noise/basis: add exp weighted perlin gradient basis

useful for terrain generation

Makefile.am

@@ -150,6 +150,8 @@ UTIL_FILES   =			\
     noise/basis/constant.cpp	\
     noise/basis/constant.hpp	\
     noise/basis/constant.ipp	\
+    noise/basis/expdist.hpp	\
+    noise/basis/expdist.ipp	\
     noise/basis/patch.hpp	\
     noise/basis/patch.ipp	\
     noise/basis/perlin.hpp	\

noise/basis/expgrad.hpp

@@ -0,0 +1,48 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2015 Danny Robson <danny@nerdcruft.net>
+ */
+
+
+#ifndef __UTIL_NOISE_BASIS_EXPGRAD_HPP
+#define __UTIL_NOISE_BASIS_EXPGRAD_HPP
+
+#include "./gradient.hpp"
+
+#include "../fwd.hpp"
+#include "../../point.hpp"
+#include "../../range.hpp"
+
+namespace util { namespace noise { namespace basis {
+    template <typename T, lerp_t<T> L>
+    struct expgrad : public gradient<T,L> {
+        explicit expgrad <T,L> (seed_t seed, T base = (T)1.02, T exponent = T{256});
+
+        T base (void) const;
+        T base (T);
+
+        T exponent (void) const;
+        T exponent (T);
+
+    protected:
+        vector<2,T> generate (point<2,intmax_t>) const;
+
+        T m_base;
+        T m_exponent;
+    };
+} } }
+
+#include "expgrad.ipp"
+
+#endif

noise/basis/expgrad.ipp

@@ -0,0 +1,44 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2012-2015 Danny Robson <danny@nerdcruft.net>
+ */
+
+#ifdef __UTIL_NOISE_BASIS_EXPGRAD_IPP
+#error
+#endif
+#define __UTIL_NOISE_BASIS_EXPGRAD_IPP
+
+#include "../rand.hpp"
+
+
+namespace util { namespace noise { namespace basis {
+    ///////////////////////////////////////////////////////////////////////////
+    template <typename T, util::noise::lerp_t<T> L>
+    expgrad<T,L>::expgrad (seed_t _seed, T _base, T _exponent):
+        gradient<T,L> (_seed),
+        m_base (_base),
+        m_exponent (_exponent)
+    { ; }
+
+
+    ///////////////////////////////////////////////////////////////////////////
+    template <typename T, util::noise::lerp_t<T> L>
+    vector<2,T>
+    expgrad<T,L>::generate (point<2,intmax_t> p) const
+    {
+        auto t = (noise::rand<float> (this->seed (), p) + 1) / 2;
+        auto factor = std::pow (m_base, -t * m_exponent);
+        return factor * gradient<T,L>::generate (p);
+    }
+} } }

noise/basis/gradient.hpp

@@ -0,0 +1,44 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2012-2015 Danny Robson <danny@nerdcruft.net>
+ */
+
+
+#ifndef __UTIL_NOISE_BASIS_GRADIENT_HPP
+#define __UTIL_NOISE_BASIS_GRADIENT_HPP
+
+#include "../fwd.hpp"
+#include "../../point.hpp"
+#include "../../range.hpp"
+
+namespace util { namespace noise { namespace basis {
+    /// Perlin: interpolated value across each grid space
+    template <typename T, lerp_t<T> L>
+    struct gradient {
+        gradient (seed_t);
+
+        seed_t seed (void) const;
+        seed_t seed (seed_t);
+
+    protected:
+        vector<2,T> generate (point<2,intmax_t>) const;
+
+        seed_t m_seed;
+    };
+} } }
+
+#include "gradient.ipp"
+
+#endif
+

