转载请注明出处: https://blog.csdn.net/weixin_44013533/article/details/138909256
作者：CSDN@|Ringleader|
目录
- Quaternion API 速览
- FromToRotation在Transform中的应用
- LookRotation 中upwards取Vector3.up和 transform.up的区别
- 旋转时如何保持Y轴不变，但朝向目标旋转呢？
- 不同旋转方法案例
- lerp与LerpUnclamped区别
- Quaternion.Slerp 、Quaternion.RotateTowards区别
- Lerp、Slerp比较
- Quaternion * operator
- 总结
主要参考：
- Unity手册 & Quaternion API
- Unity3D - 详解Quaternion类（二）
- 【Unity编程】Unity中关于四元数的API详解
Quaternion API 速览
创建旋转：
FromToRotation创建一个从 fromDirection 旋转到 toDirection 的旋转。LookRotation使用指定的 forward 和 upwards 方向创建旋转。AngleAxis创建一个围绕 axis 旋转 angle 度的旋转。Angle返回两个旋转 a 和 b 之间的角度（以度为单位）。(180°以内)
操作旋转：
Lerp在 a 和 b 之间插入 t，然后对结果进行标准化处理。参数 t 被限制在 [0, 1] 范围内。Slerp在四元数 a 与 b 之间按比率 t 进行球形插值。参数 t 限制在范围 [0, 1] 内。RotateTowards将旋转 from 向 to 旋转。
Transform 类还提供了一些方法可用于处理 Quaternion 旋转：Transform.Rotate & Transform.RotateAround
FromToRotation在Transform中的应用
Transform中有很多Quaternion的应用，比如获取对象的xyz轴向量在世界坐标系下的表示，就用到了FromToRotation：
///<para>The red axis of the transform in world space.</para>
public Vector3 right
{
get => this.rotation * Vector3.right;
set => this.rotation = Quaternion.FromToRotation(Vector3.right, value);
}
///<para>The green axis of the transform in world space.</para>
public Vector3 up
{
get => this.rotation * Vector3.up;
set => this.rotation = Quaternion.FromToRotation(Vector3.up, value);
}
///<para>Returns a normalized vector representing the blue axis of the transform in world space.
public Vector3 forward
{
get => this.rotation * Vector3.forward;
set => this.rotation = Quaternion.LookRotation(value);
}
LookRotation 中upwards取Vector3.up和 transform.up的区别
public static Quaternion LookRotation (Vector3 forward, Vector3 upwards= Vector3.up);
因为LookRotation 会使对象Z轴与forward参数向量对齐，X 轴与Vector3.Cross(upwards,forward)这个叉乘结果对齐，Y 轴与 Z 和 X 的叉乘（Vector3.Cross(transform.forward,transform.right) ）对齐。（注意unity左手坐标系，叉乘方向）
所以会看到当upwards取世界空间的向上和模型空间的向上是有区别的。
或者说，upwards取模型空间的向上时对象可以绕自身z轴旋转，对象状态并不固定。
public class LookRotationTest : MonoBehaviour
{
public Transform obt_forward;
public Transform obt_worldUp;
public Transform obt_selfUp;
public bool showCrossResult = false;// 验证叉乘方向用
private void Update()
{
// upwards取世界空间的向上
LookForward(obt_worldUp, obt_forward.position - obt_worldUp.position, Vector3.up);
// upwards取模型空间的向上
LookForward(obt_selfUp,obt_forward.position - obt_selfUp.position, obt_selfUp.up);
}
private void LookForward(Transform obt, Vector3 forward,Vector3 upwards)
{
obt.rotation = Quaternion.LookRotation(forward, upwards);
var position = obt.position;
Debug.DrawLine(obt_forward.position, position);
Debug.DrawLine(position, position + obt.right * 5, Color.red);
Debug.DrawLine(position, position + obt.up * 5, Color.green);
Debug.DrawLine(position, position + obt.forward * 5, Color.blue);
// 验证叉乘方向, 叉乘结果与LookFoward结果一致
if (showCrossResult)
{
var X_cross = Vector3.Cross(upwards,forward);
var Y_cross = Vector3.Cross(obt.forward,obt.right);
Debug.DrawLine(position, position + X_cross * 10, Color.cyan);
Debug.DrawLine(position, position + Y_cross * 10, Color.yellow);
}
}
}
旋转时如何保持Y轴不变，但朝向目标旋转呢？
使用Vector3.ProjectOnPlane将目标方向投影到xz平面。
Lookat, FromToRotation and LookRotation?
