Normalise basis values and give expected bounds

noise/basis.cpp

@@ -27,6 +27,7 @@
 #include <algorithm>
 
 using namespace util::noise;
+using util::range;
 
 ///////////////////////////////////////////////////////////////////////////////
 // Generate a type from [-UNIT..UNIT]
@@ -86,6 +87,12 @@ template <lerp_function L>
 { ; }
 
 
+template <lerp_function L>
+range<double>
+value<L>::bounds (void) const
+    { return { -1.0, 1.0 }; }
+
+
 template <lerp_function L>
 double 
 value<L>::eval (double x, double y) const {
@@ -117,11 +124,18 @@ gradient<L>::gradient (seed_t _seed):
     basis (_seed)
 { ; }
 
+
 template <lerp_function L>
 gradient<L>::gradient ()
 { ; }
 
 
+template <lerp_function L>
+range<double>
+gradient<L>::bounds (void) const
+    { return { -sqrt(2.0) / 2.0, sqrt (2.0) / 2.0 }; }
+
+
 template <lerp_function L>
 double 
 gradient<L>::eval (double x, double y) const {
@@ -130,11 +144,13 @@ gradient<L>::eval (double x, double y) const {
     double   x_fac = x - x_int;
     double   y_fac = y - y_int;
 
-    // Generate the four corner values
+    // Generate the four corner values. It's not strictly necessary to
-    vector2 p0 = generate<vector2> (x_int,     y_int,       this->seed);
+    // normalise the values, but we get a more consistent and visually
-    vector2 p1 = generate<vector2> (x_int + 1, y_int,       this->seed);
+    // appealing range of outputs with normalised values.
-    vector2 p2 = generate<vector2> (x_int,     y_int + 1,   this->seed);
+    vector2 p0 = generate<vector2> (x_int,     y_int,       this->seed).normalise ();
-    vector2 p3 = generate<vector2> (x_int + 1, y_int + 1,   this->seed);
+    vector2 p1 = generate<vector2> (x_int + 1, y_int,       this->seed).normalise ();
+    vector2 p2 = generate<vector2> (x_int,     y_int + 1,   this->seed).normalise ();
+    vector2 p3 = generate<vector2> (x_int + 1, y_int + 1,   this->seed).normalise ();
 
     double  v0 = p0.x *        x_fac  + p0.y *  y_fac;
     double  v1 = p1.x * (x_fac - 1.0) + p1.y *  y_fac;
@@ -161,6 +177,11 @@ cellular::cellular ()
 { ; }
 
 
+range<double>
+cellular::bounds (void) const
+    { return { 0.0, sqrt(2) }; }
+
+
 double
 cellular::eval (double x, double y) const {
     using util::point2;

noise/basis.hpp

@@ -22,6 +22,7 @@
 
 #include <cstdlib>
 #include "../lerp.hpp"
+#include "../range.hpp"
 
 namespace util {
     namespace noise {
@@ -35,6 +36,8 @@ namespace util {
             virtual ~basis ();
 
             seed_t seed;
+
+            virtual range<double> bounds (void) const = 0;
             virtual double eval (double x, double y) const = 0;
         };
 
@@ -42,18 +45,24 @@ namespace util {
         template <lerp_function L> struct value : public basis {
             value (seed_t);
             value ();
+
+            virtual range<double> bounds (void) const;
             virtual double eval (double x, double y) const;
         };
 
         template <lerp_function L> struct gradient : public basis {
             gradient (seed_t);
             gradient ();
+
+            virtual range<double> bounds (void) const;
             virtual double eval (double x, double y) const;
         };
 
         struct cellular : public basis {
             cellular (seed_t);
             cellular ();
+
+            virtual range<double> bounds (void) const;
             virtual double eval (double x, double y) const;
         };
     }

noise/fractal.cpp

@@ -58,13 +58,15 @@ double
 util::noise::fbm<B>::eval (double x, double y) const {
     double total = 0.0;
     double f     = this->frequency;
-    double a     = this->lacunarity;
+    double a     = 1.0;
+    double a_sum = 0.0;
 
     for (size_t i = 0; i < this->octaves; ++i) {
         total += basis.eval (x * f, y * f) * a;
-        total  = max (-1.0, min (1.0, total));
 
         f *= 2.0;
+
+        a_sum += a;
         a *= this->lacunarity;
     }