Unity矩阵平移旋转缩放Matrix4x4

Unity中的矩阵（Matrix4x4）

最近在研究帧同步定点数物理系统中需要自定义定点数矩阵，所以在这里分享下基础的矩阵案例旋转、平移、缩放。（注意这里本文中的transform组件式基于unity浮点数的教程并非帧同步定点数）参考原文

创建自定义模型

参数可以参考我上图的参数，这里注意三个顶点是一个面，这里我上述的模型是一个三角形的面。

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class Triangle : MonoBehaviour
{
    /// <summary>
    /// 网格
    /// </summary>
    Mesh mesh;
    
    /// <summary>
    /// 三角形顶点
    /// </summary>
    public Vector3[] vertices;

    /// <summary>
    /// 分配三角形顶点索引
    /// </summary>
    public int[] triangle;

    /// <summary>
    /// 材质球
    /// </summary>
    public Material mat;

    private void Start()
    {
        //实例化网格
        mesh = new Mesh();

        //分配顶点
        mesh.vertices = vertices;

        //分配三角形顶点索引
        mesh.triangles = triangle;

        //添加网格过滤器
        MeshFilter mf = gameObject.AddComponent<MeshFilter>();

        //网格赋值
        mf.mesh = mesh;
        
        //添加网格渲染器
        MeshRenderer mr = gameObject.AddComponent<MeshRenderer>();
        
        //材质赋值
        mr.materials[0] = mat;
    }
}

创建模型很简单我就不细讲了，看不懂的可以看上述的注释即可，直接黏贴也可。

平移矩阵

要做位移先搞明白矩阵中的哪几个索引值代表的坐标位置，如下图所示4x4矩阵

上图Tx，Ty，Tz为平邑的方向向量

这里可以自己做个测试，将transform的初始位置修改如下所示

代码如下

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MyTransform : MonoBehaviour
{
    public Matrix4x4 matrix;

    // Start is called before the first frame update
    void Start()
    {
        matrix.SetTRS(transform.position,transform.rotation,transform.localScale);
    }

    // Update is called once per frame
    void Update()
    {
        if (Input.GetKeyDown(KeyCode.Q)) 
        {
            MyTranslate(new Vector3 (Random.Range(-5,5),Random.Range(-5,5), Random.Range(-5, 5)));
        }
    }

    public Vector4 v;

    /// <summary>
    /// 平移矩阵对象
    /// </summary>
    /// <param name="pos"></param>
    public void MyTranslate(Vector3 pos) 
    {
        //按照当前位置进行位移
        //v = new Vector4(transform.position.x,transform.position.y,transform.position.z,1);

        //按照原点进行位移
        v = new Vector4(0, 0, 0, 1);
        matrix = Matrix4x4.identity;

        //X、Y、Z移动因子
        matrix.m03 = pos.x;
        matrix.m13 = pos.y;
        matrix.m23 = pos.z;

        //矩阵位移操作
        v = matrix * v;

        transform.position = new Vector3(v.x, v.y, v.z);
    }
}

缩放矩阵

这个就是缩放矩阵，其中“Sx”、“Sy”、“Sz”就是各个轴上的缩放因子。缩放矩阵是矩阵表现物体大小变换的矩阵。如果缩放因子小于1，表现为物体缩小；如果大于1，则表现为物体扩大，如果等于1则不发生变化。

测试的话可以根据平移矩阵的测试方式修改scale来查看矩阵点对应值得变化

修改代码如下

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MyTransform : MonoBehaviour
{
    public Matrix4x4 matrix;

    // Start is called before the first frame update
    void Start()
    {
        matrix.SetTRS(transform.position,transform.rotation,transform.localScale);
    }

    // Update is called once per frame
    void Update()
    {
        if (Input.GetKeyDown(KeyCode.Q)) 
        {
            MyTranslate(new Vector3 (Random.Range(-5,5),Random.Range(-5,5), Random.Range(-5, 5)));
        }
        if (Input.GetKeyDown(KeyCode.W)) 
        {
            int scale = Random.Range(-5,5);
            MyScale(new Vector3 (scale, scale, scale));
        }
    }

    public Vector4 v;

    /// <summary>
    /// 平移矩阵对象
    /// </summary>
    /// <param name="pos"></param>
    public void MyTranslate(Vector3 pos) 
    {
        //按照当前位置进行位移
        //v = new Vector4(transform.position.x,transform.position.y,transform.position.z,1);

        //按照原点进行位移
        v = new Vector4(0, 0, 0, 1);
        matrix = Matrix4x4.identity;

        //X、Y、Z移动因子
        matrix.m03 = pos.x;
        matrix.m13 = pos.y;
        matrix.m23 = pos.z;

        //矩阵位移操作
        v = matrix * v;

        transform.position = new Vector3(v.x, v.y, v.z);
    }

    /// <summary>
    /// 缩放矩阵对象
    /// </summary>
    /// <param name="scale"></param>
    public void MyScale(Vector3 scale) 
    {
        //设置当前对象大小
        //v = new Vector4(transform.localScale.x, transform.localScale.y, transform.localScale.z, 1);

