title: Uniformly distribute Points within an object using Graphics in Mathematica
body: <p>Considering :</p>
  
  <pre><code>preferred ={{1, 1, 63}, {2, 1, 44}, {3, 1, 27}, {4, 1, 33}, {5, 1, 33}}
  
  frmWidth  =                 20.9067;
  frmHeight =                   15.68;
  </code></pre>
  
  <p>I am displaying 5 types of stimuli 2 by 2. Subjects must choose the one they prefer. Each type of stimuli is displayed 80 times so :</p>
  
  <p>{1,1,63} indicates that the stimuli Cond 1 was preferred 63 times out of the 80 times it was displayed.
  {3, 1, 27} indicates that the stimuli Cond 3 was preferred 27 times out of the 80 times it was displayed.</p>
  
  <p>Cond1 refers to center of the screen</p>
  
  <p>Cond2 refers to Top-Left Quadrant</p>
  
  <p>Cond3 refers to Top-Right Quadrant</p>
  
  <p>Cond4 refers to Bottom-Left Quadrant</p>
  
  <p>Cond5 refers to Bottom-Right Quadrant</p>
  
  <p>I would like to express this showing results.</p>
  
  <p>This is what I have done :</p>
  
  <pre><code>Graphics[{
    Black, EdgeForm[{Thin, LightGray}], 
    Rectangle[{-1, -1}, {frmWidth + 1, frmHeight + 1}], 
  
    PointSize[0.03],
    Yellow,
    Point@Tuples[{Range[0, frmWidth/2, frmWidth/19], 
    Range[0, frmHeight/2, frmHeight/14]}][[;; preferred[[5, 3]]]],
  
    Red,
    Point@Tuples[{Range[frmWidth/2, frmWidth, frmWidth/19], 
    Range[0, frmHeight/2, frmHeight/14]}][[;; preferred[[4, 3]]]],
  
    Green,
    Point@Tuples[{Range[frmWidth/2, frmWidth, frmWidth/19], 
    Range[frmHeight/2, frmHeight, frmHeight/14]}][[;; preferred[[3, 3]]]],
  
    Orange,
    Point@Tuples[{Range[0, frmWidth/2, frmWidth/19], 
    Range[frmHeight/2, frmHeight, frmHeight/14]}][[;; 
    preferred[[2, 3]]]],
  
    Blue,
    Point@Tuples[{Range[frmWidth/4, 3/4 frmWidth, frmWidth/19], 
    Range[frmHeight/4, 3/4 frmHeight, frmHeight/14]}][[;; 
    preferred[[1, 3]]]]
  
    }]
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/UOrKe.png" alt="enter image description here"></p>
  
  <p><strong>Problem is the rectangles are gradually filled with points from left to right, instead of the points being uniformly located.</strong></p>
  
  <p>Consider the following :</p>
  
  <pre><code>Graphics[{
  
    White, EdgeForm[Thick], 
    Rectangle[{0, 0}, {frmWidth, frmHeight}],
  
    Orange, Opacity[.5],
    Rectangle[{0, frmHeight/2}, {frmWidth/2, frmHeight}, RoundingRadius -&gt; 3],
  
    Green,
    Rectangle[{frmWidth/2, frmHeight/2}, {frmWidth, frmHeight},RoundingRadius -&gt; 3],
  
    Red,
    Rectangle[{frmWidth/2, 0}, {frmWidth, frmHeight/2}, RoundingRadius -&gt; 3],
  
    Yellow,
    Rectangle[{0, 0}, {frmWidth/2, frmHeight/2}, RoundingRadius -&gt; 3],
  
    Blue,
    Rectangle[{frmWidth/4, frmHeight/4}, {3/4 frmWidth, 3/4 frmHeight}, RoundingRadius -&gt; 3]
    }]
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/fGeG3.png" alt="enter image description here"></p>
  
  <p>Now I would like to fill those edge rounded rectangles with the points but have the density changing rather than the part of the rectangles that are filled.</p>
  
  <p>Below is something very ugly I draw in PPT :</p>
  
  <p><img src="https://i.stack.imgur.com/NCwHe.png" alt="enter image description here"></p>
  
  <p><strong>Ideally, the shapes filled with Points could be of any kind.
  Points would not overlap.</strong></p>
  
  <p>Please let me know alternative ideas.</p>