Fix normal calculation in displacement shader

Recompute normals after generating the deformed mesh. Unfortunately,
significant anti-aliasing is required to get the generated normals to
look smooth in motion.

* Enable backface culling.

4 files changed, 86 insertions, 27 deletions

diff --git a/Demos/displacement_demo.gif b/Demos/displacement_demo.gif
index 90ba0d0..951b01f 100644
--- a/Demos/displacement_demo.gif
+++ b/Demos/displacement_demo.gif
diff --git a/Shaders/displacement/displacement.shader b/Shaders/displacement/displacement.shader
index 6a47853..5c0b517 100644
--- a/Shaders/displacement/displacement.shader
+++ b/Shaders/displacement/displacement.shader
@@ -4,8 +4,8 @@ Shader "yum_food/displacement"
   {
     _BaseColor("Base color", 2D) = "white" {}
     _Normal("Normal", 2D) = "bump" {}
-    _Disable_Normal_Texture("Disable normal texture", float) = 0.0
-    _Metallic("Metallic", 2D) = "black" {}
+    _Disable_Normal_Texture("Disable normal texture", float) = 1.0
+    _Metallic("Metallic", 2D) = "white" {}
     _Roughness("Roughness", 2D) = "black" {}
 		_Cubemap("Cubemap", Cube) = "" {}
 
@@ -36,7 +36,7 @@ Shader "yum_food/displacement"
       Blend SrcAlpha OneMinusSrcAlpha
       ZWrite On
       ZTest LEqual
-      Cull Off
+      Cull Back
 
       CGPROGRAM
       #pragma target 5.0
@@ -53,7 +53,7 @@ Shader "yum_food/displacement"
       // 0: no anti-aliasing
       // 1: sample 4 neighbors (diagonals)
       // 2: sample 8 neighbors (diagonals + cartesian)
-      #define OFFSET_AA_LEVEL 2
+      #define HEIGHT_AA_LEVEL 2
 
       #include "displacement_lighting.cginc"
       ENDCG
@@ -67,7 +67,7 @@ Shader "yum_food/displacement"
       Blend One One
       ZWrite On
       ZTest LEqual
-      Cull Off
+      Cull Back
 
       CGPROGRAM
       #pragma target 5.0
@@ -78,7 +78,7 @@ Shader "yum_food/displacement"
       #pragma geometry geom
       #pragma fragment frag
 
-      #define OFFSET_AA_LEVEL 2
+      #define HEIGHT_AA_LEVEL 2
 
       #include "displacement_lighting.cginc"
       ENDCG
diff --git a/Shaders/displacement/displacement_lighting.cginc b/Shaders/displacement/displacement_lighting.cginc
index d0abdb9..3a5e04b 100644
--- a/Shaders/displacement/displacement_lighting.cginc
+++ b/Shaders/displacement/displacement_lighting.cginc
@@ -80,12 +80,12 @@ v2f vert(appdata v)
   return o;
 }
 
-void displace(inout v2f vert)
+float getDisplacement(float2 uv)
 {
   // Manipulate vertex in world space.
   float height = 0;
 
-  float2 traveling_uv = vert.uv;
+  float2 traveling_uv = uv;
   traveling_uv.x += _Time[0] * _Height_Speed_X;
   traveling_uv.y += _Time[0] * _Height_Speed_Y;
   traveling_uv = glsl_mod(traveling_uv, 1.0);
@@ -93,24 +93,24 @@ void displace(inout v2f vert)
   const float duv = _Height_AA_Sample_Scale;
 
   float z0 = tex2Dlod(_Height, float4(traveling_uv.x, traveling_uv.y, _Height_LOD, 0));
-  #if OFFSET_AA_LEVEL >= 1
+  #if HEIGHT_AA_LEVEL >= 1
   float z1 = tex2Dlod(_Height, float4(traveling_uv.x + duv, traveling_uv.y + duv, _Height_LOD, 0));
   float z2 = tex2Dlod(_Height, float4(traveling_uv.x + duv, traveling_uv.y - duv, _Height_LOD, 0));
   float z3 = tex2Dlod(_Height, float4(traveling_uv.x - duv, traveling_uv.y - duv, _Height_LOD, 0));
   float z4 = tex2Dlod(_Height, float4(traveling_uv.x - duv, traveling_uv.y + duv, _Height_LOD, 0));
   #endif
-  #if OFFSET_AA_LEVEL >= 2
+  #if HEIGHT_AA_LEVEL >= 2
   float z5 = tex2Dlod(_Height, float4(traveling_uv.x + duv, traveling_uv.y, _Height_LOD, 0));
   float z6 = tex2Dlod(_Height, float4(traveling_uv.x - duv, traveling_uv.y, _Height_LOD, 0));
   float z7 = tex2Dlod(_Height, float4(traveling_uv.x, traveling_uv.y + duv, _Height_LOD, 0));
   float z8 = tex2Dlod(_Height, float4(traveling_uv.x, traveling_uv.y - duv, _Height_LOD, 0));
   #endif
 
-  #if OFFSET_AA_LEVEL == 0
+  #if HEIGHT_AA_LEVEL == 0
   height += z0;
-  #elif OFFSET_AA_LEVEL == 1
+  #elif HEIGHT_AA_LEVEL == 1
   height += (z0 + z1 + z2 + z3 + z4) / 5.0;
-  #elif OFFSET_AA_LEVEL == 2
+  #elif HEIGHT_AA_LEVEL == 2
   height += (z0 + z1 + z2 + z3 + z4 + z5 + z6 + z7 + z8) / 9.0;
   #endif
 
