Archimedean spiral: Difference between revisions
(Ada version) |
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=={{header|Ada}}== |
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{{libheader|SDLAda}} |
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<lang Ada>with Ada.Numerics.Elementary_Functions; |
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with SDL.Video.Windows.Makers; |
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with SDL.Video.Surfaces; |
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with SDL.Video.Rectangles; |
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with SDL.Video.Pixel_Formats; |
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with SDL.Events.Events; |
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procedure Archimedean_Spiral is |
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Width : constant := 800; |
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Height : constant := 800; |
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A : constant := 4.2; |
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B : constant := 3.2; |
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T_First : constant := 4.0; |
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T_Last : constant := 100.0; |
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Win : SDL.Video.Windows.Window; |
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Surface : SDL.Video.Surfaces.Surface; |
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Event : SDL.Events.Events.Events; |
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procedure Plot (X, Y : Float) is |
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use SDL.C; |
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Point : constant SDL.Video.Rectangles.Rectangle |
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:= (X => Width / 2 + SDL.C.int (X), |
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Y => Height / 2 + SDL.C.int (Y), |
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Width => 2, Height => 2); |
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begin |
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Surface.Fill (Point, SDL.Video.Pixel_Formats.To_Pixel |
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(Format => Surface.Pixel_Format, |
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Red => 0, Green => 250, Blue => 0)); |
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end Plot; |
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procedure Draw_Archimedean_Spiral is |
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use Ada.Numerics.Elementary_Functions; |
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Pi : constant := Ada.Numerics.Pi; |
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Step : constant := 0.01; |
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T : Float; |
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R : Float; |
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begin |
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T := T_First; |
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loop |
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R := A + B * T; |
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Plot (X => R * Cos (T, Cycle => 2.0 * Pi), |
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Y => R * Sin (T, Cycle => 2.0 * Pi)); |
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exit when T >= T_Last; |
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T := T + Step; |
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end loop; |
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end Draw_Archimedean_Spiral; |
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procedure Wait is |
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use type SDL.Events.Event_Types; |
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begin |
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loop |
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while SDL.Events.Events.Poll (Event) loop |
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if Event.Common.Event_Type = SDL.Events.Quit then |
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return; |
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end if; |
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end loop; |
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end loop; |
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end Wait; |
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begin |
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if not SDL.Initialise (Flags => SDL.Enable_Screen) then |
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return; |
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end if; |
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SDL.Video.Windows.Makers.Create (Win => Win, |
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Title => "Archimedean spiral", |
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Position => SDL.Natural_Coordinates'(X => 10, Y => 10), |
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Size => SDL.Positive_Sizes'(Width, Height), |
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Flags => 0); |
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Surface := Win.Get_Surface; |
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Surface.Fill (SDL.Video.Rectangles.Rectangle'(0, 0, Width, Height), |
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SDL.Video.Pixel_Formats.To_Pixel |
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(Format => Surface.Pixel_Format, |
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Red => 0, Green => 0, Blue => 0)); |
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Draw_Archimedean_Spiral; |
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Win.Update_Surface; |
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Wait; |
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Win.Finalize; |
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SDL.Finalise; |
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end Archimedean_Spiral;</lang> |
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=={{header|AWK}}== |
=={{header|AWK}}== |
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Revision as of 20:40, 17 December 2019
You are encouraged to solve this task according to the task description, using any language you may know.
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
with real numbers a and b.
- Task
Draw an Archimedean spiral.
Ada
