Constrained random points on a circle: Difference between revisions
m →{{header|Ruby}}: add image |
|||
Line 1,460:
=={{header|Ruby}}==
Create the image with [[Raster graphics operations/Ruby]]
<lang Ruby>points = (1...100).map {
# choose a random radius and angle
Line 1,471:
(-15..15).each do |row|
puts((-15..15).map { |col| points.include?([row, col]) ? "X" : " " }.join)
end
load 'raster_graphics.rb'
pixmap = Pixmap.new(321,321)
pixmap.draw_circle(Pixel.new(160,160),90,RGBColour::BLACK)
pixmap.draw_circle(Pixel.new(160,160),160,RGBColour::BLACK)
points.each {|(x,y)| pixmap[10*(x+16),10*(y+16)] = RGBColour::BLACK}
pngfile = __FILE__
pngfile[/\.rb/] = ".png"
pixmap.save_as_png(pngfile)</lang>
outputs:
[[File:constrainedrandompointsonacircle.png|thumg|right|Sample output from Ruby program]]
<pre> X X
X XX
X XXX
XX X X X X X
XXXXX
XX XX
X X X
X X
X X
X X XXX
X
XX X X
X X
X X
XXX X
XX X
XXX X X
XX X X X
XX X X
X X
X
XX X X
X X X
X X X
X
X X X
X X X
X X</pre>
=={{header|SystemVerilog}}==
|
Revision as of 15:42, 15 November 2011
![Task](http://static.miraheze.org/rosettacodewiki/thumb/b/ba/Rcode-button-task-crushed.png/64px-Rcode-button-task-crushed.png)
You are encouraged to solve this task according to the task description, using any language you may know.
Generate 100 <x,y> coordinate pairs such that x and y are integers sampled from the uniform distribution with the condition that . Then display/plot them. The outcome should be a "fuzzy" circle. The actual number of points plotted may be less than 100, given that some pairs may be generated more than once.
There are several possible approaches to accomplish this. Here are two possible algorithms.
1) Generate random pairs of integers and filter out those that don't satisfy this condition:
- .
2) Precalculate the set of all possible points (there are 404 of them) and select randomly from this set.
Ada
<lang Ada>with Ada.Text_IO; with Ada.Numerics.Discrete_Random; procedure Circle is
-- extreme coordinate values are -15:0, 15:0, 0:-15, 0:15 subtype Coordinate is Integer range -15 .. 15; type Point is record X, Y : Coordinate; end record; type Point_List is array (Positive range <>) of Point;
function Acceptable (Position : Point) return Boolean is Squared_Sum : Natural := Position.X ** 2 + Position.Y ** 2; begin return 10 ** 2 <= Squared_Sum and Squared_Sum <= 15 ** 2; end Acceptable;
-- first algorithm function Generate_Random_Points (Count : Positive := 100) return Point_List is package RNG is new Ada.Numerics.Discrete_Random (Coordinate); Generator : RNG.Generator; Next_Point : Point; Result : Point_List (1 .. Count); begin RNG.Reset (Generator); for N in Result'Range loop loop Next_Point.X := RNG.Random (Generator); Next_Point.Y := RNG.Random (Generator); exit when Acceptable (Next_Point); end loop; Result (N) := Next_Point; end loop; return Result; end Generate_Random_Points;
-- second algorithm function Choose_Precalculated (Count : Positive := 100) return Point_List is subtype Possible_Points is Positive range 1 .. 404; package RNG is new Ada.Numerics.Discrete_Random (Possible_Points); Generator : RNG.Generator; Point_Pool : Point_List (Possible_Points); Next_Point : Point; Next_Index : Possible_Points := 1; Result : Point_List (1 .. Count); begin -- precalculate Precalculate : for X in Coordinate'Range loop Next_Point.X := X; for Y in Coordinate'Range loop Next_Point.Y := Y; if Acceptable (Next_Point) then Point_Pool (Next_Index) := Next_Point; exit Precalculate when Next_Index = Possible_Points'Last; Next_Index := Next_Index + 1; end if; end loop; end loop Precalculate; -- choose RNG.Reset (Generator); for N in Result'Range loop Result (N) := Point_Pool (RNG.Random (Generator)); end loop; return Result; end Choose_Precalculated;
procedure Print_Points (Points : Point_List) is Output_String : array (Coordinate, Coordinate) of Character := (others => (others => ' ')); begin for N in Points'Range loop Output_String (Points (N).X, Points (N).Y) := '*'; end loop; for Line in Output_String'Range (2) loop for Column in Output_String'Range (1) loop Ada.Text_IO.Put (Output_String (Column, Line)); end loop; Ada.Text_IO.New_Line; end loop; end Print_Points;
My_Circle_Randomly : Point_List := Generate_Random_Points; My_Circle_Precalculated : Point_List := Choose_Precalculated;
begin
Ada.Text_IO.Put_Line ("Randomly generated:"); Print_Points (My_Circle_Randomly); Ada.Text_IO.Put_Line ("Chosen from precalculated:"); Print_Points (My_Circle_Precalculated);
end Circle;</lang>
Output:
Randomly generated: ** * * * * * * * ** * * * * ** * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * *** * * * * * * * ** * ** * * ** * * * * * *** * * ** * * * *** * * Chosen from precalculated: * * * * * ** ** ** * * * * * * * ** * * * * * * * * *** * *** * * * * * * * * * ** * * ** *** * * * * ** * * * * * ** * * * * * * * ** * * * * * ** * * * ***
ALGOL 68
- note: This specimen retains the original C coding style.
