namespace Day24;

public record Line(Vec Position, Vec Velocity)
{
    public Intersection IntersectionWith(Line other)
    {
        var a = (Position.Y - other.Position.Y) / (double)other.Velocity.Y;
        var b = (other.Position.X - Position.X) * ((double)Velocity.Y / (Velocity.X * other.Velocity.Y));
        var c = (other.Velocity.X * Velocity.Y) / (double)(Velocity.X * other.Velocity.Y);

        var t2 = (a + b) / (1 - c);
        var t1 = ((other.Position.X - Position.X) + t2 * other.Velocity.X) / (double)Velocity.X;
        var v2 = other.Velocity.Multiply(t2);
        return new Intersection(t1, t2, other.Position.X + v2.X, other.Position.Y + v2.Y);
    }
}