各向异性渲染（二）Kajiya Kay头发渲染

介绍

基于之前的各向异性得结果，我们可以再推广到头发渲染。Kajiya Kay头发渲染是一种经验模型。它把头发模型为一条一条细管。然后利用上一章的数学基础，但当然Kajiya Kay也加了几个细节。包括多Primary highlight, Second HighLight, Shift Tangent, 的各向异性得结果，我们可以再推广到头发渲染。Kajiya Kay头发渲染是一种经验模型。它把头发模型为一条一条细管。然后利用上一章的数学基础，但当然Kajiya Kay也加了几个细节。包括多Primary highlight, Second HighLight, Shift Tangent, 等概念。

各向异性高光
漫反射
Primary & Secondary 高光
Shift Tangent
Shift Tangent Map
AmbientOcclusion
最终效果
代码

各向异性高光

因为上一章已经说明了，高光部分 $I{s}{{anisotopic}} $ 由以下公式得到

Isanisotopic=Li∗ks∗(N⃗c⋅H⃗)n=Li∗ks∗(1−(T⃗⋅H⃗)2)nI{_s}{_{anisotopic}} = L_i * k_s * {(\vec N_c \cdot \vec H)} ^{n} = L_i * k_s * {(\sqrt{1- (\vec T \cdot \vec H)^2 } ) }^{n}Isanisotopic=Li∗ks∗(Nc⋅H)n=Li∗ks∗(1−(T⋅H)2)n

vec3 shiftTangent(vec3 T, vec3 N, float shift)
{return normalize(T + shift * N);
}float hairStrand(vec3 T, vec3 V, vec3 L, float specPower)
{vec3 H = normalize(V + L);float HdotT = dot(T, H);float sinTH = sqrt(1 - HdotT * HdotT);float dirAtten = smoothstep(-_SpecularWidth, 0, HdotT);return dirAtten * saturate(pow(sinTH, specPower)) * _SpecularScale;
}vec4 getSpecular(vec4 lightColor0,vec4 primaryColor, float primaryShift,vec4 secondaryColor, float secondaryShift,vec3 N, vec3 T, vec3 V, vec3 L, float specPower, vec2 uv)
{vec4 specular = vec4(0.0, 0.0, 0.0, 0.0);specular += primaryColor * hairStrand(T, V, L, specPower) * _SpecularScale;;return specular;
}vec4 frag(v2f i) : SV_Target
{vec3 N = normalize(i.normal);vec3 T = normalize(i.tangent);vec3 B = normalize(i.binormal);vec3 V = normalize(UnityWorldSpaceViewDir(i.pos));vec3 L = normalize(UnityWorldSpaceLightDir(i.pos));vec3 H = normalize(L + V);vec4 specular = getSpecular(_LightColor0, _PrimaryColor, _PrimaryShift, _SecondaryColor, _SecondaryShift, N, B, V, L, _specPower, i.uv);vec4 col = (specular);col.a = 1.0f;return col;
}

漫反射

Kajiya-Kay 的diffuse可以简单的使用N.L

Id=Li∗kd∗(N⃗c⋅L⃗)I{_d} = L_i * k_d * {(\vec N_c \cdot \vec L)}Id=Li∗kd∗(Nc⋅L)

vec4 getAmbientAndDiffuse(vec4 lightColor0, vec4 diffuseColor, vec3 N, vec3 L, vec2 uv)
{return (lightColor0 * diffuseColor * saturate(dot(N, L)) + vec4(0.2, 0.2, 0.2, 1.0))* tex2D(_HairTex, uv);
}

Primary & Secondary 高光

大家可以看一下下图的BaseColor，Primary 及 Secondary 高光。Primary高光是偏白的。然后Secondary 高光带点BaseColor。之后主色调Base Color。

vec4 getSpecular(vec4 lightColor0,vec4 primaryColor, float primaryShift,vec4 secondaryColor, float secondaryShift,vec3 N, vec3 T, vec3 V, vec3 L, float specPower, vec2 uv)
{vec4 specular = vec4(0.0, 0.0, 0.0, 0.0);specular += primaryColor * hairStrand(T, V, L, specPower) * _SpecularScale;;specular += secondaryColor * hairStrand(T, V, L, specPower) * _SpecularScale;return specular;
}

