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前言

在上篇文章中，我們推算出了Shader物體旋轉(zhuǎn)所使用的二維旋轉(zhuǎn)矩陣。

• Unity中Shader旋轉(zhuǎn)矩陣（二維旋轉(zhuǎn)矩陣）

在這篇文章中，我們來推算得到四維旋轉(zhuǎn)矩陣。

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一、圍繞X軸旋轉(zhuǎn)

圍繞X軸旋轉(zhuǎn)代表，物體頂點的X軸不變。

1、可以使用上篇文章中，同樣的方法推導(dǎo)得出圍繞X軸旋轉(zhuǎn)的點陣。

• 我們把P₂增加一維且分量為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、圍繞Y軸旋轉(zhuǎn)

圍繞Y軸旋轉(zhuǎn)代表，物體頂點的Y軸不變。

1、可以使用上篇文章中，同樣的方法推導(dǎo)得出圍繞Y軸旋轉(zhuǎn)的點陣。

• 我們把P₂增加一維且分量為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、圍繞Z軸旋轉(zhuǎn)

圍繞Z軸旋轉(zhuǎn)代表，物體頂點的Z軸不變。

1、可以使用上篇文章中，同樣的方法推導(dǎo)得出圍繞Z軸旋轉(zhuǎn)的點陣。

• 我們把P₂增加一維且分量為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函數(shù)前面的負號位置實現(xiàn)順時針還是逆時針。這篇文章中是順時針

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四、在Shader實現(xiàn)

1、在屬性面板定義四維變量，用xyz控制XYZ軸上的旋轉(zhuǎn)

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

2、在常量緩沖區(qū)申明該變量

CBUFFER_START(UnityPerMaterial)
float4 _Rotation;
CBUFFER_END

3、在 頂點著色器 定義旋轉(zhuǎn)矩陣

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、使用旋轉(zhuǎn)矩陣與模型頂點相乘輸出

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

5、最終效果

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五、最終測試代碼

//平移變換
//縮放變換
//旋轉(zhuǎn)變換（四維）
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;//平移變換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);//縮放交換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);//旋轉(zhuǎn)變換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}}
}