<lang Ada>with Ada.Numerics.Elementary_Functions;
with SDL.Video.Windows.Makers; with SDL.Video.Surfaces; with SDL.Video.Rectangles; with SDL.Video.Pixel_Formats; with SDL.Events.Events;
procedure Archimedean_Spiral is
Width : constant := 800; Height : constant := 800; A : constant := 4.2; B : constant := 3.2; T_First : constant := 4.0; T_Last : constant := 100.0;
Win : SDL.Video.Windows.Window; Surface : SDL.Video.Surfaces.Surface; Event : SDL.Events.Events.Events;
procedure Plot (X, Y : Float) is
use SDL.C;
Point : constant SDL.Video.Rectangles.Rectangle
:= (X => Width / 2 + SDL.C.int (X),
Y => Height / 2 + SDL.C.int (Y),
Width => 2, Height => 2);
begin
Surface.Fill (Point, SDL.Video.Pixel_Formats.To_Pixel
(Format => Surface.Pixel_Format,
Red => 0, Green => 250, Blue => 0));
end Plot;
procedure Draw_Archimedean_Spiral is
use Ada.Numerics.Elementary_Functions;
Pi : constant := Ada.Numerics.Pi;
Step : constant := 0.01;
T : Float;
R : Float;
begin
T := T_First;
loop
R := A + B * T;
Plot (X => R * Cos (T, Cycle => 2.0 * Pi),
Y => R * Sin (T, Cycle => 2.0 * Pi));
exit when T >= T_Last;
T := T + Step;
end loop;
end Draw_Archimedean_Spiral;
procedure Wait is
use type SDL.Events.Event_Types;
begin
loop
while SDL.Events.Events.Poll (Event) loop
if Event.Common.Event_Type = SDL.Events.Quit then
return;
end if;
end loop;
end loop;
end Wait;
begin
if not SDL.Initialise (Flags => SDL.Enable_Screen) then
return;
end if;
SDL.Video.Windows.Makers.Create (Win => Win,
Title => "Archimedean spiral",
Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
Size => SDL.Positive_Sizes'(Width, Height),
Flags => 0);
Surface := Win.Get_Surface;
Surface.Fill (SDL.Video.Rectangles.Rectangle'(0, 0, Width, Height),
SDL.Video.Pixel_Formats.To_Pixel
(Format => Surface.Pixel_Format,
Red => 0, Green => 0, Blue => 0));
Draw_Archimedean_Spiral; Win.Update_Surface;
Wait; Win.Finalize; SDL.Finalise;
end Archimedean_Spiral;</lang>
AWK
<lang AWK>
- syntax: GAWK -f ARCHIMEDEAN_SPIRAL.AWK
- converted from Applesoft BASIC
BEGIN {
x_min = y_min = 9999
x_max = y_max = 0
h = 96
w = h + h / 2
a = 1
b = 1
m = 6 * 3.1415926
step = .02
for (t=step; t<=m; t+=step) { # build spiral
r = a + b * t
x = int(r * cos(t) + w)
y = int(r * sin(t) + h)
if (x <= 0 || y <= 0) { continue }
if (x >= 280 ) { continue }
if (y >= 192) { continue }
arr[x,y] = "*"
x_min = min(x_min,x)
x_max = max(x_max,x)
y_min = min(y_min,y)
y_max = max(y_max,y)
}
for (i=x_min; i<=x_max; i++) { # print spiral
rec = ""
for (j=y_min; j<=y_max; j++) {
rec = sprintf("%s%1s",rec,arr[i,j])
}
printf("%s\n",rec)
}
exit(0)
} function max(x,y) { return((x > y) ? x : y) } function min(x,y) { return((x < y) ? x : y) } </lang>
- Output:
**********
*** ***
** **
** **
** **
** **
** ******* **
** *** *** *
* ** ** **
** ** ** *
* ** ** **
** ** * *
* * **** * *
* * *** ** * **
** * * ** * *
* * ** * * *
* * * * * *
* ** * ** * *
* ** * ** * **
* * * ** *
* * * * *
** * * ** **
* * ** ** *
* * *** *** **
** ** ****** *
* * **
* ** **
* ** **
** ** **
* **** ***
* ********
*
*
**
***
****
*****
BASIC
Applesoft BASIC
<lang ApplesoftBasic>110 LET H = 96 120 LET W = H + H / 2 130 HGR2 140 HCOLOR= 3 150 LET A = 1 160 LET B = 9 170 LET PI = 3.1415926535 180 LET M = 10 * PI 190 LET S = .02 200 FOR T = S TO M STEP S 210 LET R = A + B * T 220 LET X = R * COS (T) + W 230 LET Y = R * SIN (T) + H 240 IF X < 0 THEN 290 250 IF Y < 0 THEN 290 260 IF X > 279 THEN 290 270 IF Y > 191 THEN 290 280 HPLOT X,Y 290 NEXT </lang>
BASIC256
<lang BASIC256>
- Basic-256 ver 1.1.4
- Archimedean Spiral
width = 430 : height = 430 graphsize width, height rect 0,0, graphwidth,graphheight penwidth 1 color green
x = width/2 : y = height/2 # Center of graphics window i = 1 : t = 0 : xn = 0 : yn = 0 # Initial values iter = 150 : q = 30
line x,0,x,height
line 0,y,width,y
penwidth 2 color red
while i <= iter
t = i / q * pi xn = (1 + (1 * t)) * cos(t) +x yn = (1 + (1 * t)) * sin(t) +y line x,y,xn,yn x = xn : y = yn print i + chr(9) + int(x) + chr(9) + int(y) + chr(9) + int(t) # chr(9) = TAB i += 1
end while
imgsave "spiral-Basic-256.png", "PNG" </lang>
Commodore BASIC
Commodore BASIC 2.0 lacks in-built graphics capability. This implementation is written for Commodore BASIC 7.0 that was built into the Commodore 128 computer. Should also work for Commodore BASIC 3.5. <lang basic>1 REM ARCHIMEDEAN SPIRAL 2 REM USING COMMODORE BASIC 7.0 3 REM OF THE COMMODORE 128 4 REM ********************************** 10 GRAPHIC 1,1 20 A = 1.5 30 B = 0.7 40 X0 = 160 : Y0 = 100 50 FOR T = 0 TO 40*π STEP 0.2 60 R = A+B*T 70 X = R*COS(T)+160 : Y = R*SIN(T)+100 80 DRAW 1,X0,Y0 TO X,Y 90 X0 = X : Y0 = Y 100 NEXT T 110 GOTO 110</lang>
FreeBASIC
<lang freebasic>' version 16-10-2016 ' compile with: fbc -s gui
Const As double deg2rad = Atn(1) * 4 / 180 ' pi = atn(1) * 4, pi/180
Const As UInteger screensize = 600 ' size of window in pixels Const As Double turns = 5 ' number of turns Const As UInteger halfscrn = screensize \ 2 Const As uinteger sf = (turns * (screensize - 100)) / halfscrn
ScreenRes screensize, screensize, 32 ' screen 600 * 600 pixels, 4 byte color
Dim As Double r, x, y
For r = 0 To turns * 360 Step 0.05
x = Cos(r * deg2rad) * r / sf y = Sin(r * deg2rad) * r / sf PSet(halfscrn + x, halfscrn - y), RGB(255, 255, 255)
Next
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</lang>
IS-BASIC
<lang IS-BASIC>100 GRAPHICS LORES 2 110 OPTION ANGLE DEGREES 120 PLOT 640,360,ANGLE 90; 130 FOR I=2 TO 33.2 STEP .05 140 PLOT FORWARD I,LEFT 5; 150 NEXT</lang>
Run BASIC
<lang Run BASIC> 'archimedean spiral.bas
'runs in Run Basic 'Run Basic website http://www.runbasic.com 'From Rosettacode.org/wiki/ *** Liberty_BASIC
graphic #g, 300,300 'width and height - the center is 150 c = 255 '255 for white '0 for black print "Welcome to the Arch-Spiral Program"
pi=acs(-1)
nLoops = 5
#g cls("blue") 'blue background color
#g color(c,c,c) 'set line color - see color above
for t=0 to 2*pi*nLoops step 0.01
'c = c - 1 'changes color parameter
x=100*t/(2*pi*nLoops)*cos(t)+150 '150x150 is the center
y=100*t/(2*pi*nLoops)*sin(t)+150
#g color(c,c,c) 'changes color
#g set(x,y)
'if c <1 then c=255
next
render #g
print "Thank you and Goodbye" end
End</lang>
QBASIC
<lang basic>SCREEN 12 WINDOW (-2.67, -2!)-(2.67, 2!) PI = 4 * ATN(1) H = PI / 40 A = .2: B = .05 PSET (A, 0) FOR I = 0 TO 400
T = I * H X = (A + B * T) * COS(T) Y = (A + B * T) * SIN(T) LINE -(X, Y)
NEXT</lang>
Sinclair ZX81 BASIC
Works with the unexpanded (1k RAM) ZX81. The output is quite blocky, but identifiably a spiral. <lang basic>10 LET A=1.5 20 LET B=0.7 30 FOR T=0 TO 7*PI STEP 0.05 40 LET R=A+B*T 50 PLOT R*COS T+32,R*SIN T+22 60 NEXT T</lang>
- Output:
Screenshot here.
