Constrained random points on a circle

From Rosetta Code
Task
Constrained random points on a circle
You are encouraged to solve this task according to the task description, using any language you may know.
Task

Generate   100   <x,y>   coördinate pairs such that   x   and   y   are integers sampled from the uniform distribution,
with the condition that  

Then display/plot the coördinate pairs.   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[edit]

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;

Output:

Randomly generated:

              **
          *  *    * *
               * * *  **
     *     * *      *
    **  *              * *
   *     *           *  *
      *              *   * *
   *                   **
  *    *               *
    *
    *                       *
   *                      * *
  * *                        *
                             *

   * *                       *
  *
     *                       *
  ***                      *
     *                  *    *
                            *
   *                       *
                     **    *
         **
     *        *   **     *
         * *        * *
      ***  * *         **
        * *   * ***
               *  *

Chosen from precalculated:

            *
            *    *   *
           * **   ** ** *
           * *  * *
                      *
   *  ** *              *
    *    *               * *
  *    *                ***
  *  ***                 *
                        *  * *
                            *

  *                       * *
    *                      **

   *
 *  **                     ***
                           *
                         *   *
  * **
   *                     *
     *
    *   *
         **           *
    *  *     *  *       * *
       **  *       *  * *
      *   **
        *
           *    * ***

ALGOL 68[edit]

Translation of: C
- note: This specimen retains the original C coding style.
Works with: ALGOL 68 version Revision 1 - no extensions to language used - requires ansi/xterm & ascii
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
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)
)

Sample output:

           *  * **
        * * *  * ** **
      ***** **   ***** **
     ** **  *  * * * ***
      *  ******** *** *** *
   ** *****         ** * ***
        *            ***** *
   ** **               **** *
   * * *               ****
  ****                  * ****
 * **                    *** *
 ** **                    **
 **                      * * *
  ****                   **  *
 ** *                    ****
 ****                     ** *
 *  **                   *  **
  * **                    *  *
 * ***                    *  *
 ******                 * * **
  * * **               **** *
   ** *                ***  *
   **** **           *    **
    ** ***            * ***
    * *  *** * **  *** ***
      *  *  ** ***** ****
      ** ******* *  *
        * ** ** *******
          *  ****** *
               *

AutoHotkey[edit]

Requires the GDI+ standard library by tic: http://www.autohotkey.com/forum/viewtopic.php?t=32238
Works with individual pixels.

Ahk fuzzycircle.png
z=100 ; x = x-coord; y = y-coord; z = count; pBitmap = a pointer to the image; f = filename
 
pToken := Gdip_Startup()
pBitmap := Gdip_CreateBitmap(31, 32)
 
While z
{
Random, x, -20, 20
Random, y, -20,20
If ( t := sqrt(x**2 + y**2) ) >= 10 && t <= 15
Gdip_SetPixel(pBitmap, x+15, y+16, 255<<24), z--
}
 
Gdip_SaveBitmapToFile(pBitmap, f := A_ScriptDir "\ahk_fuzzycircle.png")
run % f
 
Gdip_DisposeImage(pBitmap)
Gdip_Shutdown(pToken)

BASIC[edit]

BBC BASIC[edit]

      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

FreeBASIC[edit]

Pre calculate and plot 100 points to the console

'Free Basic version .9
 
#define Intrange(f,l) int(Rnd*(((l)+1)-(f))+(f))
 
Type pair
As Integer x,y
End Type
 
Operator =(a As pair,b As pair) As Integer
Return a.x=b.x And a.y=b.y
End Operator
 
Function NotInArray(a() As pair,n As pair) As Integer
For z As Integer=Lbound(a) To Ubound(a)
If a(z)=n Then Return 0
Next z
Return -1
End Function
 
Redim As pair pts(0)
Dim As Integer x,y,counter
Do
counter=counter+1
x=IntRange(-20,20)
y=IntRange(-20,20)
var root=Sqr(x*x+y*y)
If 10<= root And root<=15 Then
If NotInArray(pts(),Type<pair>(x,y)) Then
Redim Preserve pts(1 To Ubound(pts)+1)
pts(Ubound(pts))=Type<pair>(x,y)
End If
End If
Loop Until counter=100000
 
'============== Plot to Console ======================
 
dim as integer yres=hiword(width)
dim as integer xres=loword(width)
 
#define map(a,b,x,c,d) ((d)-(c))*((x)-(a))/((b)-(a))+(c)
#define _X(num) int( map(0,xres,(num),0,loword(width)))
#define _Y(num) int( map(0,yres,(num),0,hiword(width)))
 
counter=0
For n As Integer=Lbound(pts) To Ubound(pts)
counter=counter+1
if counter <=100 then
var xpos=map(-20,20,pts(n).x,0,xres)
var ypos=map(-20,20,pts(n).y,0,yres)
locate _Y(ypos),_X(xpos)
print "*"
end if
Next n
 
print
locate 1,1
Print "Total number of points "; counter
print "Total number plotted ";100
print "done"
Sleep
 

Console output:

Total number of points  404
Total number plotted    100
done                                           * *
                         *                 *       *
                           *     * * *       *           *
                 * * * *     *                 * * *     *     *
                 * *                               *   * *
             *   * * * *                                         *
                                                             *
             * *                                           *     * *
           * *   *                                         * *     *
               *                                             * *   *
             * * *                                           *     *

                   *                                         * * * *
               *   * *                                     * * *
               *           *                         *
                 *         *         *   *     * *     *     *
                               *         *     * *
                     *   *   *   *   * * *   *   *     * *
                                       * *   * * *


C[edit]

#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;
}
Output
                            .   .     . .                     
. . .
. . . .
. . .
. . . . .
. . .
. . .
. .
. .
. .
. .
. . . .
. . .
 
.
.
 
. . .
. . .
. . .
. . . .
. . . . .
. .
. . . .
. . . . . . .
. . . .
. . . . . . .
. . . .
.
.

C++[edit]

Constrained rnd pts on circle.png

 
#include <windows.h>
#include <list>
#include <iostream>
 
//--------------------------------------------------------------------------------------------------
using namespace std;
 
//--------------------------------------------------------------------------------------------------
class point
{
public:
int x, y;
point() { x = y = 0; }
point( int a, int b ) { x = a; y = b; }
void set( int a, int b ) { x = a; y = b; }
};
//--------------------------------------------------------------------------------------------------
class rndCircle
{
public:
void draw()
{
createPoints();
drawPoints();
}
 
private:
void createPoints()
{
point pt;
for( int x = 0; x < 200; x++ )
{
int a, b, c;
while( true )
{
a = rand() % 31 - 15;
b = rand() % 31 - 15;
c = a * a + b * b;
if( c >= 100 && c <= 225 ) break;
}
pt.set( a, b );
_ptList.push_back( pt );
}
}
 
void drawPoints()
{
HDC dc = GetDC( GetConsoleWindow() );
for( list<point>::iterator it = _ptList.begin(); it != _ptList.end(); it++ )
SetPixel( dc, 300 + 10 * ( *it ).x, 300 + 10 * ( *it ).y, RGB( 255, 255, 0 ) );
}
 
list<point> _ptList;
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
ShowWindow( GetConsoleWindow(), SW_MAXIMIZE );
srand( GetTickCount() );
rndCircle c;
c.draw();
system( "pause" );
return 0;
}
//--------------------------------------------------------------------------------------------------
 