<lang algol68>PROC clrscr = VOID:
printf(($g"[2J"$,REPR 27)); # ansi.sys #
PROC gotoxy = (INT x,y)VOID:
printf(($g"["g(0)";"g(0)"H"$,REPR 27, y,x)); # ansi.sys #
MODE POINT = STRUCT(
INT x,y
);
INT radius = 15; INT inside radius = 10;
POINT center = (radius+1, radius+1);
FLEX[0]POINT set;
PROC swap with last set = (INT position,INT where last set)VOID: (
INT temp := x OF set[position]; x OF set[position]:=x OF set[where last set]; x OF set[where last set] := temp;
temp := y OF set[position]; y OF set[position]:=y OF set[where last set]; y OF set[where last set] := temp
);
PROC create set = VOID: (
set := HEAP[(2*radius+1)**2]POINT; INT x,y,i:=LWB set;
FOR x FROM -radius TO radius DO FOR y FROM -radius TO radius DO IF sqrt(x*x+y*y)>=inside radius AND sqrt(x*x+y*y)<=radius THEN x OF set[i] := x; y OF set[i] := y; i+:=1 FI OD OD;
set:=set[:i-1]
);
PROC plot fuzzy set = (CHAR ch)VOID: (
INT pos,i;
TO UPB set DO pos := ENTIER(random * UPB set) + 1;
gotoxy(x OF center + x OF set[pos],y OF center + y OF set[pos]);
print(ch);
swap with last set(pos,UPB set)
OD
);
main: (
# srand((INT)time(NIL)); #
clrscr; create set; plot fuzzy set("*"); gotoxy(2*radius+1, 2*radius+1); newline(stand in)
)</lang> Sample output:
* * ** * * * * ** ** ***** ** ***** ** ** ** * * * * *** * ******** *** *** * ** ***** ** * *** * ***** * ** ** **** * * * * **** **** * **** * ** *** * ** ** ** ** * * * **** ** * ** * **** **** ** * * ** * ** * ** * * * *** * * ****** * * ** * * ** **** * ** * *** * **** ** * ** ** *** * *** * * *** * ** *** *** * * ** ***** **** ** ******* * * * ** ** ******* * ****** * *
BBC BASIC
<lang bbcbasic> MODE 8
ORIGIN 640, 512 FOR i% = 1 TO 1000 x% = RND(31)-16 y% = RND(31)-16 r = SQR(x%^2 + y%^2) IF r >= 10 IF r <= 15 PLOT x%*2, y%*2 NEXT</lang>
C
<lang C>#include <stdio.h>
- include <stdlib.h>
inline int randn(int m) { int rand_max = RAND_MAX - (RAND_MAX % m); int r; while ((r = rand()) > rand_max); return r / (rand_max / m); }
int main() { int i, x, y, r2; unsigned long buf[31] = {0}; /* could just use 2d array */
for (i = 0; i < 100; ) { x = randn(31) - 15; y = randn(31) - 15; r2 = x * x + y * y; if (r2 >= 100 && r2 <= 225) { buf[15 + y] |= 1 << (x + 15); i++; } }
for (y = 0; y < 31; y++) { for (x = 0; x < 31; x++) printf((buf[y] & 1 << x) ? ". " : " "); printf("\n"); }
return 0; }</lang>Output<lang> . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </lang>
Clojure
<lang Clojure>(import '[java.awt Color Graphics Dimension] '[javax.swing JFrame JPanel])
(let [points (->> (for [x (range -15 16) y (range -15 16) :when (<= 10 (Math/sqrt (+ (* x x) (* y y))) 15)] [(+ x 15) (+ y 15)]) shuffle (take 100 ,))]
(doto (JFrame.) (.add (doto (proxy [JPanel] []
(paint [^Graphics g] (doseq [[x y] points] (.fillRect g (* 10 x) (* 10 y) 10 10)))) (.setPreferredSize (Dimension. 310 310))))
(.setResizable false) (.setDefaultCloseOperation JFrame/DISPOSE_ON_CLOSE) .pack .show))</lang>
Common Lisp
<lang lisp>(flet ((good-p (x y) (<= 100 (+ (* x x) (* y y)) 255)))
