#pragma once
#include <cmath>

// Simple 3D vector for planet geometry (metric, double precision).
struct Vec3 {
    double x = 0.0, y = 0.0, z = 0.0;

    Vec3() = default;
    Vec3(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {}

    Vec3 operator+(const Vec3& o) const { return {x + o.x, y + o.y, z + o.z}; }
    Vec3 operator-(const Vec3& o) const { return {x - o.x, y - o.y, z - o.z}; }
    Vec3 operator*(double s)      const { return {x * s, y * s, z * s}; }

    double dot(const Vec3& o) const { return x * o.x + y * o.y + z * o.z; }

    Vec3 cross(const Vec3& o) const {
        return {y * o.z - z * o.y,
                z * o.x - x * o.z,
                x * o.y - y * o.x};
    }

    double length() const { return std::sqrt(x * x + y * y + z * z); }

    Vec3 normalized() const {
        double l = length();
        if (l <= 1e-300) return {0, 0, 0};
        return {x / l, y / l, z / l};
    }
};