三角学3d数学第三人称相机算法

Question

我需要一个非语言特定算法的第三人称相机。我遇到的麻烦是如何保持相机后面的对象，并保持相机的旋转相同的对象旋转。什么好主意吗?

的例子:

UpdateCamera(camera, target){
    offset = vector(0,height,distance);
    cameraPos = targetPos+offset;
    camAngle = ?????;
}

我知道它不会那么简单，但我相信你会得到它的要点。

Answer 1

假设您有一个简单的NUV相机类，如下所示:

/// <summary>
/// An instance of this class represents a camera for a 3D view.
/// Cameras are defined with a position and three mutually-orthogonal
/// axes, namely N (points in the direction faced by the camera),
/// U (points to the left of the camera) and V (points to the top
/// of the camera).
/// </summary>
sealed class Camera
{
    //#################### PRIVATE VARIABLES ####################
    #region
    private Vector3 m_n;
    private Vector3 m_position;
    private Vector3 m_u;
    private Vector3 m_v;
    #endregion
    //#################### PROPERTIES ####################
    #region
    /// <summary>
    /// The position of the camera.
    /// </summary>
    public Vector3 Position { get { return m_position; } }
    /// <summary>
    /// A vector pointing in the direction faced by the camera.
    /// </summary>
    public Vector3 N { get { return m_n; } }
    /// <summary>
    /// A vector pointing to the left of the camera.
    /// </summary>
    public Vector3 U { get { return m_u; } }
    /// <summary>
    /// A vector pointing to the top of the camera.
    /// </summary>
    public Vector3 V { get { return m_v; } }
    #endregion
    //#################### CONSTRUCTORS ####################
    #region
    /// <summary>
    /// Constructs a new camera.
    /// </summary>
    /// <param name="position">The position of the camera.</param>
    /// <param name="look">A vector pointing in the direction faced by the camera.</param>
    /// <param name="up">The "up" direction for the camera.</param>
    public Camera(Vector3 position, Vector3 look, Vector3 up)
    {
        m_position = position;
        m_n = look;
        m_n.Normalize();
        m_v = up;
        m_v.Normalize();
        m_u = Vector3.Cross(m_v, m_n);
        m_u.Normalize();
    }
    #endregion
    //#################### PUBLIC METHODS ####################
    #region
    /// <summary>
    /// Moves the camera by the specified displacement in the n direction.
    /// </summary>
    /// <param name="delta">The displacement by which to move.</param>
    public void MoveN(float delta)
    {
        m_position += delta * m_n;
    }
    /// <summary>
    /// Moves the camera by the specified displacement in the u direction.
    /// </summary>
    /// <param name="delta">The displacement by which to move.</param>
    public void MoveU(float delta)
    {
        m_position += delta * m_u;
    }
    /// <summary>
    /// Moves the camera by the specified displacement in the v direction.
    /// </summary>
    /// <param name="delta">The displacement by which to move.</param>
    public void MoveV(float delta)
    {
        m_position += delta * m_v;
    }
    /// <summary>
    /// Rotates the camera anticlockwise by the specified angle about the specified axis.
    /// </summary>
    /// <param name="axis">The axis about which to rotate.</param>
    /// <param name="angle">The angle by which to rotate (in radians).</param>
    public void Rotate(Vector3 axis, float angle)
    {
        // Note: We try and optimise things a little by observing that there's no point rotating an axis about itself.
        if(axis != m_n) m_n = MathUtil.RotateAboutAxis(m_n, angle, axis);
        if(axis != m_u) m_u = MathUtil.RotateAboutAxis(m_u, angle, axis);
        if(axis != m_v) m_v = MathUtil.RotateAboutAxis(m_v, angle, axis);
    }
    #endregion
}

现在，每一帧:

1)获取玩家的位置pp和方向pdir。
2)重新创建您的相机位置= pp - offset * pdir, look = pdir和up =一些合理的(例如(0,0,1))。