网站速度诊断 慢/网络营销的四大基础理论

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前言

在上篇文章中，我们是实现了Shader中的观察空间推导。

• Unity中Shader观察空间推导

我们在这篇文章中，根据上篇文章的推导，在Shader中实现观察空间矩阵的推导。

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一、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_world

• 在属性面板定义测试使用到的 摄像机坐标 和 测试顶点坐标

_ViewPos(“View Pos”,vector) = (0,0,0,0)
_ViewTarget(“View Target”,vector) = (0,0,0,0)

1、求观察空间基向量

• Z坐标轴基向量

float3 ViewZ = normalize(_ViewPos - _ViewTarget);

• 假设Y坐标轴基向量为（0，1，0）

float3 ViewY = float3(0,1,0);

• 求 X 坐标基向量

float3 ViewX = cross(ViewZ,ViewY);

• 求 Y 坐标基向量

ViewY = cross(ViewX,ViewZ);

2、求观察空间的基向量在世界空间中的矩阵 的 逆矩阵

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
);

2、求平移变换矩阵

$$\begin{array}{cccc}1& 0& 0& -Tx\\ 0& 1& 0& -Ty\\ 0& 0& 1& -Tz\\ 0& 0& 0& 1\end{array}$$

float4x4 M_viewTranslate = float4x4
(
1,0,0,-_ViewPos.x,
0,1,0,-_ViewPos.y,
0,0,1,-_ViewPos.z,
0,0,0,1
);

3、相乘得出 观察空间转化矩阵

float4x4 M_view = mul(M_viewTemp,M_viewTranslate);

4、得到顶点的世界空间坐标，然后转化到观察空间

float3 vertexWS = TransformObjectToWorld(v.vertexOS);
float3 vertexVS = mul(M_view,float4(vertexWS,1));

5、把观察空间坐标转化为齐次裁剪坐标输出到屏幕

o.vertexCS = TransformWViewToHClip(vertexVS);

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二、最终效果

1、这是我们用默认Shader，在该摄像机坐标下的游戏界面

2、使用我们的Shader，并且给我们的ViewPos赋值为摄像机坐标

3、最终代码

//平移变换
//缩放变换
//旋转变换（四维）
Shader "MyShader/URP/P3_6_5"
{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)[Header(View)]_ViewPos("View Pos",vector) = (0,0,0,0)_ViewTarget("View Target",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;float4 _ViewPos;float4 _ViewTarget;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);//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);float3 vertexVS = mul(M_view,float4(vertexWS,1));o.vertexCS = TransformWViewToHClip(vertexVS);//o.vertexCS = TransformObjectToHClip(v.vertexOS.xyz);return o;}half4 frag (Varying i) : SV_Target{return 1;}ENDHLSL}}
}