Question 201550 in Javascript Question posted in
A very good W3school tutorial can be found here.

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

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

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

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2

Answers


  1. 0

    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)

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  2. 0

    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 = l - min_x;
min_y = (max_dimension-b)/2;
max_y = b - min_y;
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
}
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