Unity【Lerp & Slerp】- 线性插值与球形插值的区别

在Unity的向量Vector和四元数Quaternion类中，均包含线性插值Lerp和球形插值Slerp的函数，那么两者之间有何区别，通过下面的例子进行观察：

图一中黄色线与红色线相交的点是从点A到点B进行线性插值得出的结果，图二则是球形插值得出的结果，或许称之为弧形插值更容易理解。二者的区别从图中可以明显看出，从四元数的角度来看，线性插值每帧得出的旋转结果是不均匀的，从代数的角度思考，如果两个单位四元数之间进行插值，如图一中的线性插值，得到的四元数并不是单位四元数，因此球形插值更为合理，因为它是不改变长度的。

测试代码如下：

      using UnityEngine;
      using UnityEditor;
      /// <summary>
      /// 线性插值
      /// </summary>
      public class LerpExample : MonoBehaviour
      {
          [SerializeField] private Transform a; //点A
          [SerializeField] private Transform b; //点B
         private void OnDrawGizmos()
          {
              Handles.Label(transform.position, "O");
              Handles.Label(a.position, "A");
              Handles.Label(b.position, "B");
              Handles.color = Color.cyan;
             //以transform.position作为点O
             //绘制OA线段
              Handles.DrawLine(transform.position, a.position);
             //绘制OB线段
              Handles.DrawLine(transform.position, b.position);
             for (int i = 1; i < 10; i++)
              {
                 //插值点
                  Vector3 l = Vector3.Lerp(a.position, b.position, i * .1f);
                  Handles.color = Color.red;
                 //绘制点O到插值点的线段
                  Handles.DrawLine(transform.position, l);
                  Handles.color = Color.yellow;
                 //绘制插值点之间的线段
                  Handles.DrawLine(l, Vector3.Lerp(a.position, b.position, (i - 1) * .1f));
                  Handles.Label(l, $"线性插值{i}");
              }
              Handles.DrawLine(b.position, Vector3.Lerp(a.position, b.position, .9f));
          }
      }
  
 

      using UnityEngine;
      using UnityEditor;
      /// <summary>
      /// 球形插值
      /// </summary>
      public class SlerpExample : MonoBehaviour
      {
          [SerializeField] private Transform a; //点A
          [SerializeField] private Transform b; //点B
         private void OnDrawGizmos()
          {
              Handles.Label(transform.position, "O");
              Handles.Label(a.position, "A");
              Handles.Label(b.position, "B");
              Handles.color = Color.cyan;
             //以transform.position作为点O
             //绘制OA线段
              Handles.DrawLine(transform.position, a.position);
             //绘制OB线段
              Handles.DrawLine(transform.position, b.position);
             for (int i = 1; i < 10; i++)
              {
                 //插值点
                  Vector3 l = Vector3.Slerp(a.position, b.position, i * .1f);
                  Handles.color = Color.red;
                 //绘制点O到插值点的线段
                  Handles.DrawLine(transform.position, l);
                  Handles.color = Color.yellow;
                 //绘制插值点之间的线段
                  Handles.DrawLine(l, Vector3.Slerp(a.position, b.position, (i - 1) * .1f));
                  Handles.Label(l, $"球形插值{i}");
              }
              Handles.DrawLine(b.position, Vector3.Slerp(a.position, b.position, .9f));
          }
      }
  
 

在对Transform组件中的Position坐标和Rotation旋转进行插值运算时， 通常用Vector3中的插值函数去处理Position，用Quaternion中的插值函数去处理Rotation。

如果我们使用Vector3中的插值函数去处理Rotation，则会出现如下这种情况：

代码如下：

      using UnityEngine;
      using System.Collections;
      public class Example : MonoBehaviour
      {
          [SerializeField] private Transform point1;
          [SerializeField] private Transform point2;
         private IEnumerator ExampleCoroutine(Transform target)
          {
             float beginTime = Time.time;
              Vector3 beginPosition = transform.position;
              Vector3 beginRotation = transform.eulerAngles;
             for (var duration = 2f; (Time.time - beginTime) < duration;)
              {
                 float t = (Time.time - beginTime) / duration;
                  transform.position = Vector3.Lerp(beginPosition, target.position, t);
                  transform.eulerAngles = Vector3.Lerp(beginRotation, target.eulerAngles, t);
                 yield return null;
              }
              transform.position = target.position;
              transform.eulerAngles = target.rotation.eulerAngles;
          }
         private void OnGUI()
          {
             if (GUILayout.Button("POINT1", GUILayout.Width(200f), GUILayout.Height(50f)))
              {
                  StartCoroutine(ExampleCoroutine(point1));
              }
             if (GUILayout.Button("POINT2", GUILayout.Width(200f), GUILayout.Height(50f)))
              {
                  StartCoroutine(ExampleCoroutine(point2));
              }
          }
      }
  
 

下面是使用Quaternion.Lerp得出的结果：

代码如下：

      using UnityEngine;
      using System.Collections;
      public class Example : MonoBehaviour
      {
          [SerializeField] private Transform point1;
          [SerializeField] private Transform point2;
         private IEnumerator ExampleCoroutine(Transform target)
          {
             float beginTime = Time.time;
              Vector3 beginPosition = transform.position;
              Quaternion beginRotation = transform.rotation;
             for (var duration = 2f; (Time.time - beginTime) < duration;)
              {
                 float t = (Time.time - beginTime) / duration;
                  transform.position = Vector3.Lerp(beginPosition, target.position, t);
                  transform.rotation = Quaternion.Lerp(beginRotation, target.rotation, t);
                 yield return null;
              }
              transform.position = target.position;
              transform.rotation = target.rotation;
          }
         private void OnGUI()
          {
             if (GUILayout.Button("POINT1", GUILayout.Width(200f), GUILayout.Height(50f)))
              {
                  StartCoroutine(ExampleCoroutine(point1));
              }
             if (GUILayout.Button("POINT2", GUILayout.Width(200f), GUILayout.Height(50f)))
              {
                  StartCoroutine(ExampleCoroutine(point2));
              }
          }
      }
  
 

文章来源: coderz.blog.csdn.net，作者：CoderZ1010，版权归原作者所有，如需转载，请联系作者。

原文链接：coderz.blog.csdn.net/article/details/123281928