(loop with x with y with cnt = 0
with scr = (loop repeat 31 collect (loop repeat 31 collect " ")) while (< cnt 100) do (when (good-p (- (setf x (random 31)) 15) (- (setf y (random 31)) 15)) (setf (elt (elt scr y) x) "@ ") (incf cnt)) finally (mapc #'(lambda (row) (format t "~{~a~^~}~%" row)) scr)))</lang>
D
<lang d>import std.stdio, std.random, std.math;
void main() {
char[31][31] table = ' ';
foreach (i; 0 .. 100) { int x, y; do { x = uniform(-15, 16); y = uniform(-15, 16); } while(abs(12.5 - abs(x + y * 1i)) > 2.5); table[x + 15][y + 15] = '*'; }
foreach (row; table) writeln(row);
}</lang>
* * ** * * * ** * * ** * * * * ** * ** ** * * * * * *** * * * * * * * * * * ** * * * * * * * * * * ** * * * * * * * * * ** * * * * * * ** * ** ** * ** * * * * **
F#
This version uses method 1 from the task description and just calculates 100 suitable points to plot. The INTERACTIVE bit just permits this code in a .fsx file to be run with the interactive interpreter or compiled to an exe. <lang fsharp>module CirclePoints =
let main args = let rnd = new System.Random() let rand size = rnd.Next(size) - size/2 let size = 30 let gen n = let rec f (x,y) = let t = (int (sqrt (float (x*x + y*y)) )) if 10 <= t && t <= 15 then (x,y) else f (rand size, rand size) f (rand size, rand size) let plot = Array.init 100 (fun n -> gen n) for row in 0 .. size-1 do let chars = Array.create (size+1) ' ' Array.choose (fun (x,y) -> if y = (row-size/2) then Some(x) else None) plot |> Array.iter (fun x -> chars.[x+size/2] <- 'o') printfn "%s" (new string(chars)) 0
- if INTERACTIVE
CirclePoints.main fsi.CommandLineArgs
- else
[<EntryPoint>] let main args = CirclePoints.main args
- endif</lang>
An example of the output:
o o oo o o o o o o o o o oo o o o o o o o oo oooo o oo o o oo o oooo o o o o o o o oo o o o o o o oo oo o o o o o o o o o o o o oo oo o oo o o o o o o o o oo o o o
Fortran
<lang fortran>program Constrained_Points
implicit none integer, parameter :: samples = 100 integer :: i, j, n, randpoint real :: r type points integer :: x, y end type
type(points) :: set(500), temp
! Create set of valid points
n = 0 do i = -15, 15 do j = -15, 15 if(sqrt(real(i*i + j*j)) >= 10.0 .and. sqrt(real(i*i + j*j)) <= 15.0) then n = n + 1 set(n)%x = i set(n)%y = j end if end do end do
! create 100 random points ! Choose a random number between 1 and n inclusive and swap point at this index with point at index 1 ! Choose a random number between 2 and n inclusive and swap point at this index with point at index 2 ! Continue in this fashion until 100 points have been selected
call random_seed do i = 1, samples call random_number(r) randpoint = r * (n + 1 - i) + i temp = set(i) set(i) = set(randpoint) set(randpoint) = temp end do
! In order to facilitate printing sort random points into ascending order ! sort x in ascending order
do i = 2, samples j = i - 1 temp = set(i) do while (j>=1 .and. set(j)%x > temp%x) set(j+1) = set(j) j = j - 1 end do set(j+1) = temp end do
