1.1.31

1.1.31 #

解答 #

概率的实现方法：

例如概率是 60 %，就在 [0, 100) 之间随机一个值，小于等于 60 则执行操作，反之不执行。

需要更精确的情况可以增大随机的范围，例如 [0, 1000)。

绘图结果

N = 10,p = 0.2, 0.5, 1

完整项目可以到 Github 上下载。

代码 #

/// <summary>
/// 主绘图函数
/// </summary>
/// <param name="N">点的总数目</param>
/// <param name="p">每对点之间连接的概率</param>
public static void StartDrawing(int N, double p)
{
    int pointSize = 5;//每个点绘制的大小
    int precious = 1000;//概率判断的精度

    //新建一个绘图窗口
    Form2 DrawPad = new Form2();
    //显示绘图窗口
    DrawPad.Show();

    //新建画布
    Graphics graphics = DrawPad.CreateGraphics();

    //建立绘图区域（矩形）
    Rectangle rect = new Rectangle(10, 10, 400, 400);

    //画圆
    graphics.DrawEllipse(Pens.Black, rect);

    //计算旋转角度
    double rotateDgree = 360.0 / N;

    //计算点的坐标
    Point Center = new Point(rect.Top + rect.Height / 2, rect.Top + rect.Height / 2);
    Point[] points = new Point[N];
    points[0].X = rect.Left + rect.Width / 2;
    points[0].Y = rect.Top;

    for (int i = 1; i < N; ++i)
    {
        points[i] = Rotate(Center, points[i - 1], rotateDgree);
    }

    //绘制点
    foreach (Point point in points)
    {
        graphics.FillEllipse(Brushes.Black, point.X - pointSize, point.Y - pointSize, pointSize, pointSize);
    }

    //按照概率绘制直线
    Random random = new Random();
    for (int i = 0; i < N; ++i)
    {
        for (int j = i + 1; j < N; ++j)
        {
            //举例：输入概率为 0.6，精度为 1000
            //在 0~1000 范围内等概率取值，如果小于等于 600 则视为事件发生
            if (random.Next(0, precious) <= p * precious)
            {
                graphics.DrawLine(Pens.Gray, points[i], points[j]);
            }
        }
    }

    //释放资源
    graphics.Dispose();
}

/// <summary>
/// 计算一个点绕某点旋转之后的坐标值
/// </summary>
/// <param name="origin">旋转的圆心</param>
/// <param name="point">需要旋转的点</param>
/// <param name="dgree">旋转的角度（逆时针）</param>
/// <returns>返回旋转后的坐标</returns>
public static Point Rotate(Point origin, Point point, double dgree)
{
    Point rotated = new Point();
    double dgreePi = dgree / 180 * Math.PI;

    rotated.X = (int)((point.X - origin.X) * Math.Cos(dgreePi) -
                      (point.Y - origin.Y) * Math.Sin(dgreePi) + origin.X);
    rotated.Y = (int)((point.X - origin.X) * Math.Sin(dgreePi) +
                      (point.Y - origin.Y) * Math.Cos(dgreePi) + origin.Y);

    return rotated;
}