圆画算法说明

Question

Given the following circle drawing algorithm (variation of Bresenham) :

public static void
drawCircle(Graphics g, MyPoint center, MyPoint point)
{
    // calculate radius of circle
    final int radius = (int)(Math.sqrt((point.x()-center.x())*(point.x()-center.x())+(point.y()-center.y())*(point.y()-center.y())));

    int x = 0, y = radius, u = 0, v = 2 * radius - 1, E = 0;
    while (x < y)
    {
        drawPixel(g, new MyPoint(center.x() + x, center.y() + y)); // NNE
        drawPixel(g, new MyPoint(center.x() + y, center.y() - x)); // ESE
        drawPixel(g, new MyPoint(center.x() - x, center.y() - y)); // SSW
        drawPixel(g, new MyPoint(center.x() - y, center.y() + x)); // WNW
        ++x;
        E += u;
        u += 2;
        if (v < 2 * E){
            y--; E -= v; v -= 2;
        }
        if (x > y) break;
        drawPixel(g, new MyPoint(center.x() + y, center.y() + x)); // ENE
        drawPixel(g, new MyPoint(center.x() + x, center.y() - y)); // SSE
        drawPixel(g, new MyPoint(center.x() - y, center.y() - x)); // WSW
        drawPixel(g, new MyPoint(center.x() - x, center.y() + y)); // NNW

    }
}

I don't seem to understand why it works. I do understand that it draws a pixel at each octant because the circle is symmetric but I don't get what the variables u, v and e stand for..? e stands for the error I suppose but when does it change? and why?

help will be appreciated! thanks

Answer 1

Hope this could help you some:

http://www.ecse.rpi.edu/~wrf/Research/Short_Notes/bresenham.html

Answer 2

Its always hard to reverse-engineer optimized algorithms, because the underlying invariants are often obscured or totally omitted in the final code.

In that case take a look behind the scenes, for example Wikipedia has a detailed explanation of the math used: http://en.wikipedia.org/wiki/Bresenham%27s_circle_algorithm