From 45da878e363733457eb9cf838e1d2a4548e0d15e Mon Sep 17 00:00:00 2001
From: Sam Hocevar <sam@hocevar.net>
Date: Thu, 30 Aug 2012 21:52:03 +0000
Subject: [PATCH] tutorial: make the noise shader computationally more
 efficient.

---
 tutorial/03_noise.lolfx | 94 ++++++++++++++++++-----------------------
 1 file changed, 40 insertions(+), 54 deletions(-)

diff --git a/tutorial/03_noise.lolfx b/tutorial/03_noise.lolfx
index 3ad6fd42..ed0d362d 100644
--- a/tutorial/03_noise.lolfx
+++ b/tutorial/03_noise.lolfx
@@ -15,26 +15,17 @@ void main(void)
 
 uniform float u_Time;
 
-vec3 mod289(vec3 x)
+vec4 mod289(vec4 x)
 {
     return x - floor(x * (1.0 / 289.0)) * 289.0;
 }
 
-vec3 perm(vec3 x)
+vec4 perm(vec4 x)
 {
     return mod289(((x * 34.0) + 1.0) * x);
 }
 
-vec4 noise3d(vec3 p1, vec3 p2, vec3 p3, vec3 p4)
-{
-    p1 = perm(perm(perm(p1) + p1.zxy) + p1.yzx);
-    p2 = perm(perm(perm(p2) + p2.zxy) + p2.yzx);
-    p3 = perm(perm(perm(p3) + p3.zxy) + p3.yzx);
-    p4 = perm(perm(perm(p4) + p4.zxy) + p4.yzx);
-    return fract(vec4(p1.x, p2.x, p3.x, p4.x) / 41.0);
-}
-
-float perlin3d(vec3 p)
+float noise3d(vec3 p)
 {
     mat3 r = mat3(0.36, 0.48, -0.8, -0.8, 0.60, 0.0, 0.48, 0.64, 0.60);
     p = r * p;
@@ -43,19 +34,21 @@ float perlin3d(vec3 p)
     vec3 d = p - a;
     d = d * d * (3.0 - 2.0 * d);
 
-    vec4 o1 = noise3d(a,
-                      a + vec3(0.0, 1.0, 0.0),
-                      a + vec3(0.0, 0.0, 1.0),
-                      a + vec3(0.0, 1.0, 1.0));
-    vec4 o2 = noise3d(a + vec3(1.0, 0.0, 0.0),
-                      a + vec3(1.0, 1.0, 0.0),
-                      a + vec3(1.0, 0.0, 1.0),
-                      a + vec3(1.0, 1.0, 1.0));
+    vec4 b = a.xxyy + vec4(0.0, 1.0, 0.0, 1.0);
+    vec4 k1 = perm(b.xyxy);
+    vec4 k2 = perm(k1.xyxy + b.zzww);
+
+    vec4 c = k2 + a.zzzz;
+    vec4 k3 = perm(c);
+    vec4 k4 = perm(c + 1.0);
+
+    vec4 o1 = fract(k3 * (1.0 / 41.0));
+    vec4 o2 = fract(k4 * (1.0 / 41.0));
 
-    vec4 o3 = o2 * d.x + o1 * (1.0 - d.x);
-    vec2 o4 = o3.yw * d.y + o3.xz * (1.0 - d.y);
+    vec4 o3 = o2 * d.z + o1 * (1.0 - d.z);
+    vec2 o4 = o3.yw * d.x + o3.xz * (1.0 - d.x);
 
-    return o4.y * d.z + o4.x * (1.0 - d.z);
+    return o4.y * d.y + o4.x * (1.0 - d.y);
 }
 
 void main(void)
@@ -64,10 +57,10 @@ void main(void)
     xy.y -= u_Time * 400.0;
     float z = u_Time * 2.0;
 
-    float p = perlin3d(vec3(xy / 80.0, z + 1.5)) / 2.0
-            + perlin3d(vec3(xy / 40.0, z + 0.3)) / 4.0
-            + perlin3d(vec3(xy / 20.0, z + 3.3)) / 8.0
-            + perlin3d(vec3(xy / 10.0, z + 2.0)) / 16.0;
+    float p = noise3d(vec3(xy / 80.0, z)) / 2.0
+            + noise3d(vec3(xy / 40.0, z)) / 4.0
+            + noise3d(vec3(xy / 20.0, z)) / 8.0
+            + noise3d(vec3(xy / 10.0, z)) / 16.0;
 
