE FUNC Intersection(PointR POINTER p1,p2,p3,p4,res)
REAL det1,det2,dx1,dx2,dy1,dy2,nom,denom
Det(p1.x,p1.y,p2.x,p2.y,det1)
Det(p3.x,p3.y,p4.x,p4.y,det2)
RealSub(p1.x,p2.x,dx1)
RealSub(p1.y,p2.y,dy1)
RealSub(p3.x,p4.x,dx2)
RealSub(p3.y,p4.y,dy2)
Det(dx1,dy1,dx2,dy2,denom)
IF IsZero(denom) THEN
RETURN (0)
FI
Det(det1,dx1,det2,dx2,nom)
RealDiv(nom,denom,res.x)
Det(det1,dy1,det2,dy2,nom)
RealDiv(nom,denom,res.y)
RETURN (1)
PROC FloodFill(BYTE x0,y0)
BYTE ARRAY xs(300),ys(300)
INT first,last
first=0 last=0
xs(first)=x0
ys(first)=y0
WHILE first<=last
DO
x0=xs(first) y0=ys(first)
first==+1
IF Locate(x0,y0)=0 THEN
Plot(x0,y0)
IF Locate(x0-1,y0)=0 THEN
last==+1 xs(last)=x0-1 ys(last)=y0
FI
IF Locate(x0+1,y0)=0 THEN
last==+1 xs(last)=x0+1 ys(last)=y0
FI
IF Locate(x0,y0-1)=0 THEN
last==+1 xs(last)=x0 ys(last)=y0-1
FI
IF Locate(x0,y0+1)=0 THEN
last==+1 xs(last)=x0 ys(last)=y0+1
FI
FI
OD
RETURN
PROC Pentagram(INT x0,y0,r,a0 BYTE c1,c2)
INT ARRAY xs(16),ys(16)
INT angle
BYTE i
PointR p1,p2,p3,p4,p
REAL p1x,p1y,p2x,p2y,p3x,p3y,p4x,p4y,px,py
p1.x=p1x p1.y=p1y
p2.x=p2x p2.y=p2y
p3.x=p3x p3.y=p3y
p4.x=p4x p4.y=p4y
p.x=px p.y=py
;outer points
angle=a0
FOR i=0 TO 4
DO
xs(i)=r*Sin(angle)/256+x0
ys(i)=r*Cos(angle)/256+y0
angle==+144
OD
;intersection points
FOR i=0 TO 4
DO
IntToReal(xs(i MOD 5),p1x)
IntToReal(ys(i MOD 5),p1y)
IntToReal(xs((1+i) MOD 5),p2x)
IntToReal(ys((1+i) MOD 5),p2y)
IntToReal(xs((2+i) MOD 5),p3x)
IntToReal(ys((2+i) MOD 5),p3y)
IntToReal(xs((3+i) MOD 5),p4x)
IntToReal(ys((3+i) MOD 5),p4y)
Intersection(p1,p2,p3,p4,p)
xs(5+i)=RealToInt(px)
ys(5+i)=RealToInt(py)
OD
;centers of triangles
FOR i=0 TO 4
DO
xs(10+i)=(xs(i)+xs(5+i)+xs(5+(i+2) MOD 5))/3
ys(10+i)=(ys(i)+ys(5+i)+ys(5+(i+2) MOD 5))/3
OD
;center of pentagon
xs(15)=0 ys(15)=0
FOR i=5 TO 9
DO
xs(15)==+xs(i)
ys(15)==+ys(i)
OD
xs(15)==/5 ys(15)==/5
;draw lines
COLOR=c1
FOR i=0 TO 5
DO
IF i=0 THEN
Plot(xs(i MOD 5),ys(i MOD 5))
ELSE
DrawTo(xs(i MOD 5),ys(i MOD 5))
FI
OD
;fill
COLOR=c2
FOR i=10 TO 15
DO
FloodFill(xs(i),ys(i))
OD
RETURN
PROC Main()
BYTE CH=$02FC
Graphics(7+16)
SetColor(0,8,4)
SetColor(1,8,8)
SetColor(2,8,12)
Pentagram(40,48,40,0,1,2)
Pentagram(119,48,40,15,2,3)
DO UNTIL CH#$FF OD
CH=$FF
RETURN- Output:
Screenshot from Atari 8-bit computer
Ada
with Ada.Numerics.Elementary_Functions;