@@ -118,14 +118,14 @@ void displace(inout v2f vert)
   height *= _Height_Scale;
 
   {
-    float mask = tex2Dlod(_Height_Mask, float4(vert.uv, _Height_LOD, 0));
+    float mask = tex2Dlod(_Height_Mask, float4(uv, _Height_LOD, 0));
     mask = pow(mask, _Height_Mask_Exponent);
     height *= mask;
   }
   
   // 0 at middle, 1 or -1 at edges
   if (_Center_Out_Speed > 0.0) {
-    float2 middle_out_uv = vert.uv * 2.0 - 1.0;
+    float2 middle_out_uv = uv * 2.0 - 1.0;
 
     float center_dist2 = length2(middle_out_uv);
     float ring_radius = fmod(_Time[1] * _Center_Out_Speed,
@@ -140,11 +140,46 @@ void displace(inout v2f vert)
     height *= middle_out_height;
   }
 
+  return height;
+}
+
+void displace(inout v2f vert)
+{
+  float height = getDisplacement(vert.uv);
+
   vert.worldPos += height * vert.normal;
   vert.objPos = mul(unity_WorldToObject, float4(vert.worldPos, 1.0));
   vert.clipPos = UnityObjectToClipPos(vert.objPos);
 }
 
+float3 getNormal(
+    v2f v0,
+    v2f v1,
+    v2f v2,
+    float duv_scale) {
+  float2 duv_v0v1 = v1.uv - v0.uv;
+  float2 duv_v0v2 = v2.uv - v0.uv;
+
+  float h0 = getDisplacement(v0.uv);
+  float h1 = getDisplacement(v0.uv + duv_v0v1 * duv_scale);
+  float h2 = getDisplacement(v0.uv + duv_v0v2 * duv_scale);
+
+  float dh_v0v1 = h1 - h0;
+  float dh_v0v2 = h2 - h0;
+
+  float3 dpos_v0v1 = v1.worldPos - v0.worldPos;
+  float3 dpos_v0v2 = v2.worldPos - v0.worldPos;
+
+  float3 p0 = v0.worldPos + h0 * v0.normal;
+  float3 p1 = v0.worldPos + dpos_v0v1 * duv_scale + lerp(h0, h1, duv_scale) * v1.normal;
+  float3 p2 = v0.worldPos + dpos_v0v2 * duv_scale + lerp(h0, h2, duv_scale) * v2.normal;
+
+  float3 tangent = normalize(p1 - p0);
+  float3 bitangent = normalize(p2 - p0);
+  float3 new_normal = normalize(cross(tangent, bitangent));
+  return new_normal;
+}
+
 // maxvertexcount == the number of vertices we create
 [maxvertexcount(3)]
 void geom(triangle v2f tri_in[3],
@@ -153,17 +188,41 @@ void geom(triangle v2f tri_in[3],
 {
   float dx = 0.5;
 
-  v2f cur = tri_in[0];
-  displace(cur);
-  tri_out.Append(cur);
-
-  cur = tri_in[1];
-  displace(cur);
-  tri_out.Append(cur);
+  v2f t0 = tri_in[0];
+  v2f t1 = tri_in[1];
+  v2f t2 = tri_in[2];
+
+  displace(t0);
+  displace(t1);
+  displace(t2);
+
+  // Math from here:
+  //   http://tonfilm.blogspot.com/2007/01/calculate-normals-in-shader.html
+  for (int i = 0; i < 3; i++) {
+    v2f v0 = tri_in[(i + 0) % 3];
+    v2f v1 = tri_in[(i + 1) % 3];
+    v2f v2 = tri_in[(i + 2) % 3];
+
+    float3 aa_normal = 0;
+    aa_normal += getNormal(v0, v1, v2, 0.3);
+    aa_normal += getNormal(v0, v1, v2, 0.4);
+    aa_normal += getNormal(v0, v1, v2, 0.5);
+    aa_normal += getNormal(v0, v1, v2, 0.6);
+    aa_normal += getNormal(v0, v1, v2, 0.7);
+    aa_normal = normalize(aa_normal);
+
+    if (i == 0) {
+      t0.normal = aa_normal;
+    } else if (i == 1) {
+      t1.normal = aa_normal;
+    } else if (i == 2) {
+      t2.normal = aa_normal;
+    }
+  }
 
-  cur = tri_in[2];
-  displace(cur);
-  tri_out.Append(cur);
+  tri_out.Append(t0);
+  tri_out.Append(t1);
+  tri_out.Append(t2);
 
   tri_out.RestartStrip();
 }
@@ -185,10 +244,9 @@ float4 effect(inout v2f i, out float depth)
   if (albedo.a > 0) {
     depth = getWorldSpaceDepth(i.worldPos);
   }
+
   return getLitColor(i, albedo, i.worldPos, normal, metallic, 1.0 - roughness,
       /*custom_cubemap=*/true);
-
-  return 1;
 }
 
 fixed4 frag(v2f i, out float depth : SV_DepthLessEqual) : SV_Target
diff --git a/Shaders/displacement/pbr.cginc b/Shaders/displacement/pbr.cginc
index e552bcc..690f547 100644
--- a/Shaders/displacement/pbr.cginc
+++ b/Shaders/displacement/pbr.cginc
@@ -12,6 +12,7 @@ struct v2f
   float2 uv : TEXCOORD0;
   float3 normal : TEXCOORD1;
   float3 worldPos : TEXCOORD2;
+
   float3 objPos : TEXCOORD3;
 
   #if defined(VERTEXLIGHT_ON)