Unity【Lerp & Slerp】- 线性插值与球形插值的区别
Unity【Lerp & Slerp】- 线性插值与球形插值的区别
CoderZ
发布于 2022-08-29 16:42:34
发布于 2022-08-29 16:42:34
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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));
}
}
}本文参与 腾讯云自媒体同步曝光计划，分享自微信公众号。
原始发表：2022-03-05，如有侵权请联系 cloudcommunity@tencent.com 删除
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