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I have some area X by Y pixels and I need to fill it up pixel by pixel. The problem is that at any given moment the drawn shape should be as round as possible.

I think that this algorithm is subset of Ordered Dithering, when converting grayscale images to one-bit, but I could not find any references nor could I figure it out myself.

I am aware of Bresenham's Circle, but it is used to draw circle of certain radius not area.

I created animation of all filling percents for 10 by 10 pixel grid. As full area is 10x10=100px, then each frame is exactly 1% inc.

pixel animation

Alexii
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  • Possible duplicate of [Bresenham concentric circles leaving empty pixels](https://stackoverflow.com/questions/12201907/bresenham-concentric-circles-leaving-empty-pixels) – Adder May 28 '19 at 13:42
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    So roughly speaking the result would be the rectangle area being filled up by the an increasing size disk centered in the middle of the area? – Toady May 28 '19 at 13:45
  • Does it have to start in the centre? Can you show what you consider the roundest filling if, say X=3Y and the area is 25%, 50% and 90% full please? – Mark Setchell May 28 '19 at 13:52
  • What have **YOU** tried so far? Where did you get stuck? – MrSmith42 May 28 '19 at 15:14
  • Probably the easiest way is to use Dijkstra's algorithm to find pixels in order of increasing distance from the center. – Matt Timmermans May 28 '19 at 15:35
  • I don't see what this has to do with dithering. –  May 28 '19 at 15:48

1 Answers1

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A filled disk has the equation 

(X - Xc)² + (Y - Yc)² ≤ C.

When you increase C, the number of points that satisfies the equation increases, but because of symmetry it increases in bursts.

To obtain the desired filling effect, you can compute (X - Xc)² + (Y - Yc)² for every pixel, sort on this value, and let the pixels appear one by one (or in a single go if you know the desired number of pixels).

You can break ties in different ways:

  • keep the original order as when you computed the pixels, by using a stable sort;

  • shuffle the runs of equal values;

  • slightly alter the center coordinates so that there are no ties.

Filling with the de-centering trick.

Values:

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Order:

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