! sort y in ascending order for same x
do i = 2, samples j = i - 1 temp = set(i) do while (j>=1 .and. set(j)%x == temp%x .and. set(j)%y > temp%y) set(j+1) = set(j) j = j - 1 end do set(j+1) = temp end do
! print circle
write(*,"(a,a)", advance="no") repeat(" ", set(1)%y+15), "*" do i = 2, samples if(set(i)%x == set(i-1)%x) then write(*,"(a,a)", advance="no") repeat(" ", set(i)%y - set(i-1)%y-1), "*" else n = set(i)%x - set(i-1)%x do j = 1, n write(*,*) end do write(*,"(a,a)", advance="no") repeat(" ", set(i)%y+15), "*" end if end do
end program</lang> Output
* * * * * ** ** * ** * ** * ** * ** * *** ** * * * * * * * * ** * * * * * * * * * ** *** * * * ** * * * * * * * * ** * * * * * ** ** * * * * *** * * * ** * * * * * * * * * ** * *
Go
Algorithm 1: <lang go>package main
import (
"bytes" "fmt" "rand" "time"
)
type pt struct {
x, y int
}
func main() {
rand.Seed(time.Nanoseconds()) // generate random points, accumulate 100 distinct points meeting condition m := make(map[int]pt) // key is buffer index for len(m) < 100 { p := pt{rand.Intn(31) - 15, rand.Intn(31) - 15} rs := p.x*p.x + p.y*p.y if 100 <= rs && rs <= 225 { m[(p.x+15)*2+(p.y+15)*31*2] = p } } // plot to buffer b := bytes.Repeat([]byte{' '}, 31*31*2) for i := range m { b[i] = '*' } // print buffer to screen for i := 0; i < 31; i++ { fmt.Println(string(b[i*31*2 : (i+1)*31*2])) }
}</lang> Algorithm 2: <lang go>package main
import (
"bytes" "fmt" "rand"
)
type pt struct {
x, y int
}
func main() {
// generate possible points all := make([]pt, 0, 404) for x := -15; x <= 15; x++ { for y := -15; y <= 15; y++ { rs := x*x + y*y if 100 <= rs && rs <= 225 { all = append(all, pt{x, y}) } } } if len(all) != 404 { panic(len(all)) } // randomly order rp := rand.Perm(404) // plot 100 of them to a buffer b := bytes.Repeat([]byte{' '}, 31*31*2) for i := 0; i < 100; i++ { p := all[rp[i]] b[(p.x+15)*2+(p.y+15)*31*2] = '*' } // print buffer to screen for i := 0; i < 31; i++ { fmt.Println(string(b[i*31*2 : (i+1)*31*2])) }
}</lang> Output:
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Haskell
Using Knuth Shuffle <lang haskell>import Data.List import Control.Monad import Control.Arrow import Rosetta.Knuthshuffle
task = do
let blanco = replicate (31*31) " " cs = sequence [[-15,-14..15],[-15,-14..15]] :: Int constraint = uncurry(&&).((<= 15*15) &&& (10*10 <=)). sum. map (join (*))
-- select and randomize all circle points
pts <- knuthShuffle $ filter constraint cs
-- 'paint' first 100 randomized circle points on canvas
let canvas = foldl (\cs [x,y] -> replaceAt (31*(x+15)+y+15) "/ " cs ) blanco (take 100 pts)
-- show canvas
mapM_ (putStrLn.concat). takeWhile(not.null). map (take 31) $ iterate (drop 31) canvas</lang>
Output (added a trailing space per 'pixel'
*Main> task / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /
Icon and Unicon
Generate random points in the bounded by the outside edge. Reject any found out of the prescribed bounds and stop when the required numbers of points have been generated.