Clojure[edit]

(ns rosettacode.circle-random-points
(:import [java.awt Color Graphics Dimension]
[javax.swing JFrame JPanel]))
 
(let [points (->> (for [x (range -15 16), y (range -15 16)
:when (<= 10 (Math/hypot x 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))

CoffeeScript[edit]

 
NUM_POINTS = 100
MIN_R = 10
MAX_R = 15
 
random_circle_points = ->
rand_point = ->
Math.floor (Math.random() * (MAX_R * 2 + 1) - MAX_R)
 
points = {}
cnt = 0
while cnt < 100
x = rand_point()
y = rand_point()
continue unless MIN_R * MIN_R <= x*x + y*y <= MAX_R * MAX_R
points["#{x},#{y}"] = true
cnt += 1
points
 
plot = (points) ->
range = [-1 * MAX_R .. MAX_R]
for y in range
s = ''
for x in range
s += if points["#{x},#{y}"] then '*' else ' '
console.log s
 
plot random_circle_points()
 

The output may be a bit distorted, since even monospace fonts take more vertical space per character than horizontal space.

 
> coffee foo.coffee
 
** *
* ** * *
* * * *
* ** *
* * * *
* *
*
* *
***
** **** *
* *
* *
**
*
 
* **
* * *
**
* * **
* *
* *
* *
* *
***
*** * * * * *
*** *
* * * * *
* * *
 

Common Lisp[edit]

(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)))

D[edit]

This uses std.complex because D built-in complex numbers will be deprecated.

import std.stdio, std.random, std.math, std.complex;
 
void main() {
char[31][31] table = ' ';
 
foreach (immutable _; 0 .. 100) {
int x, y;
do {
x = uniform(-15, 16);
y = uniform(-15, 16);
} while(abs(12.5 - complex(x, y).abs) > 2.5);
table[x + 15][y + 15] = '*';
}
 
writefln("%-(%s\n%)", table);
}
Output:
                               
                   *           
          * **  *              
                  * *          
     **  * *   **  *  *        
    *    *            **  *    
        **            **  *    
                       *   *   
                        *      
       *                 ***   
 *  * *                        
   * *                     *   
   *                        *  
     *                      *  
   **                    * *   
  *                       *    
                            *  
                             * 
  *                          * 
                               
   *                           
     *                     **  
    * *                  *     
         *           * *  *    
   *     *             **      
    *     *  *  *     * *      
     **     *  **   **   *     
          **                   
        *     *  *  *          
               **              


EchoLisp[edit]

Using the plot library. For a greater visual appeal, points are plotted as circles of random radius and color. The resulting image is at [1].

 
(lib 'math)
(lib 'plot)
 
(define (points (n 100) (radius 10) (rmin 10) (rmax 15) (x) (y))
(plot-clear)
(plot-x-minmax (- rmax))
(plot-y-minmax( - rmax))
 
(for [(i n)]
(set! x (round (* (random -1) rmax)))
(set! y (round (* (random -1) rmax)))
#:when (in-interval? (pythagore x y) rmin rmax)
;; add a little bit of randomness : dots color and radius
(plot-fill-color (hsv->rgb (random) 0.9 0.9))
(plot-circle x y (random radius)))
(plot-edit))
 

Elixir[edit]

Algorithm 1: Generate random pairs[edit]

Works with: Elixir version 1.1
defmodule Random do
defp generate_point(0, _, _, set), do: set
defp generate_point(n, f, condition, set) do
point = {x,y} = {f.(), f.()}
if x*x + y*y in condition and not point in set,
do: generate_point(n-1, f, condition, MapSet.put(set, point)),
else: generate_point(n, f, condition, set)
end
 
def circle do
f = fn -> :rand.uniform(31) - 16 end
points = generate_point(100, f, 10*10..15*15, MapSet.new)
range = -15..15
for x <- range do
for y <- range do
IO.write if {x,y} in points, do: "x", else: " "
end
IO.puts ""
end
end
end
 
Random.circle

Example output:

               x
           x x xx    x
      x x  x  x xxx x
         x x x   xx    x
    x  x  x   x     x   x
        xx               x
    xx  x             x
                          xxx
     xxx
                          xxx
 x                           x

 x                          xx
   xx                        x
 x
                            xx
   x                     x  x
  xx
  x                      x
  xx x                   x   x
  x x                     x
       x                 x
      x               xx  xx
     x                x  x
          x  x      x   x
       x xx          x xx
          x    xx x    x
           x xx  x
                x  xx

Algorithm 2: Precalculate[edit]

Translation of: Ruby
Works with: Elixir version 1.2
defmodule Constrain do
def circle do
range = -15..15
r2 = 10*10..15*15
all_points = for x <- range, y <- range, x*x+y*y in r2, do: {x,y}
IO.puts "Precalculate: #{length(all_points)}"
points = Enum.take_random(all_points, 100)
Enum.each(range, fn x ->
IO.puts Enum.map(range, fn y -> if {x,y} in points, do: "o ", else: " " end)
end)
end
end
 
Constrain.circle
Example:
Precalculate: 404

                      o       o
                                          o
                  o o o     o         o         o
          o o         o                   o o
            o   o o o     o             o o
      o o   o                                   o
        o o o o                           o
    o         o                                 o       o
    o o                                       o   o     o
    o   o                                               o

                                                  o   o   o
                                                  o     o
  o       o                                               o
o     o                                               o   o o
                                                    o
      o                                           o       o
      o   o                                       o o   o o
                                                        o
                                                  o       o
    o o                                         o
            o                                   o     o
                                          o o   o o   o
            o                           o     o
                o                 o o o o       o o
          o   o           o               o o   o
                                      o
                  o o
                      o       o

Euphoria[edit]

Works with: Euphoria version 4.0.3, 4.0.0 or later

This program generates the set of 404 possible points in the ring. It randomly chooses 100 pairs from the set. The 100 pairs are a subset of that set because duplicates are discarded.

include std/console.e
 
sequence validpoints = {}
sequence discardedpoints = {}
sequence rand100points = {}
atom coordresult
integer randindex
 
--scan for all possible values. store discarded ones in another sequence, for extra reference.
for y = -15 to 15 do
for x = -15 to 15 do
 
coordresult = sqrt( x * x + y * y )
 
if coordresult >= 10 and coordresult <= 15 then --if it would fall in the ring area
validpoints &= {{x, y, coordresult}} --concatenate (add to the end) the coordinate pair x, y and the
-- result into a subsequence of sequence validpoints
else
discardedpoints &= {{x, y, coordresult}} --else put it in the discarded sequence
end if
 
end for
end for
 
for i = 1 to 100 label "oneofhundred" do --make 100 random coordinate pairs
randindex = rand(length(validpoints) ) --random value from 1 to the number of 3 value subsequences in validpoints (the data)
 
if length(rand100points) = 0 then --if rand100points sequence is empty, add the first subsequence to it.
rand100points &= {validpoints[randindex]}
 
else --if it isn't empty, then..
for j = 1 to length(rand100points) do --loop through each "data chunk" in rand100points
 
if equal(validpoints[randindex], rand100points[j]) = 1 then --if any are the same as the randomly chosen chunk in
retry "oneofhundred" -- validpoints, then retry from one line below the "oneofhundred" loop without incrementing i.
end if --the continue keyword would increment i instead.
 
