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前言

我们在上一篇文章中，进行了正交相机视图空间下转化到裁剪空间下的矩阵推导。

• Unity中Shader裁剪空间推导（正交相机到裁剪空间的转化矩阵）

我们在这篇文章中，在Unity的Shader中实现一下。

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一、在Shader中，手动把正交相机的坐标转化到裁剪空间

• OpenGL下：

$\left[\begin{array}{cccc}\frac{2}{w}& 0& 0& 0\\ 0& \frac{2}{h}& 0& 0\\ 0& 0& \frac{2}{n-f}& \frac{n+f}{n-f}\\ 0& 0& 0& 1\end{array}\right]$

• DirectX下：

$\left[\begin{array}{cccc}\frac{2}{w}& 0& 0& 0\\ 0& \frac{2}{h}& 0& 0\\ 0& 0& \frac{1}{n-f}& \frac{n}{n-f}\\ 0& 0& 0& 1\end{array}\right]$

• ReversedZ

在DirectX中，因为精度问题
会把原本的范围从[0，1]修改为[1,0]。所以，矩阵需要按照之前的方法重新推导
$\left[\begin{array}{cccc}\frac{2}{w}& 0& 0& 0\\ 0& \frac{2}{h}& 0& 0\\ 0& 0& \frac{1}{f-n}& \frac{f}{f-n}\\ 0& 0& 0& 1\end{array}\right]$

1、我们在属性面板定义一个变量，用于传入摄像机的信息

这里信息包括：
摄像机的Size（X）、近裁剪面（Y）、远裁剪面（Z） 和 屏幕宽高比（W）
1.7777……是 1920 / 1080 的比值。

_CameraParams(“Size(X),Near(Y),Far(Z) Ratio(W)”,Vector) = (0,0,0,1.777)

2、获取h、r、w、n、f

float h = _CameraParams.x * 2;
float w = h * _CameraParams.w;
float n = _CameraParams.y;
float f = _CameraParams.z;

3、获取OpenGL下的转化矩阵

//OpenGL
float4x4 M_clip01 = float4x4
(2/w,0,0,0,0,2/h,0,0,0,0,2/(n - f),(n + f) / (n - f),0,0,0,1
);

4、 获取DirectX下的转化矩阵

//DirectX
float4x4 M_clip02 = float4x4
(2/w,0,0,0,0,2/h,0,0,0,0,1/(f-n),f/(f-n),0,0,0,1
);

5、手动将观察空间下的坐标转换到裁剪空间下

//手动将观察空间下的坐标转换到裁剪空间下
o.vertexCS = mul(M_clip01,float4(vertexVS,1));

6、这里为测试模型效果，进行了纹理采样（可选）

• 属性面板接收纹理

_MainTex(“MainTex”,2D) = “white”{}

• 定义纹理 和 采样器

TEXTURE2D(_MainTex);
SAMPLER(sampler_MainTex);

• 在片元着色器中，采样并且使用

float4 mainTex = SAMPLE_TEXTURE2D(_MainTex,sampler_MainTex,i.uv);
return mainTex;

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二、最终效果

1、OpenGL下：

• Edit->ProjectSetting->Player 中修改项目渲染平台设置
  

//手动将观察空间下的坐标转换到裁剪空间下
o.vertexCS = mul(M_clip01,float4(vertexVS,1));

• 传入当前摄像机信息
  

2、DirectX下（需要注意的是，在DX平台下屏幕的 y 坐标是相反的，需要在转化矩阵的 y 对应位置乘以 -1）：

• Edit->ProjectSetting->Player 中修改项目渲染平台设置
  

//手动将观察空间下的坐标转换到裁剪空间下
o.vertexCS = mul(M_clip02,float4(vertexVS,1));

• 传入当前摄像机信息
  

3、可以使用 UNITY_NEAR_CLIP_VALUE 来判断是什么平台

裁剪空间下的近剪裁值,(DX为1,OpenGL为-1).

4、最终代码

//平移变换
//缩放变换
//旋转变换（四维）
//视图空间矩阵
//正交相机视图空间 -> 裁剪空间
Shader "MyShader/URP/P3_7_3"
{Properties{[Header(MainTexx)]_MainTex("MainTex",2D) = "white"{}[Header(Transtion)]_Translate("Translate(XYZ)",Vector) = (0,0,0,0)_Scale("Scale(XYZ)",Vector)= (1,1,1,1)_Rotation("Rotation(XYZ)",Vector) = (0,0,0,0)[Header(View)]_ViewPos("View Pos",vector) = (0,0,0,0)_ViewTarget("View Target",vector) = (0,0,0,0)[Header(Camera)]_CameraParams("Size(X),Near(Y),Far(Z) Ratio(W)",Vector) = (0,0,0,1.777)}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;float2 uv : TEXCOORD0;};struct Varying{float4 vertexCS : SV_POSITION;float2 uv : TEXCOORD0;};CBUFFER_START(UnityPerMaterial)float4 _Translate;float4 _Scale;float4 _Rotation;float4 _ViewPos;float4 _ViewTarget;float4 _CameraParams;CBUFFER_ENDTEXTURE2D(_MainTex);SAMPLER(sampler_MainTex);Varying vert (Attribute v){Varying o;o.uv = v.uv;//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);//观察空间矩阵推导//P_view = [W_view] * P_world//P_view = [V_world]^-1 * P_world//P_view = [V_world]^T * P_worldfloat3 ViewZ = normalize(_ViewPos - _ViewTarget);float3 ViewY = float3(0,1,0);float3 ViewX = cross(ViewZ,ViewY);ViewY = cross(ViewX,ViewZ);float4x4 M_viewTemp = float4x4(ViewX.x,ViewX.y,ViewX.z,0,ViewY.x,ViewY.y,ViewY.z,0,ViewZ.x,ViewZ.y,ViewZ.z,0,0,0,0,1);float4x4 M_viewTranslate = float4x4(1,0,0,-_ViewPos.x,0,1,0,-_ViewPos.y,0,0,1,-_ViewPos.z,0,0,0,1);float4x4 M_view = mul(M_viewTemp,M_viewTranslate);float3 vertexWS = TransformObjectToWorld(v.vertexOS);//世界空间转化到观察空间float3 vertexVS = mul(M_view,float4(vertexWS,1));//相机参数float h = _CameraParams.x * 2;float w = h * _CameraParams.w;float n = _CameraParams.y;float f = _CameraParams.z;//正交相机投影矩阵//P_Clip = [M_Clip] * P_viewfloat4x4 M_clip;if(UNITY_NEAR_CLIP_VALUE==-1){//OpenGLM_clip = float4x4(2/w,0,0,0,0,2/h,0,0,0,0,2/(n - f),(n + f) / (n - f),0,0,0,1);}if(UNITY_NEAR_CLIP_VALUE==1){//DirectXM_clip = float4x4(2/w,0,0,0,0,-2/h,0,0,0,0,1/(f-n),f/(f-n),0,0,0,1);}//手动将观察空间下的坐标转换到裁剪空间下o.vertexCS = mul(M_clip,float4(vertexVS,1));//观察空间 转化到 齐次裁剪空间//o.vertexCS = TransformWViewToHClip(vertexVS);//o.vertexCS = TransformObjectToHClip(v.vertexOS.xyz);return o;}half4 frag (Varying i) : SV_Target{float4 mainTex = SAMPLE_TEXTURE2D(_MainTex,sampler_MainTex,i.uv);return mainTex;}ENDHLSL}}
}