with SDL.Video.Windows.Makers;
with SDL.Video.Renderers.Makers;
with SDL.Video.Rectangles;
with SDL.Events.Events;
procedure Pentagram is
Width : constant := 600;
Height : constant := 600;
Offset : constant := 300.0;
Radius : constant := 250.0;
use SDL.Video.Rectangles;
use SDL.C;
Window : SDL.Video.Windows.Window;
Renderer : SDL.Video.Renderers.Renderer;
Event : SDL.Events.Events.Events;
type Node_Id is mod 5;
Nodes : array (Node_Id) of Point;
procedure Calculate is
use Ada.Numerics.Elementary_Functions;
begin
for I in Nodes'Range loop
Nodes (I) := (X => int (Offset + Radius * Sin (Float (I), Cycle => 5.0)),
Y => int (Offset - Radius * Cos (Float (I), Cycle => 5.0)));
end loop;
end Calculate;
function Orient_2D (A, B, C : Point) return int is
((B.X - A.X) * (C.Y - A.Y) - (B.Y - A.Y) * (C.X - A.X));
procedure Fill is
Count : Natural;
begin
for Y in int (Offset - Radius) .. int (Offset + Radius) loop
for X in int (Offset - Radius) .. int (Offset + Radius) loop
Count := 0;
for Node in Nodes'Range loop
Count := Count +
(if Orient_2D (Nodes (Node), Nodes (Node + 2), (X, Y)) > 0 then 1 else 0);
end loop;
if Count in 4 .. 5 then
Renderer.Draw (Point => (X, Y));
end if;
end loop;
end loop;
end Fill;
procedure Draw_Outline is
begin
for Node in Nodes'Range loop
Renderer.Draw (Line => (Nodes (Node), Nodes (Node + 2)));
end loop;
end Draw_Outline;
procedure Wait is
use type SDL.Events.Event_Types;
begin
loop
SDL.Events.Events.Wait (Event);
exit when Event.Common.Event_Type = SDL.Events.Quit;
end loop;
end Wait;
begin
if not SDL.Initialise (Flags => SDL.Enable_Screen) then
return;
end if;
SDL.Video.Windows.Makers.Create (Win => Window,
Title => "Pentagram",
Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
Size => SDL.Positive_Sizes'(Width, Height),
Flags => 0);
SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface);
Renderer.Set_Draw_Colour ((0, 0, 0, 255));
Renderer.Fill (Rectangle => (0, 0, Width, Height));
Calculate;
Renderer.Set_Draw_Colour ((50, 50, 150, 255));
Fill;
Renderer.Set_Draw_Colour ((0, 220, 0, 255));
Draw_Outline;
Window.Update_Surface;
Wait;
Window.Finalize;
SDL.Finalise;
end Pentagram;
ALGOL 68
Outputs SVG to standard output - this can be saved as a .svg file and opened in a browser with SVG support or other SVG viewer.