Shift Tangent

Kajiya-Kay模型有两个偏移切线的量，原因是改变切线头发高光也偏移。如果没有切线的偏移，我们最多只可以做到像下面没有发丝的感觉。

我们将切线沿着法线方向偏移一个数量。

Shift Tangent Map

除了一个全局的偏移值，我们也可以控制每像素的偏移。我们叫这个map叫Shift Tangent Map

Ambient Occlusion

最后，我们可以加上AO，这个AO的数值可以从vertex color或AO贴图得到。这个是用来模拟Base Color Shadowed。

vec4 getSpecular(vec4 lightColor0,vec4 primaryColor, float primaryShift,vec4 secondaryColor, float secondaryShift,vec3 N, vec3 T, vec3 V, vec3 L, float specPower, vec2 uv, float ambientOcc)
{vec4 specular = vec4(0.0, 0.0, 0.0, 0.0);specular += primaryColor * hairStrand(T, V, L, specPower) * _SpecularScale;;specular += secondaryColor * hairStrand(T, V, L, specPower) * _SpecularScale;specular *= ambientOcc;return specular ;
}vec4 getAmbientAndDiffuse(vec4 lightColor0, vec4 diffuseColor, vec3 N, vec3 L, vec2 uv, float ambientOcc)
{float ambientDiffuse = (lightColor0 * diffuseColor * saturate(dot(N, L)) + vec4(0.2, 0.2, 0.2, 1.0))* tex2D(_HairTex, uv) * ambientOcc;return ambientDiffuse * ambientOcc;
}

最终效果

代码

vec3 shiftTangent(vec3 T, vec3 N, float shift)
{return normalize(T + shift * N);
}float hairStrand(vec3 T, vec3 V, vec3 L, float specPower)
{vec3 H = normalize(V + L);float HdotT = dot(T, H);float sinTH = sqrt(1 - HdotT * HdotT);float dirAtten = smoothstep(-_SpecularWidth, 0, HdotT);return dirAtten * saturate(pow(sinTH, specPower)) * _SpecularScale;
}vec4 getAmbientAndDiffuse(vec4 lightColor0, vec4 diffuseColor, vec3 N, vec3 L, vec2 uv)
{return (lightColor0 * diffuseColor * saturate(dot(N, L)) + vec4(0.2, 0.2, 0.2, 1.0))* tex2D(_HairTex, uv);
}vec4 getSpecular(vec4 lightColor0,vec4 primaryColor, float primaryShift,vec4 secondaryColor, float secondaryShift,vec3 N, vec3 T, vec3 V, vec3 L, float specPower, vec2 uv)
{float shiftTex = tex2D(_SpecularShift, uv) - 0.5;vec3 t1 = shiftTangent(T, N, primaryShift + shiftTex);vec3 t2 = shiftTangent(T, N, secondaryShift + shiftTex);vec4 specular = vec4(0.0, 0.0, 0.0, 0.0);specular += primaryColor * hairStrand(t1, V, L, specPower) * _SpecularScale;;specular += secondaryColor * hairStrand(t2, V, L, specPower) * _SpecularScale;return specular;
}vec4 frag(v2f i) : SV_Target
{vec3 N = normalize(i.normal);vec3 T = normalize(i.tangent);vec3 B = normalize(i.binormal);vec3 V = normalize(UnityWorldSpaceViewDir(i.pos));vec3 L = normalize(UnityWorldSpaceLightDir(i.pos));vec3 H = normalize(L + V);vec4 ambientdiffuse = getAmbientAndDiffuse(_LightColor0, _DiffuseColor, N, L, i.uv);vec4 specular = getSpecular(_LightColor0, _PrimaryColor, _PrimaryShift, _SecondaryColor, _SecondaryShift, N, B, V, L, _specPower, i.uv);vec4 col = (ambientdiffuse + specular);col.a = 1.0f;return col;
}

