How to generate random coordinates outside the circle contained in a rectangular region?

Question

Given:

1. Rectangular region with length l & breadth b
2. Circle with radius r
3. Circle is contained in rectangular region like shown in below image

See image here - Red are expecting evenly distributed coordinates

Then how to generate random coordinates outside the circle contained in a rectangular region and evenly distributed? (in blue region of below image)

Answer 1

Generate two random values in ranges (uniform distribution in rectangle)

a = Math.random() * width
b = Math.random() * height

check if point lies outside the circle:

(a-center_x)*(a-center_x)+(b-center_y)*(b-center_y) > r*r

if not - repeat random generation until condition becomes true (this is rejection method)

Generated by this Delphi code for reference

var
  Hgt, Wdt, i, N, CX, CY, R, x, y: Integer;
begin
  Hgt := 300;
  Wdt := 400;
  CX := 220;
  CY := 120;
  R := 100;
  N := 15000;
  for i := 0 to N-1 do begin
    x := Round(Random() * Wdt);
    y := Round(Random() * Hgt);
    while (x-CX)*(x-CX)+(y-CY)*(y-CY) < R*R do begin
      x := Round(Random() * Wdt);
      y := Round(Random() * Hgt);
    end;
    Canvas.Pixels[x, y] := clRed;
  end;

Answer 2

First generate a uniform distribution of x, y values in a square and reject any x,y outside the centered rectangle.

Algorithm

max_dimension = max(l, b)
min_x = (max_dimension-l)/2;
max_x = min_x + l;
min_y = (max_dimension-b)/2;
max_y = min_y + b;
loop forever
  x = Math.random()*max_dimension
  if (x < min_x || x > max_x) continue;
  y = Math.random()*max_dimension
  if (y < min_y || x > max_y) continue;
  

Now test if x, y inside the circle

  xc = x - l/2;
  yc = y - b/2;
  if (xc*xc + yc*yc < r*r) continue
  break
}