BEGIN # draw a pentagram, using SVG #
OP SIND = ( REAL x )REAL: sin( x * pi / 180 );
OP COSD = ( REAL x )REAL: cos( x * pi / 180 );
PRIO FMT = 9;
OP FMT = ( REAL v, INT dp )STRING:
BEGIN
STRING result = IF ENTIER v = v
THEN whole( v, - dp * 16 )
ELSE fixed( v, - dp * 16, ABS dp )
FI;
INT v pos := LWB result;
WHILE result[ v pos ] = " " DO v pos +:= 1 OD;
result[ v pos : ]
END # FMT # ;
PROC point = ( REAL x, y )STRING: x FMT 2 + " " + y FMT 2;
PROC draw gram = ( INT width, height, vertices, REAL side, start x, start y, line width )VOID:
BEGIN
REAL angle = 360 / vertices;
print( ( "<svg xmlns='http://www.w3.org/2000/svg' width='"
, whole( width, 0 ), "' height='", whole( height, 0 ), "'>", newline
)
);
REAL x := start x, y := start y;
print( ( " <polygon points='", point( x, y ) ) );
REAL heading := angle;
TO vertices DO
x +:= side * COSD heading;
y +:= side * SIND heading;
print( ( " ", point( x, y ) ) );
heading -:= 180 -:= angle / 2
OD;
print( ( "'", newline ) );
print( ( " style='fill:#55cccc;stroke:#5555cc;stroke-width:" ) );
print( ( whole( line width, 0 ), "'/>", newline ) );
print( ( "</svg>", newline ) )
END # draw gram #;
draw gram( 500, 300, 5, 240, 150, 50, 3 )
ENDAutoHotkey
#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
BASIC
Applesoft BASIC
100 XO = 140
110 YO = 96
120 S = 90
130 B = 7
140 F = 6
150 C = 4
200 POKE 230,64
210 HCOLOR= B
220 HPLOT 0,0
230 CALL 62454
240 A = 49232
250 I = PEEK (A + 7) + PEEK (A + 2)
260 I = PEEK (A + 5) + PEEK (A)
300 SX = S
310 SY = S
320 PI = 3.1415926535
330 E = PI * 4
340 S = PI / 1.25
350 X = SIN (0)
360 Y = COS (0)
370 HCOLOR= F
380 PX = XO + X * SX
390 PY = YO - Y * SY
400 FOR I = 0 TO E STEP S
410 X = SIN (I)
420 Y = COS (I)
430 FOR J = 0 TO SX
440 HPLOT PX,PY TO XO + X * J,YO - Y * J
450 NEXT J
460 PX = XO + X * SX
470 PY = YO - Y * SY
480 NEXT I
500 HCOLOR= C
510 PX = XO + X * SX
520 PY = YO - Y * SY
600 FOR I = S TO E STEP S
610 X = SIN (I)
620 Y = COS (I)
630 HPLOT PX,PY TO XO + X * SX,YO - Y * SY
640 HPLOT PX + 1,PY TO XO + X * SX + 1,YO - Y * SY
650 HPLOT PX,PY + 1 TO XO + X * SX,YO - Y * SY + 1
660 HPLOT PX + 1,PY + 1 TO XO + X * SX + 1,YO - Y * SY + 1
670 PX = XO + X * SX
680 PY = YO - Y * SY
690 NEXT I
FreeBASIC
#define PI 4 * Atn(1)
#define E (PI * 4)
#define StepSize (PI / 1.25)
Const SCREEN_WIDTH = 400
Const SCREEN_HEIGHT = 400
Screenres SCREEN_WIDTH, SCREEN_HEIGHT, 8
Windowtitle "Pentagram in FreeBASIC"
Dim As Integer XO = SCREEN_WIDTH / 2
Dim As Integer YO = SCREEN_HEIGHT / 2
Dim As Integer scale = 150
Dim As Integer fillColor = 9
Dim As Integer contrastColor = 8
Pset (0, 0)
Dim As Double i, j, X, Y
Dim As Integer PX = XO, PY = YO
Dim As Integer SX = scale, SY = scale
' Draw the first part
For i = 0 To E Step StepSize
X = Sin(i)
Y = Cos(i)
For j = 0 To SX
Line (PX, PY)-(XO + X * j, YO - Y * j), fillColor
Next j
PX = XO + X * SX
PY = YO - Y * SY
Next i
' Draw the second part
For i = StepSize To E Step StepSize
X = Sin(i)
Y = Cos(i)
Line (PX, PY)-(XO + X * SX, YO - Y * SY), contrastColor
Line (PX + 1, PY)-(XO + X * SX + 1, YO - Y * SY), contrastColor
Line (PX, PY + 1)-(XO + X * SX, YO - Y * SY + 1), contrastColor
Line (PX + 1, PY + 1)-(XO + X * SX + 1, YO - Y * SY + 1), contrastColor
PX = XO + X * SX
PY = YO - Y * SY
Next i
Sleep
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,PAINTVBA
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
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.