不同旋转方法案例
下面代码比较了transform.forward 、Transform.LookAt、Quaternion.FromToRotation、LookRotation、Quaternion.RotateTowards、Vector3.ProjectOnPlane等不同方法
public class CompareImmediateAndStep : MonoBehaviour
{
public Transform turret;
public Transform enemy;
private string str;
private void Update()
{
var targetTowards = enemy.position - turret.position;
// 立刻跟随敌人
if (Input.GetKey(KeyCode.Alpha1))
{
turret.forward = targetTowards;
str = "使用turret.forward = targetTowards;";
}
// 上面本质也是使用FromToRotation方法
if (Input.GetKey(KeyCode.Alpha2))
{
turret.rotation = Quaternion.FromToRotation(Vector3.forward, targetTowards);
str = "使用turret.rotation = Quaternion.FromToRotation(Vector3.forward, targetTowards);";
}
if (Input.GetKey(KeyCode.Alpha3))
{
//当FromToRotation的fromDirection参数是forward轴时，可以用LookRotation
turret.rotation = Quaternion.LookRotation(targetTowards);
str = "turret.rotation = Quaternion.LookRotation(targetTowards);";
}
if (Input.GetKey(KeyCode.Alpha4))
{
turret.LookAt(enemy.transform);
str = "turret.LookAt(enemy.transform);";
}
// 插值方式，加入旋转速度
if (Input.GetKey(KeyCode.Alpha5))
{
var fromToRotation = Quaternion.LookRotation(targetTowards);
turret.rotation = Quaternion.RotateTowards(turret.rotation, fromToRotation, 45 * Time.deltaTime);
str = "使用worldUp的Quaternion.RotateTowards";
}
// 保持对象Y轴朝向不变，将targetTowards进行投影
if (Input.GetKey(KeyCode.Alpha6))
{
var fromToRotation = Quaternion.LookRotation(Vector3.ProjectOnPlane(targetTowards,Vector3.up),Vector3.up);
turret.rotation = Quaternion.RotateTowards(turret.rotation, fromToRotation, 45 * Time.deltaTime);
str = "保持Y轴朝向不变，将targetTowards进行投影";
}
DrawAxis(turret);
DrawAxis(enemy);
}
private void DrawAxis(Transform obt)
{
DrawAxis(obt, Color.red, Color.green, Color.blue, 5);
}
private void DrawAxis(Transform obt, Color xc, Color yc, Color zc, float length)
{
if (obt.gameObject.activeInHierarchy)
{
var position = obt.position;
Debug.DrawLine(position, position + obt.right * length, xc);
Debug.DrawLine(position, position + obt.up * length, yc);
Debug.DrawLine(position, position + obt.forward * length, zc);
}
}
private Rect rect = new Rect(100, 100, 600, 50);
private void OnGUI()
{
DrawLabel(rect, str);
}
private static void DrawLabel(Rect rect1, String str)
{
var style = new GUIStyle
{
fontSize = 38,
wordWrap = true
};
GUI.Label(rect1, str, style);
}
}
lerp与LerpUnclamped区别
区别就是Unclamp不会钳值，还能取负值。
Vector3: Lerp vs LerpUnclamped
Quaternion.Slerp 、Quaternion.RotateTowards区别
RotateTowards本质也是使用了SlerpUnclamped方法，但其旋转速度恒定，不会因target变化而改变。
public static Quaternion RotateTowards(Quaternion from, Quaternion to, float maxDegreesDelta)
{
float num = Quaternion.Angle(from, to);