<lang Icon>link graphics
procedure main(A) # points, inside r, outside r in pixels - default to task values
if \A[1] == "help" then stop("Usage: plot #points inside-radius outside-radius") points := \A[1] | 100 outside := \A[2] | 15 inside := \A[3] | 10 if inside > outside then inside :=: outside
wsize := integer(2.2*outside) wsize <:= 150 center := wsize/2
WOpen("size="||wsize||","||wsize,"bg=black","fg=white") | stop("Unable to open window")
until(points -:= 1) <= 0 do {
x := ?(2*outside)-outside # random x y := ?(2*outside)-outside # and y if (inside <= integer(sqrt(x^2+y^2)) ) <= outside then DrawPoint(x + center,y + center) }
WDone()
end</lang>
J
This version deals 100 distinct coordinates from the set of acceptable coordinates (much like dealing cards from a shuffled deck):
<lang j>gen=: ({~ 100?#)bind((#~ 1=99 225 I.+/"1@:*:),/,"0/~i:15)</lang>
Example use (gen''
generates the points, the rest of the example code deals with rendering them as a text array):
<lang j> '*' (<"1]15+gen )} 31 31$' '
* * * * * * * * * * * * * * *** ** * * ** * ** * ** * * * * * * ** * ** ** ** * *** * ** * * ** * * ** * ** * * ** * * * * * * * ** * * ** * * * * * * ** * * * * * ** * * * ** * </lang>
Java
<lang java>import java.util.Random;
public class FuzzyCircle { static final Random rnd = new Random(); public static void main(String[] args){ char[][] field = new char[31][31]; for(int i = 0; i < field.length; i++){ for(int j = 0; j < field[i].length; j++){ field[i][j] = ' '; } } int pointsInDisc = 0; while(pointsInDisc < 100){ int x = rnd.nextInt(31) - 15; int y = rnd.nextInt(31) - 15; double dist = Math.hypot(x, y); if(dist >= 10 && dist <= 15 && field[x + 15][y + 15] == ' '){ field[x + 15][y + 15] = 'X'; pointsInDisc++; } } for(char[] row:field){ for(char space:row){ System.out.print(space); } System.out.println(); } } }</lang> Output:
XX X X X X X X X XX X XXXX X X X X X XXX X X X X XXX X X X X XX X X X XX X X X X XXXXX X X X X X X X X X X X X X XX X XX X X XX X X XX X X X X X X XX X X XXX X X X X XX X X X X
JavaScript
JavaScript embedded in HTML, using canvas: <lang javascript><html><head><title>Circle</title></head> <body> <canvas id="cv" width="320" height="320"></canvas> <script type="application/javascript">
var cv = document.getElementById('cv'); var ctx = cv.getContext('2d');
var w = cv.width; var h = cv.height;
//draw circles ctx.fillStyle = 'rgba(0, 255, 200, .3)'; ctx.strokeStyle = 'rgba(0,0,0,.1)'; ctx.beginPath(); ctx.arc(w/2, h/2, 150, 0, Math.PI*2, true); ctx.arc(w/2, h/2, 100, 0, Math.PI*2, false); ctx.closePath(); ctx.fill();
// draw grids ctx.beginPath(); for (var i = 10; i < w; i += 10) { ctx.moveTo(i, 0); ctx.lineTo(i, h); ctx.moveTo(0, i); ctx.lineTo(w, i); } ctx.closePath(); ctx.stroke();
//draw points ctx.fillStyle = 'navy'; var pts = 0; while (pts < 100) { var x = Math.floor(Math.random() * 31) - 15; var y = Math.floor(Math.random() * 31) - 15; var r = x * x + y * y; if (r < 100 || r > 225) continue; x = x * 10 + w/2; y = y * 10 + h/2; ctx.fillRect(x - 2, y - 2, 4, 4); pts++; }
</script></body></html></lang>
Liberty BASIC
<lang lb>' RC Constrained Random Points on a Circle
nomainwin
WindowWidth =400 WindowHeight =430
open "Constrained Random Points on a Circle" for graphics_nsb as #w
- w "trapclose [quit]"
- w "down ; size 7 ; color red ; fill black"
for i =1 to 1000
do x =int( 30 *rnd( 1)) -15 y =int( 30 *rnd( 1)) -15 loop until IsInRange( x, y) =1 #w "set "; 200 +10 *x; " "; 200 - 10 *y
next
wait
function IsInRange( x, y)
z =sqr( x*x +y*y) if 10 <=z and z <=15 then IsInRange =1 else IsInRange =0
end function
[quit] close #w end</lang>
Locomotive Basic
<lang locobasic>10 MODE 1:RANDOMIZE TIME 20 FOR J=1 TO 100 30 X=INT(RND*30-15) 40 Y=INT(RND*30-15) 50 D=X*X+Y*Y 60 IF D<100 OR D>225 THEN GOTO 40 70 PLOT 320+10*X,200+10*Y:LOCATE 1,1:PRINT J 80 NEXT 90 CALL &BB06 ' wait for key press</lang>
Mathematica
<lang Mathematica> sample = RandomSample[Select[Partition[Flatten[Table[{x, y}, {x, -15, 15, 1}, {y, -15, 15, 1}]], 2],10 <= Sqrt[#1^2 + #2^2] <= 15 &], 100];
Show[{RegionPlot[10 <= Sqrt[x^2 + y^2] <= 15, {x, -16, 16}, {y, -16, 16}, Axes -> True, GridLines -> Automatic], ListPlot[sample]}] </lang>
MATLAB
Uses the Monte-Carlo method described above.
