中点划线法.txt

根据直线方程实现中点划线

根据直线方程：F(x, y) = ax + by + c = 0
其中, a = y0 - y1, b = x1 - x0, c = x0y1 - x1y0。
将中点代入函数得:
d = F(M) = F(xp + 1, yp + 0.5) = a(xp + 1) + b(yp + 0.5) + c
所以当d<0时， M在直线下方， 当d >= 0时， M在直线上方
采用增量法
d>=0时，取(xp+2, yp+0.5)
代入得：d1 = F(xp+2, yp+0.5) = a(xp+2)+b(yp+0.5)+c = d + a
故增量为a
d<0时，取(xp+2, yp+1.5) = a(xp+2)+b(yp+1.5)+c = d + a + b
故增量为b
d的初值:d0 = F(x0 + 1, y0 + 0.5) = a(x0 + 1) + b(y0 + 0.5) + c
                = ax0 + by0 + c + a + 0.5b
                = F(x0, y0) + a + 0.5b
因为F(x0, y0) = 0
所以d0 = a + 0.5b
只需要d的符号，所以用2d代替d
程序为：
public void MidpointLine(Graphics g, int x0, int y0, int x1, int y1, int color)
  {
    int a, b, delta1, delta2, d, x, y;
    a = y0 - y1;
    b = x1 - x0;
    d = 2 * a + b;
    delta1 = 2 * a;
    delta2 = 2 * (a + b);
    x = x0;
    y = y0;
    g.setColor(color);
    g.drawLine(x, y, x, y);
    while(x < x1)
    {
      if( d < 0)
      {
        x ++;
        y ++;
        d += delta2;
        
      }
      else 
      {
          x ++;
          d += delta1;
      }
      g.setColor(color);
      g.drawLine(x, y, x, y);
    }    
  }