end for
 
rand100points &= {validpoints[randindex]} --length of rand100points isnt 0 and no data chunks match ones that the program
--already picked before, so add this subsequence chunk to rand100points.
end if
 
end for
 
for i = 1 to 32 do --32 lines
printf(1,"\n")
for j = 1 to 32 label "xscan" do --32 characters on each line
 
for k = 1 to length(rand100points) do --for every subsequence in this
if rand100points[k][1]+16 = j and rand100points[k][2]+16 = i then --if the x and y coordinates in the picked points
printf(1, 178) --(adjusted to minimum of 1,1) are at the same place as in the console output grid
continue "xscan" --print a funny character and continue to the next "xscan"
end if
end for
 
printf(1, 176) --if no picked points were there, print another funny character to represent a blank space
 
end for
end for
 
printf(1, "\nNumber of valid coordinate pairs %d :", length(validpoints) )
printf(1, "\nNumber of discarded coordinate pairs : %d", length(discardedpoints) )
printf(1, "\nNumber of randomly picked coordinate pairs : %d\n", length(rand100points) )
any_key()

Output:

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░▓░░░░░░░░░░░░░░
░░░░░░░░░░░░░▓░░░░░░░░░░░░░░░░░░
░░░░░░░░░▓░░░▓▓░▓░░░▓░░░░░░░░░░░
░░░░░░▓░░░░░░▓░░░▓░░░░░▓░▓░░░░░░
░░░░░░░░░▓░▓░░░░░░░▓░░▓░░▓▓░░░░░
░░░▓░░░░▓░▓░░░░░░░░░░░░▓░░░░░░░░
░░░░░░░░░▓░░░░░░░░░░░▓░░░▓░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░▓▓░░▓░░░
░░░░░░▓▓░░░░░░░░░░░░░░░▓░░░░░░░░
░░░░░░▓░░░░░░░░░░░░░░░░░░░░░░░░░
░▓░░▓▓░░░░░░░░░░░░░░░░░░░░░░░▓░░
░░░░░▓░░░░░░░░░░░░░░░░░░░░░░▓░░░
░░▓░░░░░░░░░░░░░░░░░░░░░░▓▓▓▓░░░
░▓░░▓░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░▓░░░░░░░░░░░░░░░░░░░░▓▓▓░▓░░
░░░▓░░░░░░░░░░░░░░░░░░░░░▓░▓░▓░░
░▓▓░░░░░░░░░░░░░░░░░░░░░░░▓▓░░░░
░░░▓░▓░░░░░░░░░░░░░░░░░░░▓░░░░░░
░░░▓░░░░░░░░░░░░░░░░░░░░░▓░░░▓░░
░░▓░▓░░░░░░░░░░░░░░░░░░░▓░░░▓░░░
░░░░░░░▓░░░░░░░░░░░░░░░▓░░░░░░░░
░░░▓░░░░░░░░░░░░░░░░░░░▓░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░▓░░░░░░░
░░░░░░▓░░▓░░░░░░░░░░░▓░▓░░░░░░░░
░░░░░░░░░░░░░░░░░▓░░░░░░░░░░░░░░
░░░░░░░▓░░▓░░░░░░░░░░░░▓░░░░░░░░
░░░░░░░░░░░░░▓░▓▓▓▓░░░▓▓░░░░░░░░
░░░░░░░░░▓▓░░▓░░▓░░▓▓░░░░░░░░░░░
░░░░░░░░░░▓░░▓░▓▓▓░░▓░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
Number of valid coordinate pairs 404 :
Number of discarded coordinate pairs : 557
Number of randomly picked coordinate pairs : 100
Press Any Key to continue...
Extra EuSDL code :
 
for i = 1 to length(validpoints) do --simple each pixel output to screen surface
dummy=pixelColor(surface,validpoints[i][1]+18,validpoints[i][2]+18,#AA0202FF) --i is index number of each subsequence 'chunk'.
--index 1 is x, index 2 is y, inside that chunk.
end for
 
for i = 1 to length(discardedpoints) do
dummy=pixelColor(surface,discardedpoints[i][1]+18,discardedpoints[i][2]+52,#0202AAFF)
end for
 
for i = 1 to length(rand100points) do
dummy=pixelColor(surface,rand100points[i][1]+55,rand100points[i][2]+52,#02AA02FF)
end for
 
dummy=boxColor(surface,0,71,395,111,#232323FF) --background box
dummy=stringColor(surface,0,73,sprintf("Number of valid coordinate pairs %d :", length(validpoints) ),#AA0202FF)
 
dummy=stringColor(surface,0,83,sprintf("Number of discarded coordinate pairs : %d", length(discardedpoints) ),#0202AAFF)
 
dummy=stringColor(surface,0,93,sprintf("Number of randomly picked coordinate pairs : %d", length(rand100points) ),#02AA02FF)
SDL Output :

Fuzzy circle Euphoria.png That particular program used a -16 to +16 square area, so more was discarded.

F#[edit]

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.

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

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


Falcon[edit]

 
// Generate points in [min,max]^2 with constraint
function random_point (min, max, constraint)
[x, y] = [random(min, max), random(min, max)]
return constraint(x, y) ? [x, y] : random_point(min, max, constraint)
end
 
// Generate point list
in_circle = { x, y => 10**2 <= x**2 + y**2 and x**2 + y**2 <= 15**2 }
points = [].comp([0:100], {__ => random_point(-15, 15, in_circle)})
 
// Show points
for i in [-15:16]
for j in [-15:16]
>> [i, j] in points ? "x" : " "
end
>
end
 

Example output:

          xxx  x               
        xx x  x  xx            
          x    xx      xx      
      x x     x x x x x x      
              x      x         
     xx   x          x         
   x    x            x         
     xx                        
  x  x                   xx    
      x                 x      
                         x   x 
 x                        xx   
                             x 
                               
                           xx  
     x                   xx    
 x                       xx  x 
    x                          
                               
  xx  x                     xx 
  xx                    x   x  
                               
         x                 x   
       x x           x    x    
         x     x   x           
     x     x x   x  x    x     
                    x x        
              x x x x          

Fortran[edit]

Works with: Fortran version 90 and later
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

Output

                  * * 
        *   *         * 
      ** **    * **    * 
                ** 
     *  **   * **    * 
   ***   **               * 
    *    *           * 
                           * 
  *                      *  * 
     **                   * 
   *                      * 
  *  *                   * 
    *                        * 
    * 
    **                   ***  * 
    *                    * 
    **                   * 
    *                    * 
   *                      * 
  *   *                      * 
      **                 *  * 
    * *                *  ** 
   ** * *               * 
     * 
          ***         * * * 
     **         *   *    * 
         *  * * * 
         *     *  ** * 
            *