<lang MATLAB>function [xCoordinates,yCoordinates] = randomDisc(numPoints)
xCoordinates = []; yCoordinates = [];
%Helper function that samples a random integer from the uniform %distribution between -15 and 15. function nums = randInt(n) nums = round((31*rand(n,1))-15.5); end
n = numPoints;
while n > 0 x = randInt(n); y = randInt(n);
norms = sqrt((x.^2) + (y.^2)); inBounds = find((10 <= norms) & (norms <= 15)); xCoordinates = [xCoordinates; x(inBounds)]; yCoordinates = [yCoordinates; y(inBounds)]; n = numPoints - numel(xCoordinates); end xCoordinates(numPoints+1:end) = []; yCoordinates(numPoints+1:end) = [];
end</lang>
Output:
<lang MATLAB>>> [x,y] = randomDisc(100);
>> plot(x,y,'.')</lang>
OCaml
<lang ocaml>let p x y =
let d = sqrt(x ** 2.0 +. y ** 2.0) in 10.0 <= d && d <= 15.0
let () =
Random.self_init(); let rec aux i acc = if i >= 100 then acc else let x = (Random.float 40.0) -. 20.0 and y = (Random.float 40.0) -. 20.0 in if (p x y) then aux (succ i) ((x,y)::acc) else aux i acc in let points = aux 0 [] in let g = Array.init 40 (fun _ -> String.make 40 ' ') in List.iter (fun (x,y) -> let x = (int_of_float x) + 20 and y = (int_of_float y) + 20 in g.(y).[x] <- 'o' ) points; Array.iter print_endline g</lang>
o o o o oo oo oooo o o oo o oo o o o o oo o oo o oo o oo oo o o oooo o o oo o o o oo o o o o o o o o o o o o o o o oo o oo o o ooo o o o o ooo o o oo o
PARI/GP
<lang parigp>crpc()={
my(v=vector(404),t=0,i=0,vx=vy=vector(100)); for(x=1,14,for(y=1,14, t=x^2+y^2; if(t>99&t<226, v[i++]=[x,y]; v[i++]=[x,-y]; v[i++]=[-x,y]; v[i++]=[-x,-y] ) )); for(x=10,15, v[i++]=[x,0]; v[i++]=[-x,0]; v[i++]=[0,x]; v[i++]=[0,-x] ); for(i=1,#vx, t=v[random(#v)+1]; vx[i]=t[1]; vy[i]=t[2]; ); plothraw(vx,vy)
};</lang>
Perl
<lang perl>my @points; while (@points < 100) {
my ($x, $y) = (int(rand(31))-15, int(rand(31)) - 15); my $r2 = $x*$x + $y*$y; next if $r2 < 100 || $r2 > 225; push @points, [$x, $y];
}
print << 'HEAD'; %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox 0 0 400 400 200 200 translate 10 10 scale 0 setlinewidth 1 0 0 setrgbcolor 0 0 10 0 360 arc stroke 0 0 15 360 0 arcn stroke 0 setgray /pt { .1 0 360 arc fill } def HEAD
print "@$_ pt\n" for @points; print "%%EOF";</lang>
Randomly generates points and reject ones not in the ring. Writes an EPS file.
Perl 6
<lang perl6>my @range = -15..16;
my @points = gather for @range X @range -> $x, $y {
take [$x,$y] if 10 <= sqrt($x*$x+$y*$y) <= 15
} my @samples = @points.roll(100); # or .pick(100) to get distinct points
- format and print
my %matrix; for @range X @range -> $x, $y { %matrix{$y}{$x} = ' ' } %matrix{$_[1]}{$_[0]} = '*' for @samples; %matrix{$_}{@range}.join(' ').say for @range;</lang>
Turning that program completely inside-out and reducing to a single statement with a single non-parameter variable, we get this version, which also works:
<lang perl6>(say ~.map: { $_ // ' ' } for my @matrix) given do
-> [$x, $y] { @matrix[$x][$y] = '*' } for pick 100, do for ^32 X ^32 -> $x, $y { [$x,$y] when 100..225 given [+] ($x,$y X- 15) X** 2; }
</lang>
This uses, among other things, a 0-based matrix rather than a hash, a given on the first line that allows us to print the final value of the matrix straight from its initial declaration, a for statement feeding a for statement modifier, a lambda that unpacks a single x-y argument into two variables, the functional form of pick rather than the method form, a quasi-list comprehension in the middle loop that filters each given with a when, precalculated squared limits so we don't have to take the square root, use of X- and X** to subtract and exponentiate both $x and $y in parallel.
After the given do has loaded up @matrix with our circle, the map on the first line substitutes a space for any undefined matrix element, and the extra space between elements is supplied by the stringification of the list value, performed by the prefix ~ operator, the unary equivalent of concatenation in Perl 6.
