What follows below is more than what you're asking for (from what I can tell), but it so happens I was just playing around with this same thing.
The circle produced by this code is rendered with heavy Perlin perturbations. Un-comment the line that sets the Perlin variable to = 1 to see the unadulterated circle.
The code allows for the circle to be produced using either pixels or points. I'm using points here with an alpha channel. It takes a few seconds for the figure to begin to appear. Turn up the color values if it's too dark for your monitor.
It's a rough sketch, not intended as exemplary. But it should have what you need, and then some.

1. // Study: drawing a form with pixels, without scanning the full pixel array.
2. // R.A. Roberton, 2012
3. float centerX, centerY, radialX, radialY, theta, rad;
4. color paint;
5. float shade;
6. float perlinX, perlinY;
7. void setup() {
8. //  size(600, 400, P2D);
9.   size(screen.width, screen.height, P2D);
10.   background(0, 0, 5);
11.   noStroke();
12.   centerX = width/2;
13.   centerY = height/2;
14.   loadPixels();
15.   frameRate(200);
16. }
17. void draw() {
18.   for (int i = 0; i < 100; i++) {
19. //   rad = 150;
20.    rad = random((height * .3) - cos(theta) * 5, height * .3);
21. //   theta = random(2*PI);
22.    theta += .1;  // Play with me! Default .1 .
23.    radialX = centerX + sin(theta) * rad * perlinX;
24.    radialY = centerY + cos(theta) * rad * perlinY;
25.    radialX = constrain(radialX, 0, width - 1);  // Keep pixArray in bounds.
26.    radialY = constrain(radialY, 0, height - 1);
27. //   Optional distance map. Lots of possibilities with map values.  
28. //   float shade = dist(centerX, centerY, radialX, radialY);
29. //   paint = color(int(map(shade, 0, 255, -100, 255)), 0, 0, 25);
30. //   noiseDetail(4, .5);
31.    perlinX = noise(sin(theta) * 51.5) * 1.75;  // Optional Perlin perturbation.
32.    perlinY = noise(cos(theta) * 51.3) * 1.75;
33. //   perlinX = 1; perlinY = 1;  // Use this to cancel perlin.
34.      
35. //   pixels[int(radialX) + (int(radialY) * width)] = paint;
36. //   updatePixels();
37.   
38.    stroke(55, 0, 200, random(25));  // Use point instead of pixels for alpha.
39. //   stroke(paint);
40.    point(radialX, radialY);
41.   
42.   println(frameRate);
43.   }
44. }