#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();
}
Delphi
unit Main;
interface
uses
Winapi.Windows, Vcl.Graphics, Vcl.Forms, System.Math;
type
TForm1 = class(TForm)
procedure FormCreate(Sender: TObject);
procedure FormPaint(Sender: TObject);
private
procedure DrawPentagram(len, x, y: Integer; fill, stoke: TColor);
{ Private declarations }
public
{ Public declarations }
end;
var
Form1: TForm1;
degrees144: double;
degrees72: double;
degrees18: double;
implementation
{$R *.dfm}
procedure TForm1.FormCreate(Sender: TObject);
begin
ClientHeight := 640;
ClientWidth := 640;
degrees144 := DegToRad(144);
degrees72 := DegToRad(72);
degrees18 := DegToRad(18);
end;
procedure CreatePolygon(len, x, y, n: integer; ang: double; var points: TArray<TPoint>);
var
angle: Double;
index, i, x2, y2: Integer;
begin
angle := 0;
index := 0;
SetLength(points, n + 1);
points[index].Create(x, y);
for i := 1 to n do
begin
x2 := x + round(len * cos(angle));
y2 := y + round(len * sin(-angle));
x := x2;
y := y2;
angle := angle - ang;
points[index].Create(x2, y2);
inc(index);
end;
points[index].Create(points[0]);
end;
procedure TForm1.DrawPentagram(len, x, y: Integer; fill, stoke: TColor);
var
points, points_internal: TArray<TPoint>;
L, H: Integer;
begin
// Calc of sides for draw internal pollygon
// 2H+L = len -> 2H = len - L
// L = 2H*sin(36/2) (Pythagorean theorem)
// L = (len-L)sin(18)
// L = len*sin(18)/[1+sin(18)]
L := round(len * sin(degrees18) / (1 + sin(degrees18)));
// H = (len - L)/2
H := (len - L) div 2;
CreatePolygon(L, x + H, y, 5, degrees72, points_internal);
CreatePolygon(len, x, y, 5, degrees144, points);
with Canvas, Canvas.Brush do
begin
with pen do
begin
Color := stoke;
Style := psSolid;
Width := 5;
end;
Color := fill;
Polygon(points_internal);
Polygon(points);
end;
end;
procedure TForm1.FormPaint(Sender: TObject);
begin
with Canvas, Brush do
begin
Style := bsSolid;
Color := clWhite;
// fill background with white
FillRect(ClientRect);
end;
drawPentagram(500, 70, 250, $ED9564, clDkGray);
end;
end.
form code:
object Form1: TForm1
OnCreate = FormCreate
OnPaint = FormPaint
end
EasyLang
xp = 10
yp = 60
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
polygon f[]
FutureBasic
_window = 1
void local fn DrawInView
CFMutableArrayRef points = fn MutableArrayWithCapacity( 0 )
CGPoint ptA,ptB,ptC,ptD,ptE
float xo,yo, z, x,y, twoPi = 0.0174533
xo = 225
yo = 20
z = 340
ptA = fn CGPointMake( xo,yo)
x = xo - z*sin(18*TwoPi)
y = yo + z*cos(18*TwoPi)
ptB = fn CGPointMake( x,y)
ptE = fn CGPointMake( xo + z*sin(18*TwoPi),y)
x = ptB.x + z*cos(36*TwoPi)
y = ptB.y - z*sin(36*TwoPi)
ptC = fn CGPointMake( x,y)
x -= z
ptD = fn CGPointMake(x,y)
MutableArrayAddObject( points, fn ValueWithPoint( ptA ) )
MutableArrayAddObject( points, fn ValueWithPoint( ptB ) )
MutableArrayAddObject( points, fn ValueWithPoint( ptC ) )
MutableArrayAddObject( points, fn ValueWithPoint( ptD ) )
MutableArrayAddObject( points, fn ValueWithPoint( ptE ) )
MutableArrayAddObject( points, fn ValueWithPoint( ptA ) )
BezierPathStrokeFillPolygon( points, 2, fn ColorBlack, fn ColorSystemBlue )
end fn
void local fn BuildWindow
window _window, @"Pentagram", ( 0,0,450,400 )
WindowCenter(_window)
WindowSubclassContentView(_window)
ViewSetFlipped( _windowContentViewTag, YES )
ViewSetNeedsDisplay( _windowContentViewTag )
end fn
void local fn DoDialog( ev as long)
select ( ev )
case _viewDrawRect : fn DrawInView
end select
end fn
fn BuildWindow
on dialog fn DoDialog
HandleEventsGo
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")
}
- 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.