     /* Scroll by adding [-.5,.5] */
     p -= gl_FragCoord.y / 720.0 - 0.5;
@@ -96,26 +89,17 @@ void main(float2 in_Position : POSITION,
 
 -- HLSL.Frag --
 
-float3 mod289(float3 x)
+float4 mod289(float4 x)
 {
     return x - floor(x * (1.0 / 289.0)) * 289.0;
 }
 
-float3 perm(float3 x)
+float4 perm(float4 x)
 {
     return mod289(((x * 34.0) + 1.0) * x);
 }
 
-float4 noise3d(float3 p1, float3 p2, float3 p3, float3 p4)
-{
-    p1 = perm(perm(perm(p1) + p1.zxy) + p1.yzx);
-    p2 = perm(perm(perm(p2) + p2.zxy) + p2.yzx);
-    p3 = perm(perm(perm(p3) + p3.zxy) + p3.yzx);
-    p4 = perm(perm(perm(p4) + p4.zxy) + p4.yzx);
-    return frac(float4(p1.x, p2.x, p3.x, p4.x) / 41.0);
-}
-
-float perlin3d(float3 p)
+float noise3d(float3 p)
 {
     float3x3 r = float3x3(0.36, 0.48, -0.8, -0.8, 0.60, 0.0, 0.48, 0.64, 0.60);
     p = mul(r, p);
@@ -124,19 +108,21 @@ float perlin3d(float3 p)
     float3 d = p - a;
     d = d * d * (3.0 - 2.0 * d);
 
-    float4 o1 = noise3d(a,
-                        a + float3(0.0, 1.0, 0.0),
-                        a + float3(0.0, 0.0, 1.0),
-                        a + float3(0.0, 1.0, 1.0));
-    float4 o2 = noise3d(a + float3(1.0, 0.0, 0.0),
-                        a + float3(1.0, 1.0, 0.0),
-                        a + float3(1.0, 0.0, 1.0),
-                        a + float3(1.0, 1.0, 1.0));
+    float4 b = a.xxyy + float4(0.0, 1.0, 0.0, 1.0);
+    float4 k1 = perm(b.xyxy);
+    float4 k2 = perm(k1.xyxy + b.zzww);
+
+    float4 c = k2 + a.zzzz;
+    float4 k3 = perm(c);
+    float4 k4 = perm(c + 1.0);
+
+    float4 o1 = frac(k3 * (1.0 / 41.0));
+    float4 o2 = frac(k4 * (1.0 / 41.0));
 
-    float4 o3 = o2 * d.x + o1 * (1.0 - d.x);
-    float2 o4 = o3.yw * d.y + o3.xz * (1.0 - d.y);
+    float4 o3 = o2 * d.z + o1 * (1.0 - d.z);
+    float2 o4 = o3.yw * d.x + o3.xz * (1.0 - d.x);
 
-    return o4.y * d.z + o4.x * (1.0 - d.z);
+    return o4.y * d.y + o4.x * (1.0 - d.y);
 }
 
 void main(in float2 pass_Position : TEXCOORD0,
@@ -147,10 +133,10 @@ void main(in float2 pass_Position : TEXCOORD0,
     xy.y -= u_Time * 400.0;
     float z = u_Time * 2.0;
 
-    float p = perlin3d(float3(xy / 80.0, z + 1.5)) / 2.0
-            + perlin3d(float3(xy / 40.0, z + 0.3)) / 4.0
-            + perlin3d(float3(xy / 20.0, z + 3.3)) / 8.0
-            + perlin3d(float3(xy / 10.0, z + 2.0)) / 16.0;
+    float p = noise3d(float3(xy / 80.0, z)) / 2.0
+            + noise3d(float3(xy / 40.0, z)) / 4.0
+            + noise3d(float3(xy / 20.0, z)) / 8.0
+            + noise3d(float3(xy / 10.0, z)) / 16.0;
 
     /* Scroll by adding [-.5,.5] */
     p -= pass_Position.y / 1440.0;