圆方程以及圆方程组交点

public static bool IsCircleIntersect2(Vector2 c1, float r1, Vector2 c2, float r2, out Vector2 p1, out Vector2 p2)
{
    p1 = Vector2.zero;
    p2 = Vector2.zero;

    float rSum = r1 + r2;
    float sqrRSum = rSum * rSum;
    float sqrDistCenter = (c1 - c2).sqrMagnitude;
    if (sqrDistCenter > sqrRSum) //圆不相交
        return false;

    if (Mathf.Approximately(sqrDistCenter, sqrRSum)) //一个交点
    {
        p1 = c1 + (c2 - c1) * r1 / rSum;
        p2 = p1;
        return true;
    }

    float rSub = r1 - r2;
    float sqrRSub = rSub * rSub;
    if (sqrDistCenter < sqrRSub) //在圆内
        return false;

    if (Mathf.Approximately(sqrDistCenter, sqrRSum)) //一个交点
    {
        p1 = c1 + (c2 - c1) * r1 / rSub;
        p2 = p1;
        return true;
    }

    float sqrR1 = r1 * r1;
    float sqrR2 = r2 * r2;
    //(x-a)^2+(x-b)^2=r^2
    //两圆交点连成的直线点斜式: y=kx+t
    float k = (c2.x - c1.x) / (c1.y - c2.y);
    float t = (c1.x * c1.x - c2.x * c2.x + c1.y * c1.y - c2.y * c2.y + sqrR2 - sqrR1) / (2 * (c1.y - c2.y));
    //Debug.Log($"y={k}x+{t}");
    //代入圆1的方程, 化解后得到关于x的一元二次方程标准式:ax^2+bx+c=0
    float a = (1 + k * k);
    float b = (2 * k * t - 2 * c1.x - 2 * k * c1.y);
    float c = t * t - 2 * t * c1.y - sqrR1 + c1.x * c1.x + c1.y * c1.y;
    //Debug.Log($"{a}x^2+{b}y+{c}=0");
    //求根公式求出x=-b+sqrt(b^2-4ac)/(2a)
    float x1 = (-b + Mathf.Sqrt(b * b - 4 * a * c)) / (2 * a);
    p1 = new Vector2(x1, k * x1 + t);

    float x2 = (-b - Mathf.Sqrt(b * b - 4 * a * c)) / (2 * a);
    p2 = new Vector2(x2, k * x2 + t);
    return true;
}