-- 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)
J
Probably the simplest approach is:
require'plot'
plot j./2 1 o./180p_1 %~ 144*i. 6
This will give a pentagram with a blue border and a white interior.
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);
});
}
}
jq
Works with gojq, the Go implementation of jq
This entry produces SVG output which, if placed in a file with suffix .svg, can be viewed directly in most browsers.
Notice that the size of an appropriate SVG viewBox is computed.
# Input: {svg, minx, miny, maxx, maxy}
def svg:
# viewBox = <min-x> <min-y> <width> <height>
"<svg viewBox='\(.minx - 4|floor) \(.miny - 4 |floor) \(6 + .maxx - .minx|ceil) \(6 + .maxy - .miny|ceil)'",
" preserveAspectRatio='xMinYmin meet'",
" xmlns='http://www.w3.org/2000/svg' >",
.svg,
"</svg>" ;
# Input: an array of [x,y] points
def minmax:
{minx: (map(.[0])|min),
miny: (map(.[1])|min),
maxx: (map(.[0])|max),
maxy: (map(.[1])|max)} ;
# Input: an array of [x,y] points
def Polyline($fill; $stroke; $transform):
def rnd: 1000*.|round/1000;
def linearize: map( map(rnd) | join(" ") ) | join(", ");
"<polyline points='"
+ linearize
+ "'\n style='fill:\($fill); stroke: \($stroke); stroke-width:3;'"
+ "\n transform='\($transform)' />" ;
# Output: {minx, miny, maxx, maxy, svg}
def pentagram($dim):
(8 * (1|atan)) as $tau
| 5 as $sides
| [ (0, 2, 4, 1, 3, 0)
| [ 0.9 * $dim * (($tau * $v / $sides) | cos),
0.9 * $dim * (($tau * $v / $sides) | sin) ] ]
| minmax
+ {svg: Polyline("seashell"; "blue"; "rotate(-18)" )} ;
pentagram(200)
| svg- Output:
<svg viewBox='-150 -176 332 349'
preserveAspectRatio='xMinYmin meet'
xmlns='http://www.w3.org/2000/svg' >
<polyline points='180 0, -145.623 105.801, 55.623 -171.19, 55.623 171.19, -145.623 -105.801, 180 0'
style='fill:seashell; stroke: blue; stroke-width:3;'
transform='rotate(-18)' />
</svg>
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")
Kotlin
// 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
}
}
}
Lua
Using the Bitmap class here, with an ASCII pixel representation, then extending with line() as here, then extending with floodfill() as here, then extending further..
local cos, sin, floor, pi = math.cos, math.sin, math.floor, math.pi
function Bitmap:render()
for y = 1, self.height do
print(table.concat(self.pixels[y]))
end
end
function Bitmap:pentagram(x, y, radius, rotation, outlcolor, fillcolor)
local function pxy(i) return x+radius*cos(i*pi*2/5+rotation), y+radius*sin(i*pi*2/5+rotation) end
local x1, y1 = pxy(0)
for i = 1, 5 do
local x2, y2 = pxy(i*2) -- btw: pxy(i) ==> pentagon
self:line(floor(x1*2), floor(y1), floor(x2*2), floor(y2), outlcolor)
x1, y1 = x2, y2
end
self:floodfill(floor(x*2), floor(y), fillcolor)
radius = radius / 2
for i = 1, 5 do
x1, y1 = pxy(i)
self:floodfill(floor(x1*2), floor(y1), fillcolor)
end
end
bitmap = Bitmap(40*2,40)
bitmap:clear(".")
