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。
csharp
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
csharp
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
csharp
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
csharp
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