        //按照原点进行位移
        v = new Vector4(1, 1, 1, 1);

        matrix = Matrix4x4.identity;

        //X、Y、Z缩放因子
        matrix.m00 = scale.x;
        matrix.m11 = scale.y;
        matrix.m22 = scale.z;

        //矩阵缩放操作
        v = matrix * v;

        transform.localScale = new Vector3(v.x, v.y, v.z);
    }
}

旋转矩阵

测试的话可以根据平移矩阵的测试方式修改Rotation来查看矩阵点对应值得变化

修改代码如下

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MyTransform : MonoBehaviour
{
    public Matrix4x4 matrix;

    // Start is called before the first frame update
    void Start()
    {
        matrix.SetTRS(transform.position,transform.rotation,transform.localScale);
    }

    // Update is called once per frame
    void Update()
    {
        if (Input.GetKeyDown(KeyCode.Q)) 
        {
            MyTranslate(new Vector3 (Random.Range(-5,5),Random.Range(-5,5), Random.Range(-5, 5)));
        }
        if (Input.GetKeyDown(KeyCode.W)) 
        {
            int scale = Random.Range(-5,5);
            MyScale(new Vector3 (scale, scale, scale));
        }
        if (Input.GetKeyDown(KeyCode.A)) 
        {
            MyRotation( Axle.X,10f);
        }
        if (Input.GetKeyDown(KeyCode.S))
        {
            MyRotation(Axle.Y, 10f);
        }
        if (Input.GetKeyDown(KeyCode.D))
        {
            MyRotation(Axle.Z, 10f);
        }
    }

    public Vector4 v;

    /// <summary>
    /// 平移矩阵对象
    /// </summary>
    /// <param name="pos"></param>
    public void MyTranslate(Vector3 pos) 
    {
        //按照当前位置进行位移
        //v = new Vector4(transform.position.x,transform.position.y,transform.position.z,1);

        //按照原点进行位移
        v = new Vector4(0, 0, 0, 1);
        matrix = Matrix4x4.identity;

        //X、Y、Z移动因子
        matrix.m03 = pos.x;
        matrix.m13 = pos.y;
        matrix.m23 = pos.z;

        //矩阵位移操作
        v = matrix * v;

        transform.position = new Vector3(v.x, v.y, v.z);
    }

    /// <summary>
    /// 缩放矩阵对象
    /// </summary>
    /// <param name="scale"></param>
    public void MyScale(Vector3 scale) 
    {
        //设置当前对象大小
        //v = new Vector4(transform.localScale.x, transform.localScale.y, transform.localScale.z, 1);

        //按照原点进行位移
        v = new Vector4(1, 1, 1, 1);

        matrix = Matrix4x4.identity;

        //X、Y、Z缩放因子
        matrix.m00 = scale.x;
        matrix.m11 = scale.y;
        matrix.m22 = scale.z;

        //矩阵缩放操作
        v = matrix * v;

        transform.localScale = new Vector3(v.x, v.y, v.z);
    }

    public enum Axle { X, Y, Z}

    public void MyRotation(Axle axle,float angle) 
    {
        matrix = Matrix4x4.identity;

        //对应 X、Y、Z的旋转
        switch (axle)
        {
            case Axle.X:
                matrix.m11 = Mathf.Cos(angle * Mathf.Deg2Rad);
                matrix.m12 = -Mathf.Sin(angle * Mathf.Deg2Rad);
                matrix.m21 = Mathf.Sin(angle * Mathf.Deg2Rad);
                matrix.m22 = Mathf.Cos(angle * Mathf.Deg2Rad);
                break;
            case Axle.Y:
                matrix.m00 = Mathf.Cos(angle * Mathf.Deg2Rad);
                matrix.m02 = Mathf.Sin(angle * Mathf.Deg2Rad);
                matrix.m20 = -Mathf.Sin(angle * Mathf.Deg2Rad);
                matrix.m22 = Mathf.Cos(angle * Mathf.Deg2Rad);
                break;
            case Axle.Z:
                matrix.m00 = Mathf.Cos(angle * Mathf.Deg2Rad);
                matrix.m01 = -Mathf.Sin(angle * Mathf.Deg2Rad);
                matrix.m10 = Mathf.Sin(angle * Mathf.Deg2Rad);
                matrix.m11 = Mathf.Cos(angle * Mathf.Deg2Rad);
                break;
            default:
                break;
        }

        float qw = Mathf.Sqrt(1f + matrix.m00 + matrix.m11 + matrix.m22) / 2;
        float w = 4 * qw;
        float qx = (matrix.m21 - matrix.m12) / w;
        float qy = (matrix.m02 - matrix.m20) / w;
        float qz = (matrix.m10 - matrix.m01) / w;

        transform.rotation = new Quaternion(qx, qy, qz, qw);
    }

}

原文中有对应的小工具可以参考