bitmap:pentagram(20, 22, 20, -pi/2, "@", '+')
bitmap:render()
- Output:
................................................................................ ................................................................................ .......................................@@....................................... ......................................@++@...................................... ......................................@++@...................................... .....................................@++++@..................................... ....................................@++++++@.................................... ....................................@++++++@.................................... ...................................@++++++++@................................... ...................................@++++++++@................................... ..................................@++++++++++@.................................. .................................@++++++++++++@................................. .................................@++++++++++++@................................. ................................@++++++++++++++@................................ ...............................@++++++++++++++++@............................... .@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@. ....@@@+++++++++++++++++++++++@++++++++++++++++++@+++++++++++++++++++++++++@@@.. .......@@++++++++++++++++++++@++++++++++++++++++++@++++++++++++++++++++++@@..... .........@@@+++++++++++++++++@++++++++++++++++++++@+++++++++++++++++++@@@....... ............@@@+++++++++++++@++++++++++++++++++++++@+++++++++++++++@@@.......... ...............@@++++++++++@+++++++++++++++++++++++@+++++++++++++@@............. .................@@@+++++++@++++++++++++++++++++++++@+++++++++@@@............... ....................@@@+++@++++++++++++++++++++++++++@+++++@@@.................. .......................@@+@++++++++++++++++++++++++++@+++@@..................... .........................@@@++++++++++++++++++++++++++@@@....................... ........................@+++@@@++++++++++++++++++++@@@+@........................ ........................@++++++@@+++++++++++++++@@@++++@........................ .......................@+++++++++@@@++++++++++@@++++++++@....................... ......................@+++++++++++++@@@++++@@@+++++++++++@...................... ......................@++++++++++++++++@@@@++++++++++++++@...................... .....................@++++++++++++++++@@..@@++++++++++++++@..................... ....................@++++++++++++++@@@......@@@++++++++++++@.................... ....................@+++++++++++@@@............@@@+++++++++@.................... ...................@++++++++++@@..................@@++++++++@................... ...................@+++++++@@@......................@@@+++++@................... ..................@+++++@@@............................@@@+++@.................. .................@++++@@..................................@@++@................. .................@+@@@......................................@@@................. ................@@@............................................@................ ................................................................................
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);- 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 /Wolfram Language
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]]]}
]
Nim
import libgd
from math import sin, cos, degToRad
const
width = 500
height = width
outerRadius = 200
proc main() =
proc calcPosition(x: int, y: int, radius: int, posAngle: float): (cint, cint) =
var width = int(radius.float * sin(degToRad(posAngle)))
var height = int(radius.float * cos(degToRad(posAngle)))
return (cast[cint](x + width), cast[cint](y - height))
proc getPentagonPoints(startAngle = 0, radius: int): array[5, array[2, int]] =
let spacingAngle = 360 / 5
var posAngle = (90 - startAngle).float
var n = 0
var points: array[5, array[2, int]]
while n < 5:
(points[n][0], points[n][1]) = calcPosition(250, 250, radius, posAngle)
n += 1
posAngle -= spacingAngle
return points
let outerPentagon = getPentagonPoints(18, outerRadius) # rotate 18 degrees
let innerPentagon = getPentagonPoints(54, int((cos(degToRad(72.0))/cos(degToRad(36.0))) * outerRadius)) # rotate 54 degrees
var pentagram: array[10, array[2, int]]
var n = 0
for i in countup(0, 4):
pentagram[n] = outerPentagon[i]
inc(n)
pentagram[n] = innerPentagon[i]
inc(n)
withGd imageCreate(width, height) as img:
discard img.setColor(255, 255, 255)
let black = img.setColor(0x404040)
let blue = img.setColor(0x6495ed)
img.drawPolygon(
points=pentagram,
color=blue,
fill=true,
open=false)
img.setThickness(4)
img.drawPolygon(
points=pentagram,
color=black,
fill=false,
open=false)
img.drawPolygon(
points=innerPentagon,
color=black,
fill=false,
open=false)
let png_out = open("pentagram.png", fmWrite)
img.writePng(png_out)
png_out.close()
main()
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
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;
Pentagram (offsite image)
Phix
Resizable and optionally rotating gui (desktop) version
You can run this online here.
