math: simple Perlin noise for comparison purposes.

src/Makefile.am

@@ -45,7 +45,8 @@ liblolcore_headers = \
     lol/math/geometry.h lol/math/interp.h lol/math/rand.h lol/math/array2d.h \
     lol/math/array3d.h lol/math/constants.h lol/math/matrix.h lol/math/ops.h \
     lol/math/transform.h lol/math/polynomial.h \
-    lol/math/noise/gradient.h lol/math/noise/simplex.h \
+    lol/math/noise/gradient.h lol/math/noise/perlin.h \
+    lol/math/noise/simplex.h \
     \
     lol/algorithm/all.h \
     lol/algorithm/sort.h lol/algorithm/portal.h lol/algorithm/aabb_tree.h \

src/lol/math/all.h

@@ -25,4 +25,6 @@
 #include <lol/math/polynomial.h>
 
 #include <lol/math/noise/gradient.h>
+#include <lol/math/noise/perlin.h>
 #include <lol/math/noise/simplex.h>
+

src/lol/math/noise/perlin.h

@@ -0,0 +1,86 @@
+//
+// Lol Engine
+//
+// Copyright: (c) 2010-2014 Sam Hocevar <sam@hocevar.net>
+//            (c) 2013-2014 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
+//            (c) 2013-2014 Guillaume Bittoun <guillaume.bittoun@gmail.com>
+//   This program is free software; you can redistribute it and/or
+//   modify it under the terms of the Do What The Fuck You Want To
+//   Public License, Version 2, as published by Sam Hocevar. See
+//   http://www.wtfpl.net/ for more details.
+//
+
+#pragma once
+
+#include <lol/math/noise/gradient.h>
+
+namespace lol
+{
+
+template<int N>
+class perlin_noise : public gradient_provider<N>
+{
+public:
+    perlin_noise()
+      : gradient_provider<N>()
+    {
+    }
+
+    perlin_noise(int seed)
+      : gradient_provider<N>(seed)
+    {
+    }
+
+    /* Evaluate noise at a given point */
+    inline float eval(vec_t<float, N> position) const
+    {
+        int const cells = 1 << N;
+
+        /* Retrieve the containing hypercube origin */
+        vec_t<int, N> origin;
+        for (int i = 0; i < N; ++i)
+            origin[i] = (int)position[i] - (position[i] < 0);
+
+        vec_t<float, N> delta = position - (vec_t<float, N>)origin;
+
+        vec_t<float, N> t = delta;
+        /* DEBUG: original Perlin noise polynomial */
+        //t = (vec_t<float, N>(3.f) - 2.f * t) * t * t;
+        /* Improved polynomial (with null second derivative) */
+        t = ((6.f * t - vec_t<float, N>(15.f))
+                  * t + vec_t<float, N>(10.f)) * (t * t * t);
+
+        /* Compute all gradient contributions */
+        array<float> values;
+        values.Resize(cells);
+        for (int i = 0; i < cells; ++i)
+        {
+            /* FIXME: find another way to travel the hypercube that
+             * causes fewer bit flips, and compute the return value
+             * directly without allocating an array value. */
+            vec_t<float, N> v = delta;
+            vec_t<int, N> corner = origin;
+            for (int bit = 0; bit < N; ++bit)
+                if ((1 << bit) & i)
+                {
+                    ++corner[bit];
+                    v[bit] = v[bit] - 1.f;
+                }
+
+            values[i] = dot(v, this->get_gradient(corner));
+        }
+
+        /* Interpolate all contributions together */
+        for (int bit = N; bit--; )
+        {
+            for (int i = 0; i < (1 << bit); ++i)
+                values[i] = (1.f - t[bit]) * values[i]
+                                  + t[bit] * values[i + (1 << bit)];
+        }
+
+        return values[0];
+    }
+};
+
+}
+

src/lol/math/noise/simplex.h

@@ -213,7 +213,7 @@ protected:
     {
         // Finding floor point index
         for (int i = 0; i < N; ++i)
-            origin[i] = ((int)world_position[i]) - (world_position[i] < 0);
+            origin[i] = (int)world_position[i] - (world_position[i] < 0);
 
         // Extracting decimal part from simplex sample
         pos = world_position - (vec_t<float, N>)origin;

src/lolcore.vcxproj

@@ -333,6 +333,7 @@
     <ClInclude Include="lol\math\interp.h" />
     <ClInclude Include="lol\math\matrix.h" />
     <ClInclude Include="lol\math\noise\gradient.h" />
+    <ClInclude Include="lol\math\noise\perlin.h" />
     <ClInclude Include="lol\math\noise\simplex.h" />
     <ClInclude Include="lol\math\ops.h" />
     <ClInclude Include="lol\math\polynomial.h" />

src/lolcore.vcxproj.filters

@@ -456,6 +456,9 @@
     <ClInclude Include="lol\math\noise\gradient.h">
       <Filter>lol\math\noise</Filter>
     </ClInclude>
+    <ClInclude Include="lol\math\noise\perlin.h">
+      <Filter>lol\math\noise</Filter>
+    </ClInclude>
     <ClInclude Include="lol\math\noise\simplex.h">
       <Filter>lol\math\noise</Filter>
     </ClInclude>