At this point you would be justified in concluding that we are completely mad. :-)
PicoLisp
<lang PicoLisp>(let Area (make (do 31 (link (need 31 " "))))
(use (X Y) (do 100 (until (>= 15 (sqrt (+ (* (setq X (rand -15 15)) X) (* (setq Y (rand -15 15)) Y) ) ) 10 ) ) (set (nth Area (+ 16 X) (+ 16 Y)) "#") ) ) (mapc prinl Area) )</lang>
Output:
# ## # # # # ## # # # # # # # # # # # # # # # # # # # # # # # # ## # # # # # ### # # # # ## # # # # # # ## # # # # # # ### # # ### # # # # # # # ## # # # # # # # #
PL/I
<lang PL/I> constrain: procedure options (main);
declare 1 point (100), 2 x fixed binary, 2 y fixed binary; declare (i, j, a, b, c) fixed binary;
j = 0; do i = 1 to 100; a = 30*random()-15; b = 30*random()-15; c = sqrt(a**2 + b**2); if abs(c) >= 10 & abs(c) <= 15 then do; j = j + 1; x(j) = a; y(j) = b; end; end;
/* PLOT */ declare table(-15:15, -15:15) character (1); table = ' '; do i = 1 to j; table(x(i), y(i)) = '*'; end; do i = -15 to 15; put skip; do j = -15 to 15; put edit (table(i,j)) (a); end; end;
end constrain; </lang> Output:
** * * * ** ** * *** * * ** * * ** * * ** * * * *** *** *** * *
Prolog
Works with SWI-Prolog <lang Prolog>:- use_module(library(clpfd)).
circle :- bagof([X,Y], init(X,Y), BL), length(BL, N), length(L, 100), maplist(choose(BL, N), L), draw_circle(L).
% point selection
choose(BL, N, V) :-
I is random(N),
nth0(I, BL, V).
% to find all couples of numbers verifying % 100 <= x^2 + y^2 <= 225 init(X1, Y1) :- X in -15..15, Y in -15..15, X*X + Y*Y #>= 100, X*X + Y*Y #=< 225, label([X,Y]), X1 is 10 * X + 200, Y1 is 10 * Y + 200.
draw_circle(L) :-
new(D, window('Circle')),
send(D, size,size(400,400)),
forall(member([X,Y], L),
( new(C, circle(4)),
send(C, fill_pattern, colour(@default, 0, 0, 0)),
send(C, center(point(X,Y))),
send(D, display, C))),
send(D, open).
</lang>
PureBasic
<lang PureBasic>CreateImage(0,31,31) StartDrawing(ImageOutput(0))
For i=1 To 100 Repeat x=Random(30)-15 y=Random(30)-15 R.f=Sqr(x*x+y*y) Until 10<=R And R<=15 Plot(x+15,y+15,#Red) Next
StopDrawing()
Title$="PureBasic Plot"
Flags=#PB_Window_SystemMenu
OpenWindow(0,#PB_Ignore,#PB_Ignore,ImageWidth(0),ImageHeight(0),Title$,Flags)
ImageGadget(0,0,0,ImageWidth(0),ImageHeight(0),ImageID(0))
Repeat: Until WaitWindowEvent()=#PB_Event_CloseWindow</lang>
Python
Note that the diagram shows the number of points at any given position (up to a maximum of 9 points). <lang python>>>> from collections import defaultdict >>> from random import choice >>> world = defaultdict(int) >>> possiblepoints = [(x,y) for x in range(-15,16) for y in range(-15,16) if 10 <= abs(x+y*1j) <= 15] >>> for i in range(100): world[choice(possiblepoints)] += 1
>>> for x in range(-15,16): print(.join(str(min([9, world[(x,y)]])) if world[(x,y)] else ' ' for y in range(-15,16)))
1 1 1 1 11 1 1 1 1 111 1 1211 1 2 1 1 11 1 11 21 1 1 11 1 1 2 1 1 1 2 1 1 1 1 1 2 11 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 3 11 2 11 1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 1 </lang>
If the number of samples is increased to 1100: <lang python>>>> for i in range(1000): world[choice(possiblepoints)] += 1
>>> for x in range(-15,16): print(.join(str(min([9, world[(x,y)]])) if world[(x,y)] else ' ' for y in range(-15,16)))
2 41341421333 5133333131253 1 5231514 14214721 24 326 21222143234122322 54235153132123344125 22 32331432 2422 33 5453135 4144344 132595 323123 4 6353 432224 5 4323 3 5313 23214 41433 42454 33342 332 4 34314 142 1 35 53
124211 53131