noise/basis/gradient.ipp

@@ -0,0 +1,58 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2012-2015 Danny Robson <danny@nerdcruft.net>
+ */
+
+#ifdef __UTIL_NOISE_BASIS_GRADIENT_IPP
+#error
+#endif
+#define __UTIL_NOISE_BASIS_GRADIENT_IPP
+
+#include "../rand.hpp"
+
+namespace util { namespace noise { namespace basis {
+    ///////////////////////////////////////////////////////////////////////////
+    template <typename T, util::noise::lerp_t<T> L>
+    gradient<T,L>::gradient (seed_t _seed):
+        m_seed (_seed)
+    { ; }
+
+
+    //-------------------------------------------------------------------------
+    template <typename T, lerp_t<T> L>
+    seed_t
+    gradient<T,L>::seed (void) const
+    {
+        return m_seed;
+    }
+
+
+    //-------------------------------------------------------------------------
+    template <typename T, lerp_t<T> L>
+    seed_t
+    gradient<T,L>::seed (seed_t _seed)
+    {
+        return m_seed = _seed;
+    }
+
+
+    //-------------------------------------------------------------------------
+    template <typename T, util::noise::lerp_t<T> L>
+    vector<2,T>
+    gradient<T,L>::generate (point<2,intmax_t> p) const
+    {
+        return noise::rand<2,T> (m_seed, p);
+    }
+} } }
+

noise/basis/perlin.hpp

@@ -18,24 +18,27 @@
 #ifndef __UTIL_NOISE_BASIS_PERLIN_HPP
 #define __UTIL_NOISE_BASIS_PERLIN_HPP
 
+#include "./gradient.hpp"
+
 #include "../fwd.hpp"
 #include "../../point.hpp"
 #include "../../range.hpp"
 
 namespace util { namespace noise { namespace basis {
     /// Perlin: interpolated value across each grid space
-    template <typename T, lerp_t<T> L>
+    template <
-    struct perlin {
+        typename T,     // arithmetic and result value_type, must be floating point
+        lerp_t<T> L,    // gradient interpolation function
+        template <      // gradient provider class, must provide generate(point_t)
+            typename,
+            lerp_t<T>
+        > class G = gradient
+    >
+    struct perlin : public G<T,L> {
         perlin (seed_t);
 
         range<T> bounds (void) const;
         T operator() (point<2,T>) const;
-
-        seed_t seed (void) const;
-        seed_t seed (seed_t);
-
-    private:
-        seed_t m_seed;
     };
 } } }
 

noise/basis/perlin.ipp

@@ -23,16 +23,16 @@
 
 namespace util { namespace noise { namespace basis {
     ///////////////////////////////////////////////////////////////////////////
-    template <typename T, util::noise::lerp_t<T> L>
+    template <typename T, util::noise::lerp_t<T> L, template <typename,lerp_t<T>> class G>
-    perlin<T,L>::perlin (seed_t _seed):
+    perlin<T,L,G>::perlin (seed_t _seed):
-        m_seed (_seed)
+        G<T,L> (_seed)
     { ; }
 
 
     //-------------------------------------------------------------------------
-    template <typename T, util::noise::lerp_t<T> L>
+    template <typename T, util::noise::lerp_t<T> L, template <typename,lerp_t<T>> class G>
     util::range<T>
-    perlin<T,L>::bounds (void) const
+    perlin<T,L,G>::bounds (void) const
     {
         return {
             -std::sqrt (T{2}) / 2,
@@ -42,27 +42,9 @@ namespace util { namespace noise { namespace basis {
 
 
     //-------------------------------------------------------------------------
-    template <typename T, lerp_t<T> L>
+    template <typename T, util::noise::lerp_t<T> L, template <typename,lerp_t<T>> class G>
-    seed_t
-    perlin<T,L>::seed (void) const
-    {
-        return m_seed;
-    }
-
-
-    //-------------------------------------------------------------------------
-    template <typename T, lerp_t<T> L>
-    seed_t
-    perlin<T,L>::seed (seed_t _seed)
-    {
-        return m_seed = _seed;
-    }
-
-
-    //-------------------------------------------------------------------------
-    template <typename T, util::noise::lerp_t<T> L>
     T
-    perlin<T,L>::operator() (util::point<2,T> p) const
+    perlin<T,L,G>::operator() (util::point<2,T> p) const
     {
         // extract integer and fractional parts. be careful to always round down
         // (particularly with negatives) and avoid rounding errors.
@@ -78,10 +60,10 @@ namespace util { namespace noise { namespace basis {
         auto p3 = p_int + util::vector<2,intmax_t> { 1, 1 };
 
