把战场信息
还原到像素级

// 解 |P0 + V*t - S| = v*t  →  (|V|^2 - v^2)t^2 + 2(V·D)t + |D|^2 = 0
double solveIntercept(Vec3 S, Vec3 P0, Vec3 V, double v) {
    Vec3   D = P0 - S;
    double a = V.dot(V) - v * v;
    double b = 2.0 * V.dot(D);
    double c = D.dot(D);
    if (fabs(a) < 1e-6) return b > 1e-9 ? -c / b : INF;
    double disc = b * b - 4 * a * c;
    if (disc < 0)  return refineIterative(S, P0, V, v);   // 退化：迭代收敛
    double t1 = (-b - sqrt(disc)) / (2 * a);
    double t2 = (-b + sqrt(disc)) / (2 * a);
    return smallestPositive(t1, t2);
}
// 网络与施法前摇补偿
Vec3 aimPoint(Vec3 P0, Vec3 V, double t) {
    return P0 + V * (t + castDelay + rtt * 0.5);
}

// 已知水平距离 x、高差 y、初速 v、重力 g → 反解发射俯仰角
double solveElevation(double x, double y, double v, double g) {
    double v2 = v * v;
    double root = v2 * v2 - g * (g * x * x + 2 * y * v2);
    if (root < 0) return NAN;                 // 射程外，需抬速或拉近距离
    return atan((v2 - sqrt(root)) / (g * x));  // 低角解：飞行时间短，命中判定更稳
}
// 碰撞判定：曲线采样点与目标包围盒求交
bool arcHit(const Curve& c, const AABB& box, double tMin, double tMax, double step) {
    for (double t = tMin; t <= tMax; t += step)
        if (box.contains(c.pointAt(t))) return true;
    return false;
}

// 干将莫邪：双剑沿曲线飞行，交汇点命中，需同时满足路径与时间窗
struct Sword { Vec3 origin, ctrl1, ctrl2, end; double flyTime, radius; };

bool solveGanJiang(const Sword& a, const Sword& b, const Vec3& target,
                   const Vec3& vel, double* outAngle) {
    double best = INF;
    for (double t = 0.05; t <= a.flyTime; t += 0.02) {
        Vec3 hit  = target + vel * t;             // 目标预测位置
        Vec3 pa   = bezier(a, t / a.flyTime);
        Vec3 pb   = bezier(b, t / b.flyTime);
        double d  = std::min((pa - hit).len() - a.radius,
                             (pb - hit).len() - b.radius);
        if (d < 0) { *outAngle = aimAngle(pa, pb, hit); return true; }  // 已命中
        best = std::min(best, d);
    }
    *outAngle = correctAngle(best);               // 未命中：按最小距离修正
    return false;
}