代码Unity

Shader "Mac/HairShader2"
{Properties{_HairTex("Texture", 2D) = "white" {}_SpecularShift("Hair Shifted Texture", 2D) = "white" {}_DiffuseColor("DiffuseColor", Color) = (0.0, 0.0, 0.0, 0.0)_PrimaryColor("Specular1Color", Color) = (0.0, 0.0, 0.0, 0.0)_PrimaryShift("PrimaryShift", Range(-4, 4)) = 0.0_SecondaryColor("Specular2Color", Color) = (0.0, 0.0, 0.0, 0.0)_SecondaryShift("SecondaryShift", Range(-4, 4)) = 0.5_specPower("SpecularPower", Range(0, 50)) = 20_SpecularWidth("SpecularWidth", Range(0, 1)) = 0.5_SpecularScale("SpecularScale", Range(0, 1)) = 0.3}SubShader{Tags { "RenderType"="Transparent" }LOD 100Pass{Blend SrcAlpha OneMinusSrcAlphaCGPROGRAM#pragma vertex vert#pragma fragment frag// make fog work#pragma multi_compile_fog#include "UnityCG.cginc"#include "Lighting.cginc"struct appdata{float4 vertex : POSITION;float2 uv : TEXCOORD0;float3 normal: NORMAL;float4 tangent: TANGENT;};struct v2f{float2 uv : TEXCOORD0;float4 vertex : SV_POSITION;float3 tangent : TEXCOORD1;float3 normal : TEXCOORD2;float3 binormal: TEXCOORD3;float3 pos : TEXCOORD4;UNITY_FOG_COORDS(1)};sampler2D _HairTex;float4 _HairTex_ST;sampler2D _SpecularShift;float4 _SpecularShift_ST;float4 _DiffuseColor;float4 _PrimaryColor;float _PrimaryShift;float4 _SecondaryColor;float _SecondaryShift;float _specPower;float _SpecularWidth;float _SpecularScale;v2f vert (appdata v){v2f o;UNITY_INITIALIZE_OUTPUT(v2f, o);o.vertex = UnityObjectToClipPos(v.vertex);o.uv = TRANSFORM_TEX(v.uv, _HairTex);o.normal = UnityObjectToWorldNormal(v.normal);o.tangent = UnityObjectToWorldDir(v.tangent);o.binormal = cross(v.normal, v.tangent) * v.tangent.w * unity_WorldTransformParams.w;o.pos = mul(unity_ObjectToWorld, v.vertex);UNITY_TRANSFER_FOG(o,o.vertex);return o;}fixed3 shiftTangent(fixed3 T, fixed3 N, fixed shift){return normalize(T + shift * N);}fixed hairStrand(fixed3 T, fixed3 V, fixed3 L, fixed specPower){fixed3 H = normalize(V + L);fixed HdotT = dot(T, H);fixed sinTH = sqrt(1 - HdotT * HdotT);fixed dirAtten = smoothstep(-_SpecularWidth, 0, HdotT);return dirAtten * saturate(pow(sinTH, specPower)) * _SpecularScale;}fixed4 getAmbientAndDiffuse(fixed4 lightColor0, fixed4 diffuseColor, fixed3 N, fixed3 L, fixed2 uv){return (lightColor0 * diffuseColor * saturate(dot(N, L)) + fixed4(0.2, 0.2, 0.2, 1.0)) * tex2D(_HairTex, uv);}fixed4 getSpecular(fixed4 lightColor0, fixed4 primaryColor, fixed primaryShift,fixed4 secondaryColor, fixed secondaryShift,fixed3 N, fixed3 T, fixed3 V, fixed3 L, fixed specPower, fixed2 uv){float shiftTex = tex2D(_SpecularShift, uv) - 0.5;fixed3 t1 = shiftTangent(T, N, primaryShift + shiftTex);fixed3 t2 = shiftTangent(T, N, secondaryShift + shiftTex);fixed4 specular = fixed4(0.0, 0.0, 0.0, 0.0);specular += primaryColor * hairStrand(t1, V, L, specPower) * _SpecularScale;;specular += secondaryColor * hairStrand(t2, V, L, specPower) * _SpecularScale;return specular;}fixed4 frag (v2f i) : SV_Target{fixed3 N = normalize(i.normal);fixed3 T = normalize(i.tangent);fixed3 B = normalize(i.binormal);fixed3 V = normalize(UnityWorldSpaceViewDir(i.pos));fixed3 L = normalize(UnityWorldSpaceLightDir(i.pos));fixed3 H = normalize(L + V);fixed4 ambientdiffuse = getAmbientAndDiffuse(_LightColor0, _DiffuseColor, N, L, i.uv);fixed4 specular = getSpecular(_LightColor0, _PrimaryColor, _PrimaryShift, _SecondaryColor, _SecondaryShift, N, B, V, L, _specPower, i.uv);fixed4 col = (ambientdiffuse + specular);col.a = 1.0f;UNITY_APPLY_FOG(i.fogCoord, col);return col;}ENDCG}}
}