Go[edit]

Algorithm 1:

package main
 
import (
"bytes"
"fmt"
"math/rand"
"time"
)
 
const (
nPts = 100
rMin = 10
rMax = 15
)
 
func main() {
rand.Seed(time.Now().Unix())
span := rMax + 1 + rMax
rows := make([][]byte, span)
for r := range rows {
rows[r] = bytes.Repeat([]byte{' '}, span*2)
}
u := 0 // count unique points
min2 := rMin * rMin
max2 := rMax * rMax
for n := 0; n < nPts; {
x := rand.Intn(span) - rMax
y := rand.Intn(span) - rMax
// x, y is the generated coordinate pair
rs := x*x + y*y
if rs < min2 || rs > max2 {
continue
}
n++ // count pair as meeting condition
r := y + rMax
c := (x + rMax) * 2
if rows[r][c] == ' ' {
rows[r][c] = '*'
u++
}
}
for _, row := range rows {
fmt.Println(string(row))
}
fmt.Println(u, "unique points")
}

Algorithm 2:

package main
 
import (
"bytes"
"fmt"
"math/rand"
"time"
)
 
const (
nPts = 100
rMin = 10
rMax = 15
)
 
func main() {
rand.Seed(time.Now().Unix())
var poss []struct{ x, y int }
min2 := rMin * rMin
max2 := rMax * rMax
for y := -rMax; y <= rMax; y++ {
for x := -rMax; x <= rMax; x++ {
if r2 := x*x + y*y; r2 >= min2 && r2 <= max2 {
poss = append(poss, struct{ x, y int }{x, y})
}
}
}
fmt.Println(len(poss), "possible points")
span := rMax + 1 + rMax
rows := make([][]byte, span)
for r := range rows {
rows[r] = bytes.Repeat([]byte{' '}, span*2)
}
u := 0
for n := 0; n < nPts; n++ {
i := rand.Intn(len(poss))
r := poss[i].y + rMax
c := (poss[i].x + rMax) * 2
if rows[r][c] == ' ' {
rows[r][c] = '*'
u++
}
}
for _, row := range rows {
fmt.Println(string(row))
}
fmt.Println(u, "unique points")
}
Output:
404 possible points
                                                              
                            * *       *                       
                          *           * *                     
                    *     * *       * *                       
            *   *   * * *             *   *                   
          *   *     *   *     *     *       *                 
                                              * * *           
            *   *                                 * * *       
    * *   *                                       *           
    * *   *                                     * *           
        *                                                     
      *                                             *     *   
                                                              
      *                                               * *     
      * *                                                     
* *                                                       *   
    *                                                         
                                                              
      * *                                                     
    *                                               *   *     
      *                                           *           
                                                    *         
    *       *                                                 
          * *                                       *         
              *                         *                     
                  * *         *     *   *     * *             
            *     *   * *                                     
                            *     *     *     *               
                      *   *       *                           
                      *                                       
                              *                               
90 unique points

Haskell[edit]

Using Knuth Shuffle

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). unfoldr (Just . splitAt 31) $ canvas

Output (added a trailing space per 'pixel'

*Main> task
                                                              
                      /             / /                       
                          /     /       /                                       
              /                 /                                               
          /     /               /       / / /   /                               
            /                 / /       /                                       
      /     /     /                       /   /                                 
      /         /                           /                                   
        /   / /                                     /   /                       
        / / /                                 /       / /                       
                                                    /                           
    /     /                                       /                             
      / /                                             /                         
      /                                               /   /                     
        /                                                                       
/ /                                                   /     / 
                                                      /   /                     
                                                      /   /                     
      /                                                                         
      /                                             /                           
  /                                                   /       
                                                /     /                         
    /     /                                       /           
              / /                         / /         /       
        /   /       /                             /           
                          / /     / / /   / /                 
          / /             /                   /               
                            / /                               
                /   /   / / /   /       / /                   
                      /             / /

Hy[edit]

(import
[math [sqrt]]
[random [choice]]
[matplotlib.pyplot :as plt])
 
(setv possible-points (list-comp (, x y)
[x (range -15 16) y (range -15 16)]
(<= 10 (sqrt (+ (** x 2) (** y 2))) 15)))
 
(setv [xs ys] (apply zip (list-comp (choice possible-points) [_ (range 100)])))
; We can't use random.sample because that samples without replacement.
(plt.plot xs ys "bo")
(plt.show)

Icon and Unicon[edit]

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.
plot of 2000, 100, 120
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

J[edit]

This version deals 100 distinct coordinates from the set of acceptable coordinates (much like dealing cards from a shuffled deck):

gen=: ({~ 100?#)bind((#~ 1=99 225 I.+/"1@:*:),/,"0/~i:15)

Example use (gen'' generates the points, the rest of the example code deals with rendering them as a text array):

   '*' (<"1]15+gen '')} 31 31$' '
 
*
*
* * * * * *
* * * * *
* ***
** * * **
* **
* **
* * * *
* * **
* ** **
** * ***
* ** * *
** *
* ** *
** *
* ** *
* *
* *
* *
** *
* **
*
* * * *
* ** * * *
* *
**
* * *
** *

Java[edit]

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();
}
}
}

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[edit]

JavaScript embedded in HTML, using canvas:

<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>

Julia[edit]

This solution uses the "pick random x, y and cull" rather than the "calculate valid and choose randomly" approach.

 
const LO = 10
const HI = 15
const GOAL = 100
 
canvas = falses(2HI+1, 2HI+1)
i = 0
 
while i < GOAL
x = rand(-HI:HI)
y = rand(-HI:HI)
LO^2-1 < x^2 + y^2 < HI^2+1 || continue
i += 1
canvas[x+HI+1, y+HI+1] = true
end
 
for i in 1:(2HI+1)
println(" ", join(map(j -> j ? "\u25cf " : " ", canvas[i,:])))
end
 
Output:
                                                                 
                          ●                 ●                     
                          ●     ● ● ●           ●                 
                  ●         ● ●                 ●                 
                ●           ●                 ●     ●             
                    ●           ●               ● ●               
                  ●                                 ●             
                    ●                         ●       ●           
        ●       ●                                     ●           
        ●                                               ●         
                                                        ● ● ● ●   
              ●                                       ●           
          ●                                                       
        ● ● ●                                             ●   ●   
                                                        ●     ●   
                                                                  
          ●                                             ●   ●     
                                                          ●       
      ●                                                 ● ●       
            ●                                         ●           
      ●   ●                                                       
          ● ●     ●                                 ●       ●     
                ● ●                                   ●   ●       
                      ●                                           
            ● ●       ● ●                       ●                 
              ●         ● ● ● ●   ●             ● ● ● ●           
                ●   ●           ●   ● ● ●                         
                            ● ●   ●                               
                        ●             ●                           
                            ● ●                                   
                                                                  

