Unity中Shader旋转矩阵（四维旋转矩阵）

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前言

在上篇文章中，我们推算出了Shader物体旋转所使用的二维旋转矩阵。

• Unity中Shader旋转矩阵（二维旋转矩阵）

在这篇文章中，我们来推算得到四维旋转矩阵。

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一、围绕X轴旋转

围绕X轴旋转代表，物体顶点的X轴不变。

1、可以使用上篇文章中，同样的方法推导得出围绕X轴旋转的点阵。

• 我们把P₂增加一维且分量为1

2、求M_rotate

• M_rotate * P₁ = P₂
• M_rotate = P₂* P₁^-1
  
• 最后得到M_rotate
  

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二、围绕Y轴旋转

围绕Y轴旋转代表，物体顶点的Y轴不变。

1、可以使用上篇文章中，同样的方法推导得出围绕Y轴旋转的点阵。

• 我们把P₂增加一维且分量为1

2、求M_rotate

• M_rotate * P₁ = P₂
• M_rotate = P₂* P₁^-1
  
• 最后得到M_rotate
  

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三、围绕Z轴旋转

围绕Z轴旋转代表，物体顶点的Z轴不变。

1、可以使用上篇文章中，同样的方法推导得出围绕Z轴旋转的点阵。

• 我们把P₂增加一维且分量为1

2、求M_rotate

• M_rotate * P₁ = P₂
• M_rotate = P₂* P₁^-1
  
• 最后得到M_rotate
  

可以修改sin函数前面的负号位置实现顺时针还是逆时针。这篇文章中是顺时针

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四、在Shader实现

1、在属性面板定义四维变量，用xyz控制XYZ轴上的旋转

_Rotation(“Rotation(XYZ)”,Vector) = (0,0,0,0)

2、在常量缓冲区申明该变量

CBUFFER_START(UnityPerMaterial)
float4 _Rotation;
CBUFFER_END

3、在 顶点着色器 定义旋转矩阵

float4x4 M_rotateX = float4x4
(
1,0,0,0,
0,cos(_Rotation.x),sin(_Rotation.x),0,
0,-sin(_Rotation.x),cos(_Rotation.x),0,
0,0,0,1
);
float4x4 M_rotateY = float4x4
(
cos(_Rotation.y),0,sin(_Rotation.y),0,
0,1,0,0,
-sin(_Rotation.y),0,cos(_Rotation.y),0,
0,0,0,1
);
float4x4 M_rotateZ = float4x4
(
cos(_Rotation.z),sin(_Rotation.z),0,0,
-sin(_Rotation.z),cos(_Rotation.z),0,0,
0,0,1,0,
0,0,0,1
);

4、使用旋转矩阵与模型顶点相乘输出

v.vertexOS = mul(M_rotateX,v.vertexOS);
v.vertexOS = mul(M_rotateY,v.vertexOS);
v.vertexOS = mul(M_rotateZ,v.vertexOS);

5、最终效果

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五、最终测试代码

//平移变换
//缩放变换
//旋转变换（四维）
Shader "MyShader/URP/P3_5_7"
{Properties{_Translate("Translate(XYZ)",Vector) = (0,0,0,0)_Scale("Scale(XYZ)",Vector)= (1,1,1,1)_Rotation("Rotation(XYZ)",Vector) = (0,0,0,0)}SubShader{Tags{"PenderPipeline"="UniversalPipeline""RenderType"="Opaque""Queue"="Geometry"}Pass{HLSLPROGRAM#pragma vertex vert#pragma fragment frag#include "Packages/com.unity.render-pipelines.core/ShaderLibrary/Color.hlsl"#include "Packages/com.unity.render-pipelines.universal/ShaderLibrary/Core.hlsl"#include "Packages/com.unity.render-pipelines.universal/ShaderLibrary/Lighting.hlsl"struct Attribute{float4 vertexOS : POSITION;};struct Varying{float4 vertexCS : SV_POSITION;};CBUFFER_START(UnityPerMaterial)float4 _Translate;float4 _Scale;float4 _Rotation;CBUFFER_ENDVarying vert (Attribute v){Varying o;//平移变换float4x4 M_Translate = float4x4(1,0,0,_Translate.x,0,1,0,_Translate.y,0,0,1,_Translate.z,0,0,0,1);v.vertexOS = mul(M_Translate,v.vertexOS);//缩放交换float4x4 M_Scale = float4x4(_Scale.x,0,0,0,0,_Scale.y,0,0,0,0,_Scale.z,0,0,0,0,1);v.vertexOS = mul(M_Scale,v.vertexOS);//旋转变换float4x4 M_rotateX = float4x4(1,0,0,0,0,cos(_Rotation.x),sin(_Rotation.x),0,0,-sin(_Rotation.x),cos(_Rotation.x),0,0,0,0,1);float4x4 M_rotateY = float4x4(cos(_Rotation.y),0,sin(_Rotation.y),0,0,1,0,0,-sin(_Rotation.y),0,cos(_Rotation.y),0,0,0,0,1);float4x4 M_rotateZ = float4x4(cos(_Rotation.z),sin(_Rotation.z),0,0,-sin(_Rotation.z),cos(_Rotation.z),0,0,0,0,1,0,0,0,0,1);v.vertexOS = mul(M_rotateX,v.vertexOS);v.vertexOS = mul(M_rotateY,v.vertexOS);v.vertexOS = mul(M_rotateZ,v.vertexOS);o.vertexCS = TransformObjectToHClip(v.vertexOS.xyz);return o;}half4 frag (Varying i) : SV_Target{return 1;}ENDHLSL}}
}