Unity【Lerp & Slerp】- 线性插值与球形插值的区别
【摘要】
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...
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：
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using UnityEngine;
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using UnityEditor;
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/// <summary>
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/// 线性插值
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/// </summary>
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public class LerpExample : MonoBehaviour
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{
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[SerializeField] private Transform a; //点A
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[SerializeField] private Transform b; //点B
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private void OnDrawGizmos()
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{
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Handles.Label(transform.position, "O");
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Handles.Label(a.position, "A");
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Handles.Label(b.position, "B");
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Handles.color = Color.cyan;
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//以transform.position作为点O
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//绘制OA线段
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Handles.DrawLine(transform.position, a.position);
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//绘制OB线段
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Handles.DrawLine(transform.position, b.position);
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for (int i = 1; i < 10; i++)
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{
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//插值点
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Vector3 l = Vector3.Lerp(a.position, b.position, i * .1f);
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Handles.color = Color.red;
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//绘制点O到插值点的线段
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Handles.DrawLine(transform.position, l);
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Handles.color = Color.yellow;
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//绘制插值点之间的线段
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Handles.DrawLine(l, Vector3.Lerp(a.position, b.position, (i - 1) * .1f));
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Handles.Label(l, $"线性插值{i}");
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}
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Handles.DrawLine(b.position, Vector3.Lerp(a.position, b.position, .9f));
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}
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}
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using UnityEngine;
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using UnityEditor;
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/// <summary>
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/// 球形插值
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/// </summary>
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public class SlerpExample : MonoBehaviour
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{
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[SerializeField] private Transform a; //点A
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[SerializeField] private Transform b; //点B
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private void OnDrawGizmos()
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{
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Handles.Label(transform.position, "O");
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Handles.Label(a.position, "A");
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Handles.Label(b.position, "B");
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Handles.color = Color.cyan;
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//以transform.position作为点O
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//绘制OA线段
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Handles.DrawLine(transform.position, a.position);
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//绘制OB线段
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Handles.DrawLine(transform.position, b.position);
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for (int i = 1; i < 10; i++)
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{
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//插值点
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Vector3 l = Vector3.Slerp(a.position, b.position, i * .1f);
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Handles.color = Color.red;
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//绘制点O到插值点的线段
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Handles.DrawLine(transform.position, l);
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Handles.color = Color.yellow;
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//绘制插值点之间的线段
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Handles.DrawLine(l, Vector3.Slerp(a.position, b.position, (i - 1) * .1f));
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Handles.Label(l, $"球形插值{i}");
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}
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Handles.DrawLine(b.position, Vector3.Slerp(a.position, b.position, .9f));
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}
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}
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：
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using UnityEngine;
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using System.Collections;
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public class Example : MonoBehaviour
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{
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[SerializeField] private Transform point1;
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[SerializeField] private Transform point2;
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private IEnumerator ExampleCoroutine(Transform target)
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{
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float beginTime = Time.time;
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Vector3 beginPosition = transform.position;
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Vector3 beginRotation = transform.eulerAngles;
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for (var duration = 2f; (Time.time - beginTime) < duration;)
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{
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float t = (Time.time - beginTime) / duration;
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transform.position = Vector3.Lerp(beginPosition, target.position, t);
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transform.eulerAngles = Vector3.Lerp(beginRotation, target.eulerAngles, t);
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yield return null;
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}
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transform.position = target.position;
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transform.eulerAngles = target.rotation.eulerAngles;
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}
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private void OnGUI()
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{
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if (GUILayout.Button("POINT1", GUILayout.Width(200f), GUILayout.Height(50f)))
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{
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StartCoroutine(ExampleCoroutine(point1));
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}
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if (GUILayout.Button("POINT2", GUILayout.Width(200f), GUILayout.Height(50f)))
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{
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StartCoroutine(ExampleCoroutine(point2));
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}
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}
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}
下面是使用Quaternion.Lerp得出的结果：
代码如下：
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using UnityEngine;
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using System.Collections;
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public class Example : MonoBehaviour
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{
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[SerializeField] private Transform point1;
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[SerializeField] private Transform point2;
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private IEnumerator ExampleCoroutine(Transform target)
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{
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float beginTime = Time.time;
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Vector3 beginPosition = transform.position;
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Quaternion beginRotation = transform.rotation;
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for (var duration = 2f; (Time.time - beginTime) < duration;)
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{
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float t = (Time.time - beginTime) / duration;
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transform.position = Vector3.Lerp(beginPosition, target.position, t);
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transform.rotation = Quaternion.Lerp(beginRotation, target.rotation, t);
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yield return null;
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}
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transform.position = target.position;
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transform.rotation = target.rotation;
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}
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private void OnGUI()
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{
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if (GUILayout.Button("POINT1", GUILayout.Width(200f), GUILayout.Height(50f)))
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{
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StartCoroutine(ExampleCoroutine(point1));
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}
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if (GUILayout.Button("POINT2", GUILayout.Width(200f), GUILayout.Height(50f)))
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{
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StartCoroutine(ExampleCoroutine(point2));
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}
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}
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}
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
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