C
Interactive code which asks the parameters a and b as inputs, the number of cycles and the division steps. Requires the WinBGIm library. <lang C>
- include<graphics.h>
- include<stdio.h>
- include<math.h>
- define pi M_PI
int main(){ double a,b,cycles,incr,i;
int steps,x=500,y=500;
printf("Enter the parameters a and b : "); scanf("%lf%lf",&a,&b);
printf("Enter cycles : "); scanf("%lf",&cycles);
printf("Enter divisional steps : "); scanf("%d",&steps);
incr = 1.0/steps;
initwindow(1000,1000,"Archimedean Spiral");
for(i=0;i<=cycles*pi;i+=incr){ putpixel(x + (a + b*i)*cos(i),x + (a + b*i)*sin(i),15); }
getch();
closegraph(); } </lang>
C++
<lang cpp>
- include <windows.h>
- include <string>
- include <iostream>
const int BMP_SIZE = 600;
class myBitmap { public:
myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
~myBitmap() {
DeleteObject( pen ); DeleteObject( brush );
DeleteDC( hdc ); DeleteObject( bmp );
}
bool create( int w, int h ) {
BITMAPINFO bi;
ZeroMemory( &bi, sizeof( bi ) );
bi.bmiHeader.biSize = sizeof( bi.bmiHeader );
bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
bi.bmiHeader.biCompression = BI_RGB;
bi.bmiHeader.biPlanes = 1;
bi.bmiHeader.biWidth = w;
bi.bmiHeader.biHeight = -h;
HDC dc = GetDC( GetConsoleWindow() );
bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
if( !bmp ) return false;
hdc = CreateCompatibleDC( dc );
SelectObject( hdc, bmp );
ReleaseDC( GetConsoleWindow(), dc );
width = w; height = h;
return true;
}
void clear( BYTE clr = 0 ) {
memset( pBits, clr, width * height * sizeof( DWORD ) );
}
void setBrushColor( DWORD bClr ) {
if( brush ) DeleteObject( brush );
brush = CreateSolidBrush( bClr );
SelectObject( hdc, brush );
}
void setPenColor( DWORD c ) {
clr = c; createPen();
}
void setPenWidth( int w ) {
wid = w; createPen();
}
void saveBitmap( std::string path ) {
BITMAPFILEHEADER fileheader;
BITMAPINFO infoheader;
BITMAP bitmap;
DWORD wb;
GetObject( bmp, sizeof( bitmap ), &bitmap );
DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
infoheader.bmiHeader.biCompression = BI_RGB;
infoheader.bmiHeader.biPlanes = 1;
infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
infoheader.bmiHeader.biHeight = bitmap.bmHeight;
infoheader.bmiHeader.biWidth = bitmap.bmWidth;
infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
fileheader.bfType = 0x4D42;
fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS,
FILE_ATTRIBUTE_NORMAL, NULL );
WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
CloseHandle( file );
delete [] dwpBits;
}
HDC getDC() const { return hdc; }
int getWidth() const { return width; }
int getHeight() const { return height; }
private:
void createPen() {
if( pen ) DeleteObject( pen );
pen = CreatePen( PS_SOLID, wid, clr );
SelectObject( hdc, pen );
}
HBITMAP bmp; HDC hdc;
HPEN pen; HBRUSH brush;
void *pBits; int width, height, wid;
DWORD clr;
}; class spiral { public:
spiral() {
bmp.create( BMP_SIZE, BMP_SIZE );
}
void draw( int c, int s ) {
double a = .2, b = .3, r, x, y;
int w = BMP_SIZE >> 1;
HDC dc = bmp.getDC();
for( double d = 0; d < c * 6.28318530718; d += .002 ) {
r = a + b * d; x = r * cos( d ); y = r * sin( d );
SetPixel( dc, ( int )( s * x + w ), ( int )( s * y + w ), 255 );
}
// saves the bitmap
bmp.saveBitmap( "./spiral.bmp" );
}
private:
myBitmap bmp;
}; int main(int argc, char* argv[]) {
spiral s; s.draw( 16, 8 ); return 0;
} </lang>
C#
<lang csharp>using System; using System.Linq; using System.Drawing; using System.Diagnostics; using System.Drawing.Drawing2D;
class Program {
const int width = 380;
const int height = 380;
static PointF archimedeanPoint(int degrees)
{
const double a = 1;
const double b = 9;
double t = degrees * Math.PI / 180;
double r = a + b * t;
return new PointF { X = (float)(width / 2 + r * Math.Cos(t)), Y = (float)(height / 2 + r * Math.Sin(t)) };
}
static void Main(string[] args)
{
var bm = new Bitmap(width, height);
var g = Graphics.FromImage(bm);
g.SmoothingMode = SmoothingMode.AntiAlias;
g.FillRectangle(new SolidBrush(Color.White), new Rectangle { X = 0, Y = 0, Width = width, Height = height });
var pen = new Pen(Color.OrangeRed, 1.5f);
var spiral = Enumerable.Range(0, 360 * 3).AsParallel().AsOrdered().Select(archimedeanPoint);
var p0 = new PointF(width / 2, height / 2);
foreach (var p1 in spiral)
{
g.DrawLine(pen, p0, p1);
p0 = p1;
}
g.Save(); // is this really necessary ?
bm.Save("archimedes-csharp.png");
Process.Start("archimedes-csharp.png"); // Launches default photo viewing app
}
} </lang>
Common Lisp
Common Lisp doesn't provide native graphical output. Libraries or bitmapped output could be used instead, but for this solution, the output is accomplished with character printing.