22221 152 4 22213 34562 654 4 4 212 24354 52232 544222 283323 411123 453325 251321 124332 2124134 2443226 2 113315 64324334 2412452 324 32121132363 4222434324635 5433 3113333123432112633 2131181233 424 47414232164 4 </lang>
R
<lang R> RMin <- 10 RMax <- 15 NPts <- 100
- instead of a for loop, we generate what should be enough points
- also take care to have enough range to avoid rounding inaccuracies
nBlock <- NPts * ((RMax/RMin) ^ 2) nValid <- 0 while (nValid < NPts) { X <- round(runif(nBlock, -RMax - 1, RMax + 1)) Y <- round(runif(nBlock, -RMax - 1, RMax + 1)) R <- sqrt(X^2 + Y^2) Valid <- ( (R >= RMin) & (R <= RMax) ) nValid <- sum(Valid) nBlock <- 2 * nBlock } plot(X[Valid][1:NPts],Y[Valid][1:NPts], pch=19, cex=0.25, col="blue", xlab="x",ylab="y",main="Fuzzy circle", xlim=c(-RMax,RMax), ylim=c(-RMax,RMax) ) </lang>
Example of solution
Ruby
Create the image with Raster graphics operations/Ruby <lang Ruby>points = (1...100).map {
# choose a random radius and angle angle = rand * 2.0 * Math::PI rad = rand * 5.0 + 10.0 # convert back from polar to cartesian coordinates [rad * Math::cos(angle), rad * Math::sin(angle)].map(&:round) }
(-15..15).each do |row|
puts((-15..15).map { |col| points.include?([row, col]) ? "X" : " " }.join)
end
load 'raster_graphics.rb'
pixmap = Pixmap.new(321,321) pixmap.draw_circle(Pixel.new(160,160),90,RGBColour::BLACK) pixmap.draw_circle(Pixel.new(160,160),160,RGBColour::BLACK) points.each {|(x,y)| pixmap[10*(x+16),10*(y+16)] = RGBColour::BLACK} pngfile = __FILE__ pngfile[/\.rb/] = ".png" pixmap.save_as_png(pngfile)</lang>
outputs:
![Sample output from Ruby program](http://static.miraheze.org/rosettacodewiki/4/4f/Constrainedrandompointsonacircle.png)
X X X XX X XXX XX X X X X X XXXXX XX XX X X X X X X X X X XXX X XX X X X X X X XXX X XX X XXX X X XX X X X XX X X X X X XX X X X X X X X X X X X X X X X X X
SystemVerilog
<lang SystemVerilog>program main;
bit [39:0] bitmap [40];
class Point; rand bit signed [4:0] x; rand bit signed [4:0] y;
constraint on_circle_edge { (10*10) <= (x*x + y*y); (x*x + y*y) <= (15*15); };
function void do_point(); randomize; bitmap[x+20][y+20] = 1; endfunction endclass
initial begin Point p = new; repeat (100) p.do_point; foreach (bitmap[row]) $display( "%b", bitmap[row]); end
endprogram</lang>
Piping the output through sed to improve the contrast of the output:
% vcs -sverilog -R circle.sv | sed 's/0/ /g' 1 11 1 1 1 1 1 11 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 11 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 11 1111 1 1 111 1 11 1 111 1 11 1 1 1 1 1 1 1 11 1 1 1 11 1 1
Tcl
<lang tcl>package require Tcl 8.5
- Generate random point at specified distance from the centre
proc getPoint {range from to} {
set r2 [expr {$range / 2}] set f2 [expr {$from ** 2}] set t2 [expr {$to ** 2}] while 1 {
set x [expr {int($range * rand())}] set y [expr {int($range * rand())}] set d2 [expr {($x-$r2)**2 + ($y-$r2)**2}] if {$d2 >= $f2 && $d2 <= $t2} { return [list $y $x] }
}
}
- Make somewhere to store the counters
set ary [lrepeat 31 [lrepeat 31 0]]
- Generate 100 random points
for {set i 0} {$i < 100} {incr i} {
set location [getPoint 31 10 15] # Increment the counter for the point lset ary $location [expr {1 + [lindex $ary $location]}]
}
- Simple renderer
foreach line $ary {
foreach c $line {
puts -nonewline [expr {$c == 0 ? " " : $c > 9 ? "X" : $c}]
} puts ""
}</lang> Example output:
1 1 1 1 1 1 2 1 1 11 1 1 1 11 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 1 1 11 1 1 1 1 1 2 1 1 1 1 1 1 1 11 1 2 1 1 11 11 1 1 1 1 2 1 11 121 1 1 1 1 1 1