Liberty BASIC[edit]

'   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

Locomotive Basic[edit]

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

Points on a circle locomotive basic.png

Maple[edit]

 a := table():
i := 1:
while i < 100 do
ba := (rand(-15 .. 15))():
bb := (rand(-15 .. 15))():
b := evalf(sqrt(ba^2+bb^2)):
if b <= 15 and b >= 10
then a[i] := [ba, bb]:
i := i+1:
end if:
end do:
plots:-pointplot(convert(a,list));

Mathematica / Wolfram Language[edit]

This algorithm generates 500 pairs of random integers between +/- 15, picks out the ones that satisfy the inequality, and then takes the first 100 of those. It oversamples to reduce the chance of having less than 100 "candidates", which is not impossible, though extremely unlikely.

sample = Take[Cases[RandomInteger[{-15, 15}, {500, 2}], {x_, y_} /; 10 <= Sqrt[x^2 + y^2] <= 15], 100];
 
Show[{RegionPlot[10 <= Sqrt[x^2 + y^2] <= 15, {x, -16, 16}, {y, -16, 16}, Axes -> True], ListPlot[sample]}]

MATLAB[edit]

Uses the Monte-Carlo method described above.

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

Output:

>> [x,y] = randomDisc(100);
>> plot(x,y,'.')

Matlab-randomDisc-output.png

Maxima[edit]

randomDisc(numPoints):= block([p: []],
local(goodp, random_int),
goodp(x, y):=block([r: sqrt(x^2+y^2)],
r>=10 and r<=15
),
random_int():= block([m: 15], m - random(2*(m+1)-1)),
while length(p)<numPoints do block (
[x: random_int(), y : random_int()],
if goodp(x, y) then (
p: cons([x, y], p)
)
),
p)$
 
p: randomDisc(100)$
plot2d(['discrete, p], ['style, 'points]);

Nim[edit]

Translation of: Python
import tables, math, strutils, complex
randomize()
 
proc random[T](a: openarray[T]): T =
result = a[random(low(a)..len(a))]
 
type Point = tuple[x, y: int]
 
var world = initCountTable[Point]()
 
var possiblePoints = newSeq[Point]()
for x in -15..15:
for y in -15..15:
if abs((x.float, y.float)) in 10.0..15.0:
possiblePoints.add((x,y))
 
for i in 0..100: world.inc possiblePoints.random
 
for x in -15..15:
for y in -15..15:
if world[(x,y)] > 0:
stdout.write min(9, world[(x,y)])
else:
stdout.write ' '
echo ""

Output:

               1               
          1211      1          
                               
      1 1 3       1   1        
                3     11       
    1  11    1   1    1        
       122           21  1     
                               
                        1 1 2  
                        1      
      1                   1    
 11                      11    
   1 1                   1     
   1                           
  11                      1    
  1  1                      11 
 2   1                         
                           1   
     1                       1 
                         1 1   
                           11  
                       11      
    1 1                   111  
    1                1 1 1     
       1            11         
                 1 1     1     
     12 2        11   1  1     
              1 1 1 1 1        
        11 1                   
              1                

OCaml[edit]

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


                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[edit]

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)
};

Perl[edit]

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";

Randomly generates points and reject ones not in the ring. Writes an EPS file.

Perl 6[edit]

Works with: rakudo version 2015.09
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;

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:

(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;
}
 

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. :-)

Phix[edit]

sequence screen = repeat(repeat(' ',31),31)
integer x, y, count = 0
atom r
while 1 do
x = rand(31)
y = rand(31)
r = sqrt(power(x-16,2)+power(y-16,2))
if r>=10 and r<=15 then
screen[x][y] = 'x'
count += 1
if count>=100 then exit end if
end if
end while
puts(1,join(screen,"\n"))
Output:
                x  xx
              x   x   x
         x x   x  x    x
          x     x   x   x
     x     x      xx
    x                x x  x
   xx xx              x
                         x
       x
  x
  x                       x
                           x
    x                    x  x
 xx                      xxxx
    x                       x
                          x  x
                           x
  x x                     x
     x
  x                       x
  xx x                   x x
   x                     x
        x             x   x
       x  x         x   x
          x x xx          x
      x  x       x  xx xx
                   xx x
          x    xx
             x   x  x

PicoLisp[edit]

(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) )

Output:

           #
        ##
           #  #  #  #
         ## #    #  #   #
       #      #   # # #
    #       #     # #   #
      #   #         #    #
      #                #   #
                       #
       #               #
     ##                      #
                          #
   #                      # #
  ###                      #
 #                         # #
##                          # #
  #                        #
 #                        #
 ## #
                           #
   #
     #                 #
     #
   ###                  #   #
      ###           # #    #
    #      #
         #  #   ##
                 # #
      #     #           #
                # #  #

PL/I[edit]

version 1[edit]

 
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;
 

Output:

        **  *                  
                *   *          
                               
    **                         
         **                    
                               
                         *     
                           *** 
      *                        
                               
                               
                         *     
    **                         
                               
                           *   
 * **                          
                               
                               
                        * *    
  **                        *  
     * *                       
                               
                     ***       
                         ***   
       ***                     
            *                  
                     *

version 2[edit]

*process source attributed xref or(!);
annulus: procedure options (main);
/* version 1 does not handle (0/15) etc. this does. */
/* we show 1000 points here */
declare 1 point(10000),
2 x fixed binary,
2 y fixed binary;
declare (i, j, a, b, a2, b2, c) fixed binary(31);
j = 0;
do i = 1 to 1000;
r=rand(31); a=r-16;
r=rand(31); b=r-16;
a2=a*a;
b2=b*b;
c2=a2+b2;
if c2>= 100 & c2 <= 225 then
do; j = j + 1; x(j) = a; y(j) = b;
/* put Edit(a,b,c)(3(F(3))); */ end;
end;
/* PLOT */
declare table(-15:15, -15:15) character (2);
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;
 
rand: Proc(n) Returns(Bin Fixed(31));
/*--------------------------------------------------------------------
* Return a random integer between 1 and n
*-------------------------------------------------------------------*/
Dcl r Bin Float(31);
Dcl (n,d) Bin Fixed(31);
r=random();
d=r*n+1;
Return(d);
End;
End annulus;

output

                             *
                      * *   *   * *   * *
                  * * * * *   * *   * * *
            * * * * *   * * * *     * *   * * * *
          * * * * * * * *       * * * *   * * * *
        * * * * * *     * *   *     * *       * * * *
      *     * *     *                   * * *     *   *
          *   * *                           * *   *   *
        * *   *                               * *   * * *
      * * * * *                               * *     * *
        *   *                                     *     * *
  *   * * *                                       * *   * *
  * * *   *                                       *   *   *
  * * * *                                         * * * * *
    *   *                                         * *     *
* * * *   *                                       * *   * * *
  * * *                                           * * *
    *   * *                                       *   * *
    *   * *                                       *   * * *
    * * *                                         * * *   *
  *   * *   *                                     *     * *
      * * * * *                                         *
      * *                                     * * * * * *
      * *   * * * *                       * * * *     *
          * * * *   *                     * *     * * *
        * * * * *   * *   *     * *   *   *   *     *
          *       * * * *   * *   * * * *   *   *
              * *   *   * * *   *     * * * *   *
                  * * * *     * *     * *
                        * * *   *     * *
          