<lang lisp>(defun draw-coords-as-text (coords size fill-char)
(let* ((min-x (apply #'min (mapcar #'car coords)))
(min-y (apply #'min (mapcar #'cdr coords)))
(max-x (apply #'max (mapcar #'car coords)))
(max-y (apply #'max (mapcar #'cdr coords)))
(real-size (max (+ (abs min-x) (abs max-x)) ; bounding square
(+ (abs min-y) (abs max-y))))
(scale-factor (* (1- size) (/ 1 real-size)))
(center-x (* scale-factor -1 min-x))
(center-y (* scale-factor -1 min-y))
(intermediate-result (make-array (list size size)
:element-type 'char
:initial-element #\space)))
(dolist (c coords)
(let ((final-x (floor (+ center-x (* scale-factor (car c)))))
(final-y (floor (+ center-y (* scale-factor (cdr c))))))
(setf (aref intermediate-result final-x final-y)
fill-char)))
; print results to output
(loop for i below (array-total-size intermediate-result) do
(when (zerop (mod i size))
(terpri))
(princ (row-major-aref intermediate-result i)))))
(defun spiral (a b step-resolution step-count)
"Returns a list of coordinates for r=a+b*theta stepping theta by step-resolution"
(loop for theta
from 0 upto (* step-count step-resolution)
by step-resolution
for r = (+ a (* b theta))
for x = (* r (cos theta))
for y = (* r (sin theta))
collect (cons x y)))
(draw-coords-as-text (spiral 10 10 0.01 1500) 30 #\*)
- Output
- *
- ****** *
- **** *** **
- *** ** *
- ** ** *
- ** ** *
- * ** **
- ** * *
- ** ****** * *
- * ** ** ** *
- * ** * * *
- * ** * * **
- * * * * *
- * * * ** * *
- * * *** ** *
- * ** * *
- * * ** *
- * ** ** **
- ** ** ** *
- * ** ** **
- ** ******** *
- * **
- ** **
- ** **
- ** ***
- ** **
- **** ***
- *******
</lang>
Clojure
<lang clojure> (use '(incanter core stats charts io))
(defn Arquimidean-function
[a b theta] (+ a (* theta b)))
(defn transform-pl-xy [r theta]
(let [x (* r (sin theta))
y (* r (cos theta))]
[x y]))
(defn arq-spiral [t] (transform-pl-xy (Arquimidean-function 0 7 t) t))
(view (parametric-plot arq-spiral 0 (* 10 Math/PI)))
</lang>
Frege
<lang frege>module Archimedean where
import Java.IO import Prelude.Math
data BufferedImage = native java.awt.image.BufferedImage where
pure native type_3byte_bgr "java.awt.image.BufferedImage.TYPE_3BYTE_BGR" :: Int native new :: Int -> Int -> Int -> STMutable s BufferedImage native createGraphics :: Mutable s BufferedImage -> STMutable s Graphics2D
data Color = pure native java.awt.Color where
pure native orange "java.awt.Color.orange" :: Color pure native white "java.awt.Color.white" :: Color pure native new :: Int -> Color
data BasicStroke = pure native java.awt.BasicStroke where
pure native new :: Float -> BasicStroke
data RenderingHints = native java.awt.RenderingHints where
pure native key_antialiasing "java.awt.RenderingHints.KEY_ANTIALIASING" :: RenderingHints_Key pure native value_antialias_on "java.awt.RenderingHints.VALUE_ANTIALIAS_ON" :: Object
data RenderingHints_Key = pure native java.awt.RenderingHints.Key
data Graphics2D = native java.awt.Graphics2D where
native drawLine :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s () native drawOval :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s () native fillRect :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s () native setColor :: Mutable s Graphics2D -> Color -> ST s () native setRenderingHint :: Mutable s Graphics2D -> RenderingHints_Key -> Object -> ST s () native setStroke :: Mutable s Graphics2D -> BasicStroke -> ST s ()
data ImageIO = mutable native javax.imageio.ImageIO where
native write "javax.imageio.ImageIO.write" :: MutableIO BufferedImage -> String -> MutableIO File -> IO Bool throws IOException
width = 640 center = width `div` 2
roundi = fromIntegral . round
drawGrid :: Mutable s Graphics2D -> ST s () drawGrid g = do
g.setColor $ Color.new 0xEEEEEE
g.setStroke $ BasicStroke.new 2
let angle = toRadians 45
margin = 10
numRings = 8
spacing = (width - 2 * margin) `div` (numRings * 2)
forM_ [0 .. numRings-1] $ \i -> do
let pos = margin + i * spacing
size = width - (2 * margin + i * 2 * spacing)
ia = fromIntegral i * angle
multiplier = fromIntegral $ (width - 2 * margin) `div` 2
x2 = center + (roundi (cos ia * multiplier))
y2 = center - (roundi (sin ia * multiplier))
g.drawOval pos pos size size
g.drawLine center center x2 y2
drawSpiral :: Mutable s Graphics2D -> ST s () drawSpiral g = do
g.setStroke $ BasicStroke.new 2
g.setColor $ Color.orange
let degrees = toRadians 0.1
end = 360 * 2 * 10 * degrees
a = 0
b = 20
c = 1
drSp theta = do
let r = a + b * theta ** (1 / c)
x = r * cos theta
y = r * sin theta
theta' = theta + degrees
plot g (center + roundi x) (center - roundi y)
when (theta' < end) (drSp (theta' + degrees))
drSp 0
plot :: Mutable s Graphics2D -> Int -> Int -> ST s () plot g x y = g.drawOval x y 1 1
main = do
buffy <- BufferedImage.new width width BufferedImage.type_3byte_bgr g <- buffy.createGraphics g.setRenderingHint RenderingHints.key_antialiasing RenderingHints.value_antialias_on g.setColor Color.white g.fillRect 0 0 width width drawGrid g drawSpiral g f <- File.new "SpiralFrege.png" void $ ImageIO.write buffy "png" f</lang>
Output is here due to Is file uploading blocked forever?
Go
Creates a PNG file using only built-in packages. <lang go>package main
import ( "image" "image/color" "image/draw" "image/png" "log" "math" "os" )
func main() { const ( width, height = 600, 600 centre = width / 2.0 degreesIncr = 0.1 * math.Pi / 180 turns = 2 stop = 360 * turns * 10 * degreesIncr fileName = "spiral.png" )
img := image.NewNRGBA(image.Rect(0, 0, width, height)) // create new image bg := image.NewUniform(color.RGBA{255, 255, 255, 255}) // prepare white for background draw.Draw(img, img.Bounds(), bg, image.ZP, draw.Src) // fill the background fgCol := color.RGBA{255, 0, 0, 255} // red plot
a := 1.0 b := 20.0
for theta := 0.0; theta < stop; theta += degreesIncr { r := a + b*theta x := r * math.Cos(theta) y := r * math.Sin(theta) img.Set(int(centre+x), int(centre-y), fgCol) }
imgFile, err := os.Create(fileName) if err != nil { log.Fatal(err) } defer imgFile.Close()
if err := png.Encode(imgFile, img); err != nil { imgFile.Close() log.Fatal(err) } }</lang>
Haskell
<lang haskell>#!/usr/bin/env stack -- stack --resolver lts-7.0 --install-ghc runghc --package Rasterific --package JuicyPixels
import Codec.Picture( PixelRGBA8( .. ), writePng ) import Graphics.Rasterific import Graphics.Rasterific.Texture import Graphics.Rasterific.Transformations
archimedeanPoint a b t = V2 x y
where r = a + b * t
x = r * cos t
y = r * sin t
main :: IO () main = do
let white = PixelRGBA8 255 255 255 255
drawColor = PixelRGBA8 0xFF 0x53 0x73 255
size = 800
points = map (archimedeanPoint 0 10) [0, 0.01 .. 60]
hSize = fromIntegral size / 2
img = renderDrawing size size white $
withTransformation (translate $ V2 hSize hSize) $
withTexture (uniformTexture drawColor) $
stroke 4 JoinRound (CapRound, CapRound) $
polyline points
writePng "SpiralHaskell.png" img</lang>
Output is here due to Is file uploading blocked forever?