-- -- demo\rosetta\Pentagram.exw -- ========================== -- -- Start/stop rotation by pressing space. Resizeable. -- ZXYV stop any rotation and orient up/down/left/right. -- with javascript_semantics include pGUI.e Ihandle dlg, canvas, timer cdCanvas 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*/, /*posy*/) integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE"), cx = floor(w/2), cy = floor(h/2), radius = floor(min(cx,cy)*0.9) cdCanvasActivate(cdcanvas) cdCanvasClear(cdcanvas) cdCanvasSetFillMode(cdcanvas, CD_WINDING) cdCanvasSetLineWidth(cdcanvas, round(radius/100)+1) for mode=FILL to BORDER do cdCanvasSetForeground(cdcanvas,colours[mode]) cdCanvasBegin(cdcanvas,modes[mode]) for a=90 to 666 by 144 do atom r = (a+rot)*CD_DEG2RAD, x = floor(radius*cos(r)+cx), y = floor(radius*sin(r)+cy) cdCanvasVertex(cdcanvas, x, y) end for cdCanvasEnd(cdcanvas) end for cdCanvasFlush(cdcanvas) return IUP_DEFAULT end function function map_cb(Ihandle ih) cdcanvas = cdCreateCanvas(CD_IUP, ih) cdCanvasSetBackground(cdcanvas, CD_PARCHMENT) return IUP_DEFAULT end function function timer_cb(Ihandle /*ih*/) rot = mod(rot+359,360) IupRedraw(canvas) return IUP_IGNORE end function function key_cb(Ihandle /*ih*/, atom c) if c=K_ESC then return IUP_CLOSE end if c = upper(c) if c=' ' then IupSetInt(timer,"RUN",not IupGetInt(timer,"RUN")) else c = find(c,"ZYXV") if c then IupSetInt(timer,"RUN",false) rot = (c-1)*90 IupRedraw(canvas) end if end if return IUP_CONTINUE end function procedure main() IupOpen() canvas = IupCanvas("RASTERSIZE=640x640") IupSetCallback(canvas, "MAP_CB", Icallback("map_cb")) IupSetCallback(canvas, "ACTION", Icallback("redraw_cb")) dlg = IupDialog(canvas,`TITLE="Pentagram"`) IupSetCallback(dlg, "KEY_CB", Icallback("key_cb")) IupShow(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) timer = IupTimer(Icallback("timer_cb"), 80, active:=false) if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
And a quick svg version, output identical to sidef
without js 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())
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
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...
%!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
Processing
//Aamrun, 29th June 2022
size(1000,1000);
translate(width/2,height/2);
rotate(3*PI/2);
fill(#0000ff);
beginShape();
for(int i=0;i<10;i+=2){
vertex(450*cos(i*2*PI/5),450*sin(i*2*PI/5));
}
endShape(CLOSE);
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()
Quackery
[ $ "turtleduck.qky" loadfile ] now!
[ [ 1 1
30 times
[ tuck + ]
swap join ] constant
do ] is phi ( --> n/d )
[ 5 times
[ 2dup walk
1 5 turn
2dup walk
3 5 turn ]
2drop ] is star ( n/d --> )
[ 5 times
[ 2dup walk
2 5 turn ]
2drop ] is pentagram ( n/d --> )
turtle
' [ 79 126 229 ] fill [ 200 1 star ]
10 wide
-1 10 turn
200 1 phi v* phi v* pentagram
1 10 turn- Output:
R
Very simple approach,
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)
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
#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)
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"))
Raku
(formerly Perl 6)
Generate an SVG file to STDOUT. Redirect to a file to capture and display it.
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)")
],
],
);
See Pentagram (offsite svg image)
Ever wondered what a regular 7 sided star looks like? Change $sides to 7 and re-run. See Heptagram
Red
Red [
Source: https://github.com/vazub/rosetta-red
Tabs: 4
Needs: 'View
]
canvas: 500x500
center: as-pair canvas/x / 2 canvas/y / 2
radius: 200
points: collect [
repeat vertex 10 [
angle: vertex * 36 + 18 ;-- +18 is required for pentagram rotation
either vertex // 2 = 1 [
keep as-pair (cosine angle) * radius + center/x (sine angle) * radius + center/y
][
keep as-pair (cosine angle) * radius * 0.382 + center/x (sine angle) * radius * 0.382 + center/y
]
]
]
view [
title "Pentagram"
base canvas white
draw compose/deep [
fill-pen mint
polygon (points)
line-width 3
line (points/1) (points/5) (points/9) (points/3) (points/7) (points/1)
]
]
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
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() }
returnOutput:
https://www.dropbox.com/s/znbcsoatlc00n4w/Pentagram.jpg?dl=0
Scala
Java Swing Interoperability
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)
}
)
}
Sidef
Generates a SVG image to STDOUT.