PowerShell[edit]

Works with: PowerShell version 3
$MinR2 = 10 * 10
$MaxR2 = 15 * 15
 
$Points = @{}
 
While ( $Points.Count -lt 100 )
{
$X = Get-Random -Minimum -16 -Maximum 17
$Y = Get-Random -Minimum -16 -Maximum 17
$R2 = $X * $X + $Y * $Y
 
If ( $R2 -ge $MinR2 -and $R2 -le $MaxR2 -and "$X,$Y" -notin $Points.Keys )
{
$Points += @{ "$X,$Y" = 1 }
}
}
 
ForEach ( $Y in -16..16 ) { ( -16..16 | ForEach { ( " ", "*" )[[int]$Points["$_,$Y"]] } ) -join '' }
Output:
            ***                  
           *     **   *          
           *     ***     *       
           * * * ** *    *       
     *    *    *     *           
           *          *     *    
    * *               ***  *     
    *                    *****   
      **                * *      
   * *                    ***    
  ** *                    ***    
  *                        * *   
     *                           
  *                       *   *  
      *                          
    *                            
    **                        *  
    * *                    **    
     *                           
                           *     
                                 
        *                **      
         *            * * *      
    * *   **           *         
      *   **          **   *     
        * * *       * *          
         *                       
                      **         
             ** * 

Prolog[edit]

Works with SWI-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).
 

Prolog-Circle.jpg

PureBasic[edit]

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

PureBasic Circle plot.png

Python[edit]

Note that the diagram shows the number of points at any given position (up to a maximum of 9 points).

>>> 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

If the number of samples is increased to 1100:

>>> 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

R[edit]

 
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) )
 

Example of solution

FuzzyCircle.jpg

Racket[edit]

#lang racket
 
(require plot plot/utils)
 
(plot (points (for*/lists (result)
([_ (in-naturals)]
#:break (= 100 (length result))
[xy (in-value (v- (vector (random 31) (random 31))
#(15 15)))]
#:when (<= 10 (vmag xy) 15))
xy)))

REXX[edit]

version 0, without aspect adjustment[edit]

No aspect adjustment is done in version of the REXX program.

Both version 0 and version 1 suppress the displaying of blank lines at the top and bottom of the plot.

/*REXX program  generates  100  random points  in an  annulus:   10  ≤  √(x²≤y²)  ≤  15 */
parse arg points low high . /*obtain optional args from the C.L. */
if points=='' then points=100
if low=='' then low=10; low2= low**2 /*define a shortcut for squaring LOW. */
if high=='' then high=15; high2=high**2 /* " " " " " HIGH.*/
$=
do x=-high; x2=x*x /*generate all possible annulus points.*/
if x<0 & x2>high2 then iterate
if x>0 & x2>high2 then leave
do y=-high; s=x2+y*y
if (y<0 & s>high2) | s<low2 then iterate
if y>0 & s>high2 then leave
$=$ x','y /*add a point─set to the $ list. */
end /*y*/
end /*x*/
 
plotChar='Θ'; minY=high2; maxY=-minY; ap=words($); @.=
 
do j=1 for points /*define the x,y points [character O].*/
parse value word($,random(1,ap)) with x ',' y /*pick a random point in the annulus.*/
@.y=overlay(plotChar, @.y, x+high+1) /*define: the data point. */
minY=min(minY,y); maxY=max(maxY,y) /*perform the plot point restricting. */
end /*j*/
/* [↓] only show displayable section. */
do y=minY to maxY; say @.y; end /*display the annulus to the terminal. */
/*stick a fork in it, we're all done. */

output   (without aspect adjustment)   when using the default input:

                Θ
            ΘΘ     ΘΘ
     ΘΘ         Θ Θ     Θ
        Θ              Θ Θ
    ΘΘ Θ  Θ               Θ
    Θ                Θ  Θ

  ΘΘ   Θ                Θ  Θ
   Θ Θ                   Θ
 Θ Θ                        ΘΘ
 Θ Θ                      Θ
                          Θ
 Θ                         Θ
Θ                           Θ Θ
 Θ ΘΘ
                          Θ
                             Θ
  ΘΘ
 Θ                      Θ Θ
                          Θ
  Θ  Θ                    Θ
    Θ  Θ             Θ     Θ
    Θ Θ                    Θ
         Θ  ΘΘ    Θ    Θ
       ΘΘΘΘ   Θ  Θ      Θ
      Θ Θ Θ      Θ    ΘΘ
        Θ Θ Θ        Θ
            Θ  Θ

version 1, with aspect adjustment[edit]

Aspect adjustment is done in this version of the REXX program.

/*REXX program  generates  100  random points  in an  annulus:   10  ≤  √(x²≤y²)  ≤  15 */
parse arg points low high . /*obtain optional args from the C.L. */
if points=='' then points=100
if low=='' then low=10; low2= low**2 /*define a shortcut for squaring LOW. */
if high=='' then high=15; high2=high**2 /* " " " " " HIGH.*/
$=
do x=-high; x2=x*x /*generate all possible annulus points.*/
if x<0 & x2>high2 then iterate
if x>0 & x2>high2 then leave
do y=-high; s=x2+y*y
if (y<0 & s>high2) | s<low2 then iterate
if y>0 & s>high2 then leave
$=$ x','y /*add a point─set to the $ list. */
end /*y*/
end /*x*/
 
plotChar='Θ'; minY=high2; maxY=-minY; ap=words($); @.=
 
do j=1 for points /*define the x,y points [character O].*/
parse value word($,random(1,ap)) with x ',' y /*pick a random point in the annulus.*/
@.y=overlay(plotChar, @.y, 2*x+2*high+1) /*define: the data point. */
minY=min(minY,y); maxY=max(maxY,y) /*perform the plot point restricting. */
end /*j*/
/* [↓] only show displayable section. */
do y=minY to maxY; say @.y; end /*display the annulus to the terminal. */
/*stick a fork in it, we're all done. */

output   (with aspect adjustment)   when using the default input:

                              Θ
                Θ   Θ               Θ
                    Θ Θ       Θ         Θ   Θ Θ
          Θ Θ   Θ           Θ Θ               Θ Θ
        Θ         Θ             Θ   Θ     Θ   Θ
                                                    Θ
                                          Θ     Θ Θ
            Θ Θ                               Θ       Θ Θ
          Θ
    Θ Θ Θ Θ                                             Θ Θ
      Θ                                             Θ
        Θ                                                 Θ

      Θ                                             Θ     Θ
                                                        Θ Θ
        Θ
      Θ
  Θ                                               Θ     Θ
  Θ     Θ                                           Θ     Θ
      Θ     Θ                                             Θ
    Θ         Θ                                       Θ
      Θ                                         Θ Θ