J
<lang j>require'plot' 'aspect 1' plot (*^)j.0.01*i.1400</lang>
Java
<lang java>import java.awt.*; import static java.lang.Math.*; import javax.swing.*;
public class ArchimedeanSpiral extends JPanel {
public ArchimedeanSpiral() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
}
void drawGrid(Graphics2D g) {
g.setColor(new Color(0xEEEEEE));
g.setStroke(new BasicStroke(2));
double angle = toRadians(45);
int w = getWidth();
int center = w / 2;
int margin = 10;
int numRings = 8;
int spacing = (w - 2 * margin) / (numRings * 2);
for (int i = 0; i < numRings; i++) {
int pos = margin + i * spacing;
int size = w - (2 * margin + i * 2 * spacing);
g.drawOval(pos, pos, size, size);
double ia = i * angle;
int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2);
int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2);
g.drawLine(center, center, x2, y2);
}
}
void drawSpiral(Graphics2D g) {
g.setStroke(new BasicStroke(2));
g.setColor(Color.orange);
double degrees = toRadians(0.1);
double center = getWidth() / 2;
double end = 360 * 2 * 10 * degrees;
double a = 0;
double b = 20;
double c = 1;
for (double theta = 0; theta < end; theta += degrees) {
double r = a + b * pow(theta, 1 / c);
double x = r * cos(theta);
double y = r * sin(theta);
plot(g, (int) (center + x), (int) (center - y));
}
}
void plot(Graphics2D g, int x, int y) {
g.drawOval(x, y, 1, 1);
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
drawGrid(g);
drawSpiral(g);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Archimedean Spiral");
f.setResizable(false);
f.add(new ArchimedeanSpiral(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}</lang>
JavaScript
<lang html> <html> <head><title>Archimedean spiral</title></head> <body onload="pAS(35,'navy');">
Archimedean spiral
<canvas id="canvId" width="640" height="640" style="border: 2px outset;"></canvas> <script> // Plotting Archimedean_spiral aev 3/17/17 // lps - number of loops, clr - color. function pAS(lps,clr) {
var a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Math.PI,n=as/ai;
var cvs=document.getElementById("canvId");
var ctx=cvs.getContext("2d");
ctx.fillStyle="white"; ctx.fillRect(0,0,cvs.width,cvs.height);
var x=y=0, s=cvs.width/2;
ctx.beginPath();
for (var i=1; i<n; i++) {
x=r*Math.cos(a), y=r*Math.sin(a);
ctx.lineTo(x+s,y+s);
r+=ri; a+=ai;
}//fend i
ctx.strokeStyle = clr; ctx.stroke();
} </script></body></html> </lang>
- Output:
Page with Archimedean spiral like ASjs.png. Right-clicking on the canvas you can save spiral as a png-file, for example.
Julia
<lang julia>using UnicodePlots
spiral(θ, a=0, b=1) = @. b * θ * cos(θ + a), b * θ * sin(θ + a)
x, y = spiral(1:0.1:10) println(lineplot(x, y))</lang>
- Output:
┌────────────────────────────────────────┐
10 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠤⠤⡧⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠓⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀│
│⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀│
│⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡴⠥⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡼⠤⠤⠤⠤⠤⠤⠄│
│⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀│
│⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⡇⠀⠀⠀⣀⣀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-10 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
└────────────────────────────────────────┘
-10 10
Kotlin
<lang scala>// version 1.1.0
import java.awt.* import javax.swing.*
class ArchimedeanSpiral : JPanel() {
init {
preferredSize = Dimension(640, 640)
background = Color.white
}
private fun drawGrid(g: Graphics2D) {
g.color = Color(0xEEEEEE)
g.stroke = BasicStroke(2f)
val angle = Math.toRadians(45.0)
val w = width
val center = w / 2
val margin = 10
val numRings = 8
val spacing = (w - 2 * margin) / (numRings * 2)
for (i in 0 until numRings) {
val pos = margin + i * spacing
val size = w - (2 * margin + i * 2 * spacing)
g.drawOval(pos, pos, size, size)
val ia = i * angle
val x2 = center + (Math.cos(ia) * (w - 2 * margin) / 2).toInt()
val y2 = center - (Math.sin(ia) * (w - 2 * margin) / 2).toInt()
g.drawLine(center, center, x2, y2)
}
}
private fun drawSpiral(g: Graphics2D) {
g.stroke = BasicStroke(2f)
g.color = Color.magenta
val degrees = Math.toRadians(0.1)
val center = width / 2
val end = 360 * 2 * 10 * degrees
val a = 0.0
val b = 20.0
val c = 1.0
var theta = 0.0
while (theta < end) {
val r = a + b * Math.pow(theta, 1.0 / c)
val x = r * Math.cos(theta)
val y = r * Math.sin(theta)
plot(g, (center + x).toInt(), (center - y).toInt())
theta += degrees
}
}
private fun plot(g: Graphics2D, x: Int, y: Int) {
g.drawOval(x, y, 1, 1)
}
override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawGrid(g)
drawSpiral(g)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Archimedean Spiral"
f.isResizable = false
f.add(ArchimedeanSpiral(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.isVisible = true
}
}</lang>
Maple
<lang Maple> plots[polarplot](1+2*theta, theta = 0 .. 6*Pi) </lang>
Mathematica
The built-in function PolarPlot easily creates the desired plot <lang Mathematica>With[{a = 5, b = 4}, PolarPlot[a + b t, {t, 0, 10 Pi}]]</lang>
MATLAB
<lang MATLAB>a = 1; b = 1; turns = 2; theta = 0:0.1:2*turns*pi; polarplot(theta, a + b*theta);</lang>
PARI/GP
Note: cartes2() can be found here on PARI/GP page.
