Unity Vector3.Slerp() 球形插值详解之一

using UnityEngine;
using System.Collections;

/// 

/// 在日出和日落之间动画弧线
/// 网上看到有人对Vector3.Slerp()的详解，但是经过962f之力将他的思路看明白。
/// 受到启发，就有了自己对Vector3.Slerp()的理解。tt2()函数是自己的写的，tt3()是别人的。
/// 

public class Vector3_Slerp_2 : MonoBehaviour
{
    public Transform sunrise;
    public Transform sunset;

    /// 

    /// 插值中心点的影响因素
    /// 
    public float m_moveTowardsValue = 1f;
    /// 

    /// 插值的个数
    /// 
    public int m_lineNum = 10;

    private Vector3 mStart = Vector3.zero;
    private Vector3 mEnd = Vector3.zero;

    void Update()
    {
        tt2();
        //tt3();
    }

    /// 

    /// 官方用例
    /// 
    private void tt1()
    {
        //弧线的中心
        Vector3 center = (sunrise.position + sunset.position) * 0.5f;

        //向下移动中心，垂直于弧线
        center -= new Vector3(0, 1, 0);

        //相对于中心在弧线上插值
        Vector3 riseRelCenter = sunrise.position - center;
        Vector3 setRelCenter = sunset.position - center;

        transform.position = Vector3.Slerp(riseRelCenter, setRelCenter, Time.time);
        transform.position += center;
    }

    /// 

    ///  球面插值
    ///  自己的理解
    ///  只在垂直平面上做球面插值。
    /// 
    private void tt2()
    {
        mStart = sunrise.position;
        mEnd = sunset.position;

        /// 绘制世界坐标系
        Debug.DrawLine(new Vector3(-100, 0, 0), new Vector3(100, 0, 0), Color.green);
        Debug.DrawLine(new Vector3(0, -100, 0), new Vector3(0, 100, 0), Color.green);
        Debug.DrawLine(new Vector3(0, 0, -100), new Vector3(0, 0, 100), Color.green);
        
        /// 求出起始点与终点的中心点
        Vector3 center = (mStart + mEnd) * 0.5f;

        ////////////////////////////////////
        /// 1. center、mStart、mEnd 构成一个平面A
        ////////////////////////////////////

        Debug.DrawLine(new Vector3(center.x, 0f, center.z), center, Color.white);

        /// 绘制一个三角形
        Debug.DrawLine(new Vector3(center.x, 0f, center.z), mStart, Color.white);
        Debug.DrawLine(new Vector3(center.x, 0f, center.z), mEnd, Color.white);
        Debug.DrawLine(mStart, mEnd, Color.white);

        Vector3 normal = mEnd - mStart;
        ///只在垂直平面上做球面插值。
        Vector3 tangent = new Vector3(center.x, 0f, center.z) - center;

        /// 两个坐标轴的正交化。
        Vector3.OrthoNormalize(ref normal, ref tangent);
        Vector3 center2 = center + tangent * m_moveTowardsValue;

        ////////////////////////////////////
        /// 2. 两个坐标轴的正交化后 center2、mStart、mEnd 构成一个平面B，
        /// 3. 平面B与平面A是同一平面。
        ////////////////////////////////////

        Debug.DrawLine(center2, mStart, Color.blue);
        Debug.DrawLine(center2, mEnd, Color.blue);
        Debug.Log(string.Format("{0} : {1}", Vector3.Distance(center2, mStart), Vector3.Distance(center2, mEnd)));

        for (int i = 1; i < m_lineNum; ++i)
        {
            Vector3 drawVec = Vector3.Slerp(mEnd - center2, mStart - center2, 1f / m_lineNum * i);
            drawVec += center2;
            Debug.DrawLine(center2, drawVec, Color.yellow);
        }

        /// 绘制起始点与终点的中心点到计算出的插值的中心点
        Debug.DrawLine(center, center2, Color.black);
    }

    /// 

    /// 球面插值
    /// http://www.manew.com/thread-43314-1-1.html 文章用例
    /// 
    private void tt3()
    {
        mStart = sunrise.position;
        mEnd = sunset.position;

        Debug.DrawLine(new Vector3(-100, 0, 0), new Vector3(100, 0, 0), Color.green);
        Debug.DrawLine(new Vector3(0, -100, 0), new Vector3(0, 100, 0), Color.green);
        Debug.DrawLine(new Vector3(0, 0, -100), new Vector3(0, 0, 100), Color.green);
     
        Debug.DrawLine(Vector3.zero, mStart, Color.white);
        Debug.DrawLine(Vector3.zero, mEnd, Color.white);
        Debug.DrawLine(mStart, mEnd, Color.white);

        /// 求出起始点与终点的中心点
        Vector3 centor = (mStart + mEnd) * 0.5f;
        Debug.DrawLine(Vector3.zero, centor, Color.blue);

        Vector3 centorProject = Vector3.Project(centor, mStart - mEnd); // 中心点在两点之间的投影
        centor = Vector3.MoveTowards(centor, centorProject, m_moveTowardsValue);        // 沿着投影方向移动移动距离（距离越大弧度越小）

        Debug.DrawLine(centor, mStart, Color.blue);
        Debug.DrawLine(centor, mEnd, Color.blue);

        Debug.Log(string.Format("{0} : {1}", Vector3.Distance(centor, mStart), Vector3.Distance(centor, mEnd)));

        for (int i = 1; i < m_lineNum; ++i)
        {
            Vector3 drawVec = Vector3.Slerp(mEnd - centor, mStart - centor, 1f / m_lineNum * i);
            drawVec += centor;
            Debug.DrawLine(centor, drawVec, Color.yellow);
            //Debug.DrawLine(centor, drawVec, 5 == i ? Color.blue : Color.yellow);
        }
    }
}

本文参考：
http://www.manew.com/thread-43314-1-1.html