                    Θ                   Θ         Θ   Θ
                      Θ               Θ     Θ Θ Θ
            Θ Θ
                      Θ     Θ           Θ     Θ
                Θ Θ                     Θ Θ

                              Θ

version 2[edit]

/* REXX ---------------------------------------------------------------
* show 100 random points of an annulus with radius 10 to 15
* 18.06.2014 Walter Pachl 'derived/simplified' from REXX version 1
*--------------------------------------------------------------------*/

Parse Arg points low high scale . /* allow parms from command line.*/
If points=='' Then points=100 /* number of points */
If low=='' Then low=10 /* inner radius */
If high=='' Then high=15 /* outer radius */
If scale=='' Then scale=2 /* horizontal scaling */
low2=low**2
high2=high**2
/* first compute all possible points */
point.=0
Do x=-high To high
x2=x*x
Do y=-high To high
y2=y*y
s=x2+y2
If s>=low2 &s<=high2 Then Do
z=point.0+1
point.z=x y
point.0=z
End
End
End
plotchar='O'
line.=''
np=point.0 /* available points */
Do j=1 To points /* pick the needed points */
r=random(1,np)
Parse Var point.r x y /* coordinates */
line.y=overlay(plotchar,line.y,scale*(x+high)+1) /* put into line*/
point.r=point.np /* replace taken point by last*/
np=np-1 /* reduce available points */
If np=0 Then Leave /* all possible points taken */
End
/* now draw the picture */
Do y=-high To high
Say line.y
End

output using default parameters

                                  O
                    O O           O
                          O O         O     O   O
          O O O       O   O O       O         O   O
        O     O       O             O O O O O
                    O                     O O O O O O
      O         O
        O
        O                                         O
  O         O
          O
    O   O O                                             O O
      O   O                                         O
                                                        O
  O       O                                           O
    O
                                                  O
        O
          O                                             O
      O   O O                                   O
      O                                         O       O
        O   O                                     O   O O
              O                               O O   O O
                O                               O
                      O   O O O   O
            O                                   O
              O O O   O O O               O O   O
                  O       O O             O O
                    O               O

output using rexx fcaa 100 3 4 2

        O
    O O O O O
  O           O
  O           O
O O           O O
  O           O
  O           O
    O O O O O
        O 

version 3[edit]

/* REXX ---------------------------------------------------------------
* 19.06.2014 Walter Pachl alternate algorithm
* the idea: yl is a list of y coordinates which may have unused points
* one of the y's is picked at random
* Then we look for unused x coordinates in this line
* we pick one at random or drop the y from yl if none is found
* When yl becomes empty, all points are used and we stop
*--------------------------------------------------------------------*/

Parse Arg n r rr scale
If r='' Then r=10
If rr='' Then rr=15
If n='' Then n=100
If scale='' Then scale=2
r2=r*r
rr2=rr*rr
ymin=0
ymax=rr*2
ol=''
pp.=0
used.=0
yl='' /* list of available y values */
Do y=-rr To rr
yl=yl y
End
Do Until pp.0=n /*look for the required points*/
If yl='' Then Do /* no more points available */
Say 'all points filled'
Leave
End
yi=random(1,words(yl)) /* pick a y */
y=word(yl,yi)
y2=y*y
p.=0
Do x=0 To rr /* Loop through possible x's */
x2=x*x
xy2=x2+y2
If xy2>=r2&xy2<=rr2 Then Do /* within the annulus */
Call take x y
Call take (-x) y
End
End
If p.0>0 Then Do /* some x's found (or just 1) */
xi=random(1,p.0) /* pick an x */
z=pp.0+1
pp.z=p.xi
pp.0=z
Parse Var pp.z xa ya
used.xa.ya=1 /* remember it's taken */
End
Else Do /* no x for this y */
yi=wordpos(y,yl) /* remove y from yl */
Select
When yi=1 Then yl=subword(yl,yi+1)
When yi=words(yl) Then yl=subword(yl,1,yi-1)
Otherwise yl=subword(yl,1,yi-1) subword(yl,yi+1)
End
End
End
line.='' /* empty the raster */
Do i=1 To pp.0 /* place the points */
Parse Var pp.i x y
line.y=overlay('+',line.y,scale*(rr+x)+1)
End
Do y=-rr To rr /* show the result */
Say line.y
End
say pp.0 'points filled'
Exit
Return
 
take: Procedure Expose p. used. /* add x to p. if its not used*/
Parse Arg x y
If used.x.y=0 Then Do
z=p.0+1
p.z=x y
p.0=z
End
Return

output using rexx fcaa 100 3 5 2

all points filled
          +
    + + + + + + +
  + + + + + + + + +
  + +           + +
  + +           + +
+ + +           + + +
  + +           + +
  + +           + +
  + + + + + + + + +
    + + + + + + +
          +
56 points filled

Ring[edit]

 
load "guilib.ring"
 
new qapp
{
win1 = new qwidget() {
setwindowtitle("drawing using qpainter")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(200,400,100,30)
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(1)
}
new qpainter() {
begin(p1)
setpen(pen)
 
for i = 1 to 1000
x = random(31)-16
y = random(31)-16
r = sqrt (pow(x,2) + pow(y,2))
if r >= 10 if r <= 15 drawpoint(x*2, y*2) ok ok
next
 
endpaint()
}
label1 { setpicture(p1) show() }
 

Output:

CalmoSoftDrawCircle.jpg

Ruby[edit]

Create the image with Raster graphics operations/Ruby

points = (1..100).map do
# 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)
end
 
(-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)
Output:
Sample output from Ruby program
          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

algorithm 2:[edit]

r2 = 10*10..15*15
range = (-15..15).to_a
points = range.product(range).select {|i,j| r2.cover?(i*i + j*j)}
 
puts "Precalculate: #{points.size}"
pt = Hash.new(" ")
points.sample(100).each{|ij| pt[ij] = " o"}
puts range.map{|i| range.map{|j| pt[[i,j]]}.join}
Output:
Precalculate: 404
                                                              
                               o o o                          
                 o o o     o                                  
                 o           o     o o       o                
           o   o     o                 o         o o          
               o       o             o   o           o        
                                               o     o        
       o                                       o              
                                                   o o o      
     o         o                                     o        
     o o                                           o       o  
       o                                             o        
                                                           o  
         o                                                    
           o                                             o    
         o                                               o   o
                                                              
                                                           o  
   o o   o                                         o   o      
   o       o                                         o        
   o   o     o                                         o      
                                                   o          
             o                                   o     o      
                 o                                   o o      
       o       o                           o   o   o   o      
           o o     o   o     o       o     o o   o            
                         o           o   o o   o              
             o     o o   o                 o o                
                   o o   o o             o                    
                         o o                                  
                               o                              

Run BASIC[edit]

w = 320
h = 320
dim canvas(w,h)
for pts = 1 to 1000
x = (rnd(1) * 31) - 15
y = (rnd(1) * 31) - 15
r = x * x + y * y
if (r > 100) and (r < 225) then
x = int(x * 10 + w/2)
y = int(y * 10 + h/2)
canvas(x,y) = 1
end if
next pts
 