<lang parigp> \\ The Archimedean spiral \\ ArchiSpiral() - Where: lps is a number of loops, c is a direction 0/1 \\ (counter-clockwise/clockwise). 6/6/16 aev \\ Note: cartes2() can be found here on \\ http://rosettacode.org/wiki/Polyspiral#PARI.2FGP page. ArchiSpiral(size,lps,c=0)={ my(a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Pi,n=as/ai,x,y,vc,vx=List(.0),vy=vx); if(c<0||c>1, c=0); if(c, ai*=-1); print(" *** The Archimedean spiral: size=",size," loops=",lps," c=",c); for(i=1, n, vc=cartes2(r,a); x=vc[1]; y=vc[2];
listput(vx,x); listput(vy,y); r+=ri; a+=ai;
);\\fend i plothraw(Vec(vx),Vec(vy)); } {\\ Executing: ArchiSpiral(640,5); \\ArchiSpiral1.png ArchiSpiral(640,5,1); \\ArchiSpiral2.png } </lang>
- Output:
> ArchiSpiral(640,5); \\ArchiSpiral1.png *** The Archimedean spiral: size=640 loops=5 c=0 > ArchiSpiral(640,5,1); \\ArchiSpiral2.png *** The Archimedean spiral: size=640 loops=5 c=1
Perl
<lang Perl>use Imager; use constant PI => 3.14159265;
my ($w, $h) = (400, 400); my $img = Imager->new(xsize => $w, ysize => $h);
for ($theta = 0; $theta < 52*PI; $theta += 0.025) {
$x = $w/2 + $theta * cos($theta/PI); $y = $h/2 + $theta * sin($theta/PI); $img->setpixel(x => $x, y => $y, color => '#FF00FF');
}
$img->write(file => 'Archimedean-spiral.png'); </lang>
Perl 6
<lang perl6>use Image::PNG::Portable;
my ($w, $h) = (400, 400);
my $png = Image::PNG::Portable.new: :width($w), :height($h);
(0, .025 ... 52*π).race.map: -> \Θ {
$png.set: |((cis( Θ / π ) * Θ).reals »+« ($w/2, $h/2))».Int, 255, 0, 255;
}
$png.write: 'Archimedean-spiral-perl6.png';</lang>
Phix
<lang Phix>-- -- demo\rosetta\Archimedean_spiral.exw -- include pGUI.e
Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) integer a = 0, b = 5 integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE") integer {centerX,centerY} = sq_floor_div({width,height},2)
cdCanvasActivate(cddbuffer)
for deg=0 to 360*7 do
atom rad = deg*PI/180
atom r = rad*b + a
integer x = centerX + floor(r*cos(rad))
integer y = centerY + floor(r*sin(rad))
cdCanvasPixel(cddbuffer, x, y, #00FF00)
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_RED) return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "340x340") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Archimedean spiral")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupMap(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation IupShowXY(dlg,IUP_CENTER,IUP_CENTER) IupMainLoop() IupClose()
end procedure
main()</lang>
Processing
<lang java>float x, y, theta; void setup() {
theta = 0; size(500,500);
}
void draw() {
x = (width/2)+theta*cos(theta/PI); y = (height/2)+(theta)*sin(theta/PI); point(x,y); theta = theta + 0.025;
}</lang>
PureBasic
<lang PureBasic>#MAXLOOP = 7*360
- XCENTER = 640/2
- YCENTER = 480/2
- SCALAR = 200
If OpenWindow(0, 100, 200, 640, 480, "Archimedean spiral")
If CreateImage(0, 640, 480,24,RGB(255,255,255))
If StartDrawing(ImageOutput(0))
i.f=0.0
While i<=#MAXLOOP
x.f=#XCENTER+Cos(Radian(i))*#SCALAR*i/#MAXLOOP
y.f=#YCENTER+Sin(Radian(i))*#SCALAR*i/#MAXLOOP
Plot(x,y,RGB(50,50,50))
i+0.05
Wend
StopDrawing()
EndIf
EndIf
ImageGadget(0, 0, 0, 0, 0, ImageID(0))
Repeat : Event = WaitWindowEvent() : Until Event = #PB_Event_CloseWindow
EndIf End</lang>
Python
Using the turtle module.
<lang python>from turtle import * from math import * color("blue") down() for i in range(200):
t = i / 20 * pi x = (1 + 5 * t) * cos(t) y = (1 + 5 * t) * sin(t) goto(x, y)
up() done()</lang>
R
<lang r>with(list(s=seq(0, 10 * pi, length.out=500)),
plot((1 + s) * exp(1i * s), type="l"))</lang>
Racket
File:Archemedian-spiral-racket.png <lang racket>#lang racket/base (require plot
racket/math)
- x and y bounds set to centralise the circle
(define (archemedian-spiral-renderer2d a b θ/τ-max
#:samples (samples (line-samples)))
(define (f θ) (+ a (* b θ)))
(define max-dim (+ a (* θ/τ-max 2 pi b)))
(polar f
0 (* θ/τ-max 2 pi)
#:x-min (- max-dim)
#:x-max max-dim
#:y-min (- max-dim)
#:y-max max-dim
#:samples samples))
(plot (list (archemedian-spiral-renderer2d 0.0 24 4)))
- writes to a file so hopefully, I can post it to RC...
(plot-file (list (archemedian-spiral-renderer2d 0.0 24 4))
"images/archemidian-spiral-racket.png")</lang>
REXX
This REXX version allows the user to specify (or override) the various constants used to calculate and display the spiral (plot).
Note: the value of a doesn't mean that much as the plot is automatically centered. <lang rexx>/*REXX pgm plots several cycles (half a spiral) of the Archimedean spiral (ASCII plot).*/ parse arg cy a b inc chr . /*obtain optional arguments from the CL*/ if cy== | cy=="," then cy= 3 /*Not specified? Then use the default.*/ if a== | a=="," then a= 1 /* " " " " " " */ if b== | b=="," then b= 9 /* " " " " " " */ if inc== | inc=="," then inc= 0.02 /* " " " " " " */ if chr== | chr=="," then chr= '∙' /* " " " " " " */ if length(chr)==3 then chr= d2c(chr) /*plot character coded in decimal? */ if length(chr)==2 then chr= x2c(chr) /* " " " " hexadecimal? */ cy= max(2, cy); LOx= . /*set the LOx variable (a semaphore).*/ parse value scrsize() with sd sw . /*get the size of the terminal screen. */ w= sw - 1 ; mw= w * (cy-1) * 4 /*set useable width; max width for calc*/ h= sd - 1 + cy*10; mh= h * (cy-1) /* " " depth; " depth " " */ @.= /*initialize the line based plot field.*/
do t=1 to pi()*cy by inc /*calc all the coördinates for spiral. */
r= a + b* t /* " " " R " " */
x= w + r*cos(t); xx= x % 2 /* " " " X " " */
y= h + r*sin(t); yy= y % 2 /* " " " Y " " */
if x<0 | y<0 | x>mw | y>mh then iterate /*Is X or Y out of bounds? Then skip.*/
if LOx==. then do; LOx=xx; HIx=xx; LOy=yy; HIy=yy
end /* [↑] find the minimums and maximums.*/
LOx= min(LOx, xx); HIx= max(HIx, xx) /*determine the X MIN and MAX. */
LOy= min(LOy, yy); HIy= max(HIy, yy) /* " " Y " " " */
@.yy= overlay(chr, @.yy, xx+1) /*assign the plot character (glyph). */
end /*t*/
call plot /*invoke plotting subroutine (to term).*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078; return pi plot: do row=HIy to LOy by -1; say substr(@.row, LOx+1); end; return r2r: return arg(1) // (pi() * 2) /*normalize radians ───► a unit circle.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ cos: procedure; parse arg x; x= r2r(x); a= abs(x); hpi= pi * .5
numeric fuzz min(6, digits() - 3); if a=pi then return -1
if a=hpi | a=hpi*3 then return 0 if a=pi / 3 then return .5
if a=pi * 2 / 3 then return -.5; return .sinCos(1, -1)
/*──────────────────────────────────────────────────────────────────────────────────────*/ sin: procedure; parse arg x; x= r2r(x); numeric fuzz min(5, max(1, digits() -3))
if x=pi * .5 then return 1; if x==pi*1.5 then return -1
if abs(x)=pi | x=0 then return 0; return .sinCos(x, 1)
/*──────────────────────────────────────────────────────────────────────────────────────*/ .sinCos: parse arg z 1 _,i; q= x*x
do k=2 by 2 until p=z; p= z; _= -_*q/(k*(k+i)); z= z+_; end; return z</lang>
- output when using the following inputs: 13 , 5 , db
(Output is shown at 1/20 size.)
