circle.py

class circle:
    center = 0 + 0j
    radius = 0

    def __init__(self, x, y, r):
        self.center = complex(x, y)
        self.radius = abs(r)

    def print(self):
        x = self.center.real
        y = self.center.imag
        r = self.radius

        print("Center\t(%f,%f) \t Radrius\t%f" % (x, y, r))

    def Distance(self, cir2):  # 计算两个圆之间的距离
        c_1 = self.center
        c_2 = cir2.center
        r_1 = self.radius
        r_2 = cir2.radius
        return abs(c_1 - c_2) - (r_1 + r_2)

    def OverLap(self, cir2):  # 判断对象是否和另一个circle对象clr2有重叠部分

        Dist = self.Distance(cir2)  # 计算两个圆间的距离，若小于0则有重叠部分
        if Dist < 0:
            return True
        elif Dist >= 0:
            return False

    def Append_To(self, c_list):  # 将此对象添加到列表c_list中,返回是否添加成功
        # 判断该圆是否和列表中其他圆有重合部分
        OverLap = False
        if len(c_list) == 0:
            c_list.append(self)
            return True
        else:
            for c in c_list:
                OverLap += self.OverLap(c)
            if not OverLap:
                c_list.append(self)
                return True
            else:
                return False

    # 判断该圆的圆心是否在其他的圆内
    def Center_Inside(self, c_list):
        if len(c_list) == 0:
            return False
        else:
            Inside = False
            for cir in c_list:
                c_1 = cir.center
                r_1 = cir.radius
                dis = abs(self.center - c_1)
                if dis <= r_1:
                    Inside += True
                    break
                else:
                    Inside += False
            return Inside

    # 计算最大可行半径
    def Max_Radius(self, c_list):
        x = self.center.real
        y = self.center.imag
        # 计算到边界的距离
        R_list = [1 - x, x + 1, 1 - y, y + 1]
        if not len(c_list) == 0:
            # 计算到其他各圆的距离
            for c in c_list:
                r = c.Distance(self) + self.radius
                R_list.append(r)
        # 从中取最小值，作为该圆的半径
        self.radius = min(R_list)


# 计算c_list中所有圆的r^2之和
def Total_R_Square(c_list):
    R2 = 0
    for c in c_list:
        R2 += c.radius ** 2
    return R2


# 输出c_list中所有圆的信息
def Print_All(c_list):
    for c in c_list:
        c.print()


# 计算在给定圆的数量的情况下，r^2最大时对应的圆的列表 返回这一列表


def Max_R_Square(circle_num):
    circle_list = []
    # 向列表中添加新圆，直到总数符合要求
    while len(circle_list) < circle_num:
        if len(circle_list) == 0:
            # 第一个圆，强制设定为单位圆
            x = 0
            y = 0
            r = 1
        else:
            # 随机下一个圆的圆心坐标
            import random
            x = random.uniform(-1, 1)
            y = random.uniform(-1, 1)
            r = 0
        cir = circle(x, y, r)
        # 判断随机生成的新圆心坐标是否在已经存在的圆内
        if not cir.Center_Inside(circle_list):
            # 若不在，则计算这个圆的最大半径，并添加进列表
            cir.Max_Radius(circle_list)
            cir.Append_To(circle_list)
    return circle_list


if __name__ == "__main__":
    circle_num = 1000
    c_list = Max_R_Square(circle_num)
    R2 = Total_R_Square(c_list)
    print("对应圆的参数")
    Print_All(c_list)
    print("sum r^2的最大值为\t", R2)