' -----------------------------
' display the graphic
' -----------------------------
graphic #g, w,h
for x = 1 to w
for y = 1 to h
if canvas(x,y) = 1 then #g "color green ; set "; x; " "; y else #g "color blue ; set "; x; " "; y
next y
next x
render #g
#g "flush"

Scala[edit]

Library: Scala
import java.awt.{ Color, geom,Graphics2D ,Rectangle}
import scala.math.hypot
import scala.swing.{MainFrame,Panel,SimpleSwingApplication}
import scala.swing.Swing.pair2Dimension
import scala.util.Random
 
object CirculairConstrainedRandomPoints extends SimpleSwingApplication {
//min/max of display-x resp. y
val dx0, dy0 = 30; val dxm, dym = 430
val prefSizeX, prefSizeY = 480
 
val palet = Map("b" -> Color.blue, "g" -> Color.green, "r" -> Color.red, "s" -> Color.black)
val cs = List((0, 0, 10, "b"), (0, 0, 15, "g")) //circle position and color
val xmax, ymax = 20; val xmin, ymin = -xmax
 
class Coord(x: Double, y: Double) {
def dx = (((dxm - dx0) / 2 + x.toDouble / xmax * (dxm - dx0) / 2) + dx0).toInt
def dy = (((dym - dy0) / 2 - y.toDouble / ymax * (dym - dy0) / 2) + dy0).toInt
}
 
object Coord {
def apply(x: Double, y: Double) = new Coord(x, y)
}
 
//points:
val points =
new Iterator[Int] { val r = new Random;def next = r.nextInt(31) - 15; def hasNext = true }.toStream.
zip(new Iterator[Int] { val r = new Random; def next = r.nextInt(31) - 15; def hasNext = true }.toStream).
map { case (x, y) => (x, y, hypot(x, y)) }.filter { case (x, y, r) => r >= 10 && r <= 15 }.take(100).toSeq.
map { case (x, y, r) => new Rectangle(Coord(x, y).dx - 2, Coord(x, y).dy - 2, 4, 4) }
 
private def ui = new Panel {
background = Color.white
preferredSize = (prefSizeX, prefSizeY)
 
class Circle(center: Coord, r: Double, val color: Color) {
val dr = (Coord(r, 0).dx - pcentre.dx) * 2
val dx = center.dx - dr / 2
val dy = center.dy - dr / 2
}
 
object Circle {
def apply(x: Double, y: Double, r: Double, color: Color) =
new Circle(Coord(x, y), r, color)
}
 
val pcentre = Coord(0, 0)
val pxmax = Coord(xmax, 0); val pxmin = Coord(xmin, 0)
val pymax = Coord(0, ymax); val pymin = Coord(0, ymin)
 
//axes:
val a_path = new geom.GeneralPath
a_path.moveTo(pxmin.dx, pxmin.dy); a_path.lineTo(pxmax.dx, pxmax.dy) //x-axis
a_path.moveTo(pymin.dx, pymin.dy); a_path.lineTo(pymax.dx, pymax.dy) //y-axis
 
//labeling:
val labels = List(-20, -15, -10, -5, 5, 10, 15, 20)
labels.foreach { x => { val p = Coord(x, 0); a_path.moveTo(p.dx, p.dy - 3); a_path.lineTo(p.dx, p.dy + 3) } }
labels.foreach { y => { val p = Coord(0, y); a_path.moveTo(p.dx - 3, p.dy); a_path.lineTo(p.dx + 3, p.dy) } }
val xlabels = labels.map(x => { val p = Coord(x, 0); Triple(x.toString, p.dx - 3, p.dy + 20) })
val ylabels = labels.map(y => { val p = Coord(0, y); Triple(y.toString, p.dx - 20, p.dy + 5) })
 
//circles:
val circles = cs.map { case (x, y, r, c) => Circle(x, y, r, palet(c)) }
 
override def paintComponent(g: Graphics2D) = {
super.paintComponent(g)
circles.foreach { c => { g.setColor(c.color); g.drawOval(c.dx, c.dy, c.dr, c.dr) } }
g.setColor(palet("r")); points.foreach(g.draw(_))
g.setColor(palet("s")); g.draw(a_path)
xlabels.foreach { case (text, px, py) => g.drawString(text, px, py) }
ylabels.foreach { case (text, px, py) => g.drawString(text, px, py) }
}
} // def ui
 
def top = new MainFrame {
title = "Rosetta Code >>> Task: Constrained random points on a circle | Language: Scala"
contents = ui
}
}

Sidef[edit]

Translation of: Perl

Generates an EPS file.

var points = [];
while (points.len < 100) {
var (x, y) = 2.of{31.rand.int - 15}...;
var r2 = (x**2 + y**2);
if ((r2 >= 100) && (r2 <= 225)) {
points.append([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
 
points.each { |pt| say "#{pt.join(' ')} pt" };
print '%%EOF';

SystemVerilog[edit]

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

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[edit]

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 ""
}

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               

XPL0[edit]

DonutXPL0.gif
include c:\cxpl\codes;  \intrinsic 'code' declarations
int X, Y, C, R2;
[SetVid($13); \set 320x200x8 graphics mode
C:= 0; \initialize point counter
repeat X:= Ran(31)-15; \range -15..+15
Y:= Ran(31)-15;
R2:= X*X + Y*Y;
if R2>=10*10 & R2<=15*15 then
[Point(X+160, Y+100, $F); C:= C+1];
until C >= 100;
C:= ChIn(1); \wait for keystroke
SetVid(3); \restore normal text mode
]

zkl[edit]

xy:=(0).walker(*).tweak(fcn{  // generate infinite random pairs (lazy)
x:=(-15).random(16); y:=(-15).random(16);
if(not (100<=(x*x + y*y)<=225)) Void.Skip else T(x,y)
});
 
const N=31; // [-15..15] includes 0
array:=(" ,"*N*N).split(",").copy(); // bunch of spaces (list)
 
xy.walk(100).apply2(fcn([(x,y)],array){array[x+15 + N*(y+15)]="*"},array);
foreach n in ([0..30]){ array[n*N,30].concat().println(); }
Output:
                              
          *   *     *         
               **   ***       
         *  *  * **     *     
       * **                   
        *      *    *     *   
       *                *  *  
    *                *   ***  
       *                      
      *                   *   
  * *                    *   *
 *                       *    
     *                     *  
                           *  
                         *   *
  ****                      **
                           *  
   *                          
 *  *                         
                          *  *
 **  *                       *
   * *                        
                       * *  * 
        *             *       
   *      *                   
            ** * **           
         *         *  ***     
       * *        *           
        *    *                
           *                  

ZX Spectrum Basic[edit]

Translation of: BBC_BASIC
10 FOR i=1 TO 1000
20 LET x=RND*31-16
30 LET y=RND*31-16
40 LET r=SQR (x*x+y*y)
50 IF (r>=10) AND (r<=15) THEN PLOT 127+x*2,88+y*2
60 NEXT i