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 pline(q) {
<<-EOT
<polyline points="#{{|n| '%0.3f' % n }.map(q, q[0], q[1]).join(' ')}"
style="fill:blue; stroke:white; stroke-width:3;"
transform="translate(#{dim}, #{dim}) rotate(-18)" />
EOT
}
var v = {|k| 0.9 * dim * cis(k * Num.tau / sides) }.map(^sides)
pentagram += pline([v[range(0, v.end, 2)], v[range(1, v.end, 2)]].map{.reals})
pentagram += '</svg>'
return pentagram
}
say pentagram()
- 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
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)
<Tcl
This implementation draws a simple pentagram on a Canvas widget.
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!
Wren
import "graphics" for Canvas, Color, Point
import "dome" for Window
class Game {
static init() {
Window.title = "Pentagram"
var width = 640
var height = 640
Window.resize(width, height)
Canvas.resize(width, height)
Canvas.cls(Color.white)
var col = Color.hex("#6495ed") // cornflower blue
for (i in 1..240) pentagram(320, 320, i, col)
for (i in 241..250) pentagram(320, 320, i, Color.black)
}
static update() {}
static draw(alpha) {}
static pentagram(x, y, r, col) {
var points = List.filled(5, null)
for (i in 0..4) {
var angle = 2*Num.pi*i/5 - Num.pi/2
points[i] = Point.new(x + r*angle.cos, y + r*angle.sin)
}
var prev = points[0]
for (i in 1..5) {
var index = (i * 2) % 5
var curr = points[index]
Canvas.line(prev.x, prev.y, curr.x, curr.y, col)
prev = curr
}
}
}
XPL0
proc FillArea(X, Y, C0, C); \Replace area colored C0 with color C
int X, Y, \starting coordinate for flood fill algorithm
C0, C; \initial color, and color to replace it with
def S=8000; \size of queue (must be an even number)
int Q(S), \queue (FIFO)
F, E; \fill and empty indexes
proc EnQ(X, Y); \Enqueue coordinate
int X, Y;
[Q(F):= X;
F:= F+1;
Q(F):= Y;
F:= F+1;
if F >= S then F:= 0;
]; \EnQ
proc DeQ; \Dequeue coordinate
[X:= Q(E);
E:= E+1;
Y:= Q(E);
E:= E+1;
if E >= S then E:= 0;
]; \DeQ
[if C0 = C then return;
F:= 0; E:= 0;
EnQ(X, Y);
while E # F do
[DeQ;
if ReadPix(X, Y) = C0 then
[Point(X, Y, C);
EnQ(X+1, Y); \enqueue adjacent pixels
EnQ(X-1, Y);
EnQ(X, Y+1);
EnQ(X, Y-1);
];
];
]; \FillArea
def Size = 200.;
def Pi = 3.141592654;
def Deg144 = 4.*Pi/5.;
int X, Y, N;
[SetVid($12); \set 640x480x4 VGA graphics
for Y:= 0 to 480-1 do \fill screen
[Move(0, Y); Line(640-1, Y, $F\white\)];
for N:= 0 to 5 do \draw pentagram
[X:= fix(Size*Sin(float(N)*Deg144));
Y:= fix(Size*Cos(float(N)*Deg144));
if N = 0 then Move(X+320, 240-Y)
else Line(X+320, 240-Y, 4\red\);
];
FillArea(0, 0, $F, 1); \replace white (F) with blue (1)
]zkl
Generate an SVG file to STDOUT. Redirect to a file to capture and display it.
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>");- 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.
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