█ █ █ ██ █
█ █ █ █ █ █ █ █ █ █
█ █ █ █ █
█ █ █ █ █
█ █ █
█ █ █ █
█ █ █
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Ring
<lang ring> /*
+--------------------------------------------------------------------------------------------------------- + Program Name : Archimedean spiral +---------------------------------------------------------------------------------------------------------
- /
Load "guilib.ring"
horzSize = 400 vertSize = 400
counter = 0 ### cycle thru colors colorRed = new qcolor() { setrgb(255,000,000,255) } colorGreen = new qcolor() { setrgb(000,255,000,255) } colorBlue = new qcolor() { setrgb(000,000,255,255) } colorYellow = new qcolor() { setrgb(255,255,000,255) }
penUseR = new qpen() { setcolor(colorRed) setwidth(1) } penUseG = new qpen() { setcolor(colorGreen) setwidth(1) } penUseB = new qpen() { setcolor(colorBlue) setwidth(1) } penUseY = new qpen() { setcolor(colorYellow) setwidth(1) }
deg2rad = atan(1) * 4 / 180
screensize = 600
turns = 5
halfscrn = screensize / 2
sf = (turns * (screensize - 100)) / halfscrn
x = 1
y = 1
r = 0
inc = 0.50 ### control increment speed of r
New qapp {
win1 = new qwidget()
{
setwindowtitle("Draw Spiral")
setgeometry(100,100,600,600)
label1 = new qlabel(win1)
{
setgeometry(10,10,600,600)
settext("")
}
Canvas = new qlabel(win1)
{
MonaLisa = new qPixMap2( 600,600)
color = new qcolor(){ setrgb(255,0,0,255) }
daVinci = new qpainter()
{
begin(MonaLisa)
penUse = new qpen() { setcolor(colorRed) setwidth(1) }
setpen(penUseR)
#endpaint() ### This will Stop the Painting
}
setpixmap(MonaLisa)
}
oTimer = new qTimer(win1)
{
setinterval(1) ### 1 millisecond
settimeoutevent("DrawCounter()")
start()
}
show() ### Will show Painting ONLY after exec
}
exec()
}
- ====================================================
Func DrawCounter()
x = cos(r * deg2rad) * r / sf y = sin(r * deg2rad) * r / sf r += inc ### 0.20 fast, 0.90 slow
if r >= turns * 360
r = inc
x = 1
y = 1
counter++
whichColor = counter % 4
See "whichColor: "+ whichColor +nl
if whichColor = 0 daVinci.setpen(penUseR) ok
if whichColor = 1 daVinci.setpen(penUseG) ok
if whichColor = 2 daVinci.setpen(penUseB) ok
if whichColor = 3 daVinci.setpen(penUseY) ok
ok
hpoint = halfscrn + x ypoint = halfscrn - y
daVinci.drawpoint(hpoint, ypoint) Canvas.setpixmap(MonaLisa) ### Need this setpixmap to display imageLabel win1.show() ### Need this show to display imageLabel
return </lang>
Rust
<lang rust>#[macro_use(px)] extern crate bmp;
use bmp::{Image, Pixel}; use std::f64;
fn main() {
let width = 600u32; let half_width = (width / 2) as i32; let mut img = Image::new(width, width); let draw_color = px!(255, 128, 128);
// Constants defining the spiral size. let a = 1.0_f64; let b = 9.0_f64;
// max_angle = number of spirals * 2pi. let max_angle = 5.0_f64 * 2.0_f64 * f64::consts::PI;
let mut theta = 0.0_f64;
while theta < max_angle {
theta = theta + 0.002_f64;
let r = a + b * theta;
let x = (r * theta.cos()) as i32 + half_width;
let y = (r * theta.sin()) as i32 + half_width;
img.set_pixel(x as u32, y as u32, draw_color);
}
// Save the image
let _ = img.save("archimedean_spiral.bmp").unwrap_or_else(|e| panic!("Failed to save: {}", e));
}</lang>
SAS
<lang sas>data xy; h=constant('pi')/40; do i=0 to 400;
t=i*h; x=(1+t)*cos(t); y=(1+t)*sin(t); output;
end; keep x y; run;
proc sgplot; series x=x y=y; run;</lang>
Scala
Java Swing Interoperability
<lang Scala>
object ArchimedeanSpiral extends App {
SwingUtilities.invokeLater(() =>
new JFrame("Archimedean Spiral") {
class ArchimedeanSpiral extends JPanel {
setPreferredSize(new Dimension(640, 640))
setBackground(Color.white)
private def drawGrid(g: Graphics2D): Unit = {
val (angle, margin, numRings) = (toRadians(45), 10, 8)
val w = getWidth
val (center, spacing) = (w / 2, (w - 2 * margin) / (numRings * 2))
g.setColor(new Color(0xEEEEEE))
for (i <- 0 until numRings) {
val pos = margin + i * spacing
val size = w - (2 * margin + i * 2 * spacing)
g.drawOval(pos, pos, size, size)
val ia = i * angle
val x2 = center + (cos(ia) * (w - 2 * margin) / 2).toInt
val y2 = center - (sin(ia) * (w - 2 * margin) / 2).toInt
g.drawLine(center, center, x2, y2)
}
}
private def drawSpiral(g: Graphics2D): Unit = {
val (degrees: Double, center) = (toRadians(0.1), getWidth / 2)
val (a, b, c, end) = (0, 20, 1, 360 * 2 * 10 * degrees)
def plot(g: Graphics2D, x: Int, y: Int): Unit = g.drawOval(x, y, 1, 1)
def iter(theta: Double): Double = {
if (theta < end) {
val r = a + b * pow(theta, 1 / c)
val x = r * cos(theta)
val y = r * sin(theta)
plot(g, (center + x).toInt, (center - y).toInt)
iter(theta + degrees)
} else theta
}
g.setStroke(new BasicStroke(2))
g.setColor(Color.orange)
iter(0)
}
override def paintComponent(gg: Graphics): Unit = {
super.paintComponent(gg)
val g = gg.asInstanceOf[Graphics2D]
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawGrid(g)
drawSpiral(g)
}
}
add(new ArchimedeanSpiral, BorderLayout.CENTER)
pack()
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
}
)
}</lang>
Scilab
<lang>a = 3; b = 2;
theta = linspace(0,10*%pi,1000); r = a + b .* theta;
//1. Plot using polar coordinates scf(1); polarplot(theta,r);
