Circle Drawing with 4-way Symmetry

    The following code fragment takes advantage of the 4-way symmetry of circles.

    public void circleSym4(int xCenter, int yCenter, int radius, Color c)
    {
        int pix = c.getRGB();
        int x, y, r2;
        
        r2 = radius * radius;
        raster.setPixel(pix, xCenter, yCenter + radius);
        raster.setPixel(pix, xCenter, yCenter - radius);
        for (x = 1; x <= radius; x++) {
            y = (int) (Math.sqrt(r2 - x*x) + 0.5);
            raster.setPixel(pix, xCenter + x, yCenter + y);
            raster.setPixel(pix, xCenter + x, yCenter - y);
            raster.setPixel(pix, xCenter - x, yCenter + y);
            raster.setPixel(pix, xCenter - x, yCenter - y);
        }
    }


    On average how much faster would you expect this algorithm to be?
Lecture 6 Slide 5 6.837 Fall '98



We can quickly modify our previous algorithm to take advantage of this fact as shown below. 
    public void circleSym4(int xCenter, int yCenter, int radius, Color c)
    {
        int pix = c.getRGB();
        int x, y, r2;
        
        r2 = radius * radius;
        raster.setPixel(pix, xCenter, yCenter + radius);
        raster.setPixel(pix, xCenter, yCenter - radius);
        for (x = 1; x <= radius; x++) {
            y = (int) (Math.sqrt(r2 - x*x) + 0.5);
            raster.setPixel(pix, xCenter + x, yCenter + y);
            raster.setPixel(pix, xCenter + x, yCenter - y);
            raster.setPixel(pix, xCenter - x, yCenter + y);
            raster.setPixel(pix, xCenter - x, yCenter - y);
        }
    }
This circle-drawing algorithm uses 4-way symmetry.