         // generate the corner gradients
-        auto g0 = noise::rand<2,T> (m_seed, p0);
+        auto g0 = G<T,L>::generate (p0);
-        auto g1 = noise::rand<2,T> (m_seed, p1);
+        auto g1 = G<T,L>::generate (p1);
-        auto g2 = noise::rand<2,T> (m_seed, p2);
+        auto g2 = G<T,L>::generate (p2);
-        auto g3 = noise::rand<2,T> (m_seed, p3);
+        auto g3 = G<T,L>::generate (p3);
 
         // compute the dot products
         T v0 = dot (g0, p - p0);

tools/noise.cpp

@@ -8,6 +8,7 @@
 #include "noise/fractal/runtime.hpp"
 #include "noise/lerp.hpp"
 #include "noise/basis/constant.hpp"
+#include "noise/basis/expgrad.hpp"
 #include "noise/basis/value.hpp"
 #include "noise/basis/patch.hpp"
 #include "noise/basis/perlin.hpp"
@@ -36,7 +37,8 @@ enum basis_t {
     VALUE,
     PERLIN,
     WORLEY,
-    PATCH
+    PATCH,
+    EXPDIST
 };
 
 
@@ -66,10 +68,11 @@ operator>> (std::istream &is, basis_t &b)
     std::string name;
     is >> name;
 
-    b = name == "value"     ? VALUE  :
+    b = name == "value"     ? VALUE     :
-        name == "perlin"    ? PERLIN :
+        name == "perlin"    ? PERLIN    :
-        name == "worley"    ? WORLEY :
+        name == "worley"    ? WORLEY    :
-        name == "patch"     ? PATCH  :
+        name == "patch"     ? PATCH     :
+        name == "expgrad"   ? EXPDIST   :
         (is.setstate (std::istream::failbit), b);
 
     return is;
@@ -81,10 +84,11 @@ std::ostream&
 operator<< (std::ostream &os, basis_t b)
 {
     switch (b) {
-        case VALUE:     os << "value";  return os;
+        case VALUE:     os << "value";      return os;
-        case PERLIN:    os << "perlin"; return os;
+        case PERLIN:    os << "perlin";     return os;
-        case WORLEY:    os << "worley"; return os;
+        case WORLEY:    os << "worley";     return os;
-        case PATCH:     os << "patch";  return os;
+        case PATCH:     os << "patch";      return os;
+        case EXPDIST:   os << "expgrad";    return os;
 
         default:
             unreachable ();
@@ -268,6 +272,20 @@ main (int argc, char **argv)
             break;
         }
 
+        case EXPDIST: {
+            switch (lerp) {
+                case LINEAR:    b.reset<basis::perlin<float,util::lerp::linear,basis::expgrad>> (seed); break;
+                case CUBIC:     b.reset<basis::perlin<float,util::lerp::cubic,basis::expgrad>> (seed);    break;
+                case QUINTIC:   b.reset<basis::perlin<float,util::lerp::quintic,basis::expgrad>> (seed);  break;
+                case COSINE:    b.reset<basis::perlin<float,util::lerp::cosine,basis::expgrad>> (seed);   break;
+                case TRUNC:     b.reset<basis::perlin<float,util::lerp::trunc,basis::expgrad>> (seed);    break;
+
+            default:
+                unreachable ();
+            }
+            break;
+        }
+
         case VALUE: {
             switch (lerp) {
                 case LINEAR:    b.reset<basis::value<float,util::lerp::linear>> (seed); break;