//2. Plot using rectangular coordinates //2.1 Convert coordinates using Euler's formula z = r .* exp(%i .* theta); x = real(z); y = imag(z);
scf(2); plot2d(x,y);</lang>
Scheme
<lang scheme> (import (scheme base)
(scheme complex)
(rebottled pstk))
- settings for spiral
(define *resolution* 0.01) (define *count* 2000) (define *a* 10) (define *b* 10) (define *center*
(let ((size 200)) ; change this to alter size of display (* size 1+i)))
(define (draw-spiral canvas)
(define (coords theta)
(let ((r (+ *a* (* *b* theta))))
(make-polar r theta)))
;
(do ((i 0 (+ i 1))) ; loop to draw spiral
((= i *count*) )
(let ((c (+ (coords (* i *resolution*)) *center*)))
(canvas 'create 'line
(real-part c) (imag-part c)
(+ 1 (real-part c)) (imag-part c)))))
(let ((tk (tk-start)))
(tk/wm 'title tk "Archimedean Spiral")
(let ((canvas (tk 'create-widget 'canvas)))
(tk/pack canvas)
(canvas 'configure
'height: (* 2 (real-part *center*))
'width: (* 2 (imag-part *center*)))
(draw-spiral canvas))
(tk-event-loop tk))
</lang>
Seed7
<lang seed7>$ include "seed7_05.s7i";
include "draw.s7i"; include "keybd.s7i";
const proc: main is func
local
const float: xCenter is 117.0;
const float: yCenter is 139.0;
const float: maxTheta is 10.0 * PI;
const float: delta is 0.01;
const float: a is 1.0;
const float: b is 7.0;
var float: theta is 0.0;
var float: radius is 0.0;
begin
screen(256, 256);
clear(curr_win, black);
KEYBOARD := GRAPH_KEYBOARD;
while theta <= maxTheta do
radius := a + b * theta;
point(round(xCenter + radius * cos(theta)),
round(yCenter - radius * sin(theta)), white);
theta +:= delta;
end while;
DRAW_FLUSH;
ignore(getc(KEYBOARD));
end func;</lang>
Sidef
<lang ruby>require('Imager') define π = Num.pi
var (w, h) = (400, 400) var img = %O<Imager>.new(xsize => w, ysize => h)
for Θ in (0 .. 52*π -> by(0.025)) {
img.setpixel(
x => floor(cos(Θ / π)*Θ + w/2),
y => floor(sin(Θ / π)*Θ + h/2),
color => [255, 0, 0]
)
}
img.write(file => 'Archimedean_spiral.png')</lang> Output image: Archimedean spiral
Stata
<lang stata>clear all scalar h=_pi/40 set obs 400 gen t=_n*h gen x=(1+t)*cos(t) gen y=(1+t)*sin(t) line y x</lang>
Tcl
This creates a little Tk GUI where you can interactively enter values for `a` and `b`. The spiral will be re-drawn automatically thanks to `trace`:
<lang Tcl>package require Tk
- create widgets
canvas .canvas frame .controls
ttk::label .legend -text " r = a + b θ " ttk::label .label_a -text "a =" ttk::entry .entry_a -textvariable a ttk::label .label_b -text "a =" ttk::entry .entry_b -textvariable b button .button -text "Redraw" -command draw
- layout
grid .canvas .controls -sticky nsew grid .legend - -sticky ns -in .controls grid .label_a .entry_a -sticky nsew -in .controls grid .label_b .entry_b -sticky nsew -in .controls grid .button - -sticky ns -in .controls
- make the canvas resize with the window
grid columnconfigure . 0 -weight 1 grid rowconfigure . 0 -weight 1
- spiral parameters:
set a .2 set b .05
proc draw {} {
variable a variable b
# make sure inputs are valid:
if {![string is double $a] || ![string is double $b]} return
if {$a == 0 || $b == 0} return
set w [winfo width .canvas]
set h [winfo height .canvas]
set r 0
set pi [expr {4*atan(1)}]
set step [expr {$pi / $w}]
for {set t 0} {$r < 2} {set t [expr {$t + $step}]} {
set r [expr {$a + $b * $t}]
set y [expr {sin($t) * $r}]
set x [expr {cos($t) * $r}]
# transform to canvas co-ordinates
set y [expr {entier((1+$y)*$h/2)}]
set x [expr {entier((1+$x)*$w/2)}]
lappend coords $x $y
}
.canvas delete all
set id [.canvas create line $coords -fill red]
}
- draw whenever parameters are changed
- ";#" so extra trace arguments are ignored
trace add variable a write {draw;#} trace add variable b write {draw;#}
wm protocol . WM_DELETE_WINDOW exit ;# exit when window is closed
update ;# lay out widgets before trying to draw draw vwait forever ;# go into event loop until window is closed</lang>
VBA
<lang vb>Private Sub plot_coordinate_pairs(x As Variant, y As Variant)
Dim chrt As Chart
Set chrt = ActiveSheet.Shapes.AddChart.Chart
With chrt
.ChartType = xlXYScatter
.HasLegend = False
.SeriesCollection.NewSeries
.SeriesCollection.Item(1).XValues = x
.SeriesCollection.Item(1).Values = y
End With
End Sub Public Sub main()
Dim x(1000) As Single, y(1000) As Single
a = 1
b = 9
For i = 0 To 1000
theta = i * WorksheetFunction.Pi() / 60
r = a + b * theta
x(i) = r * Cos(theta)
y(i) = r * Sin(theta)
Next i
plot_coordinate_pairs x, y
End Sub</lang>
Yabasic
<lang Yabasic>5 OPEN WINDOW 320, 200 : WINDOW ORIGIN "CC" 10 LET A=1.5 20 LET B=0.7 30 FOR T=0 TO 30*PI STEP 0.05 40 LET R=A+B*T 50 LINE TO R*COS(T),R*SIN(T) 60 NEXT T</lang>
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>fcn archimedeanSpiral(a,b,circles){
w,h:=640,640; centerX,centerY:=w/2,h/2; bitmap:=PPM(w+1,h+1,0xFF|FF|FF); // White background
foreach deg in ([0.0 .. 360*circles]){
rad:=deg.toRad();
r:=rad*b + a;
x,y:=r.toRectangular(rad);
bitmap[centerX + x, centerY + y] = 0x00|FF|00; // Green dot
}
bitmap.writeJPGFile("archimedeanSpiral.jpg");
}(0,5,7);</lang>
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