return (double) num == 0.0 ? to : Quaternion.SlerpUnclamped(from, to, Mathf.Min(1f, maxDegreesDelta / num));
}
这篇帖子 Use Quaternion.RotateTowards() instead of Quaternion.Slerp() 提到了：
如果旋转操作的from和to都已知，使用 Quaternion.Slerp() - 例如打开一扇门或箱子盖。
如果要以恒定角速度转向某物，则使用 Quaternion.RotateTowards() - 例如，在塔防类游戏中要转向塔的炮塔。
Lerp、Slerp比较
Quaternion的插值分析及总结
Lerp求得的是四元数在圆上的弦上的等分，而Slerp求得的是四元数载圆上的圆弧的等分
进行代码验证：
public class SlerpTest : MonoBehaviour
{
public Transform obtLerp;
public Transform obtSlerp;
public Transform towardsObt;
public bool towardsNotChanged;
private Quaternion currentLookRotation,lastLookRotation;
private Quaternion initRotationLerp, initRotationSlerp;
public float speed = 0.1f;
float total = 0.0f;
private void Start()
{
lastLookRotation = Quaternion.LookRotation(towardsObt.position-obtLerp.position);
initRotationLerp = obtLerp.rotation;
initRotationSlerp = obtSlerp.rotation;
}
void Update()
{
CompareSlerpAndLerp();
}
private void CompareSlerpAndLerp()
{
currentLookRotation = Quaternion.LookRotation(towardsObt.position - obtLerp.position);
towardsNotChanged = currentLookRotation == lastLookRotation;
// 改变朝向时，重置初始位置、重置total
if (!towardsNotChanged)
{
lastLookRotation = currentLookRotation;
// 重置执行Lerp、Slerp时的初始旋转
initRotationLerp = obtLerp.rotation;
initRotationSlerp = obtSlerp.rotation;
total = 0;
return;
}
lastLookRotation = currentLookRotation;
total += Time.deltaTime * speed;
if (total >= 1.0f)
total = 1.0f;
obtLerp.rotation = Quaternion.Lerp(initRotationLerp, currentLookRotation, total);
obtSlerp.rotation = Quaternion.Slerp(initRotationSlerp, currentLookRotation, total);
DrawAxis(obtLerp);
DrawAxis(obtSlerp, Color.cyan, Color.magenta, Color.yellow, 10);
}
private void DrawAxis(Transform obt)
{
DrawAxis(obt, Color.red, Color.green, Color.blue, 5);
}
private void DrawAxis(Transform obt,Color xc,Color yc,Color zc,float length)
{
if (obt.gameObject.activeInHierarchy)
{
var position = obt.position;
Debug.DrawLine(position, position + obt.right * length, xc);
Debug.DrawLine(position, position + obt.up * length, yc);
Debug.DrawLine(position, position + obt.forward * length, zc);
}
}
private Rect rect = new Rect(100, 100, 600, 50);
private void OnGUI()
{
DrawLabel(rect,"Total:"+total);
}
private void DrawLabel(Rect rect1, String str)
{
var style = new GUIStyle
{
fontSize = 38,
wordWrap = true
};
GUI.Label(rect1, str, style);
}
}
如下图，RGB颜色的轴是Lerp方法，青紫黄轴是Slerp方法。可以看到Lerp相对Slerp来说先慢，中间快，最后慢。和上面的弦等分和弧等分理论一致。
Quaternion * operator
关于Quaternion 左乘右乘和坐标系的关系看我这篇：【Unity学习笔记】第十六 World space、Parent space和Self space及Quaternion左乘右乘辨析
总结
本文主要辨析Quaternion中Lerp、Slerp、RotateTowards等方法，并进行代码验证。至此，对Quaternion核心方法的理解已比较清晰，但其中的数学原理比如四元数、和欧拉角的关系、万向锁、逆和共轭等问题还是有待进一步学习。
