Populate custom shape (vertex) with dots in p5

Question

Trying to populate this red custom shape with dots like the ellipse. See image / code example below. Any help would be appreciated.

This Populating a circle with dots, using bias towards the edge of the cirlcle explains how to populate an ellipse but how to do the same technique in a custom shape?

Image with explanation of what I'm trying to do

function setup() {
  createCanvas(750, 750);
  background(0);
  noStroke();
  fill(255);
  noLoop();
}

function draw() {
  translate(width / 2, height / 2);
  for (let i = 0; i < 5000; i++) {
    let theta = random(0, TWO_PI);
    let h = randomGaussian(3.3); //experiment with different means
    let r = (exp(h) - 1) / (exp(h) + 1);
    let x = width / 2 * r * cos(theta);
    let y = height / 2 * r * sin(theta);
    ellipse(x,y,1,1); 


  }


// Trying to populate this custom shape with dots like the above ellipse
    beginShape();
      fill("#ff0000");
      vertex(179, 136);
      quadraticVertex(245, 30, 400, 140);
      bezierVertex(430, 360, 174, 306, 176, 211);
   endShape(CLOSE)


}

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