n/fractal: use hurst parameters consistently
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e98709bfc6
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bc1c576297
@ -37,12 +37,14 @@ namespace util { namespace noise { namespace fractal {
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using seed_t = uint64_t;
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static constexpr unsigned DEFAULT_OCTAVES = 8;
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static constexpr T DEFAULT_H = 1;
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static constexpr T DEFAULT_FREQUENCY = T(0.1);
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static constexpr T DEFAULT_LACUNARITY = 2;
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static constexpr T DEFAULT_AMPLITUDE = 1;
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static constexpr T DEFAULT_GAIN = 1 / T(2);
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static constexpr T DEFAULT_GAIN = 1 / DEFAULT_LACUNARITY;
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fbm (unsigned octaves,
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T H,
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T frequency,
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T lacunarity,
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T amplitude,
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@ -52,6 +54,7 @@ namespace util { namespace noise { namespace fractal {
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seed_t seed;
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unsigned octaves;
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T H;
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T frequency;
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T lacunarity;
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@ -61,6 +64,10 @@ namespace util { namespace noise { namespace fractal {
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B basis;
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constexpr T operator() (util::point<2,T>) const;
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private:
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T invAH;
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T invGH;
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};
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} } }
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@ -25,6 +25,7 @@ namespace util { namespace noise { namespace fractal {
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///////////////////////////////////////////////////////////////////////////
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template <typename T, typename B>
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fbm<T,B>::fbm (unsigned _octaves,
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T _H,
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T _frequency,
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T _lacunarity,
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T _amplitude,
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@ -32,11 +33,14 @@ namespace util { namespace noise { namespace fractal {
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seed_t _seed):
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seed (_seed),
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octaves (_octaves),
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H (_H),
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frequency (_frequency),
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lacunarity (_lacunarity),
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amplitude (_amplitude),
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gain (_gain),
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basis (_seed)
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basis (_seed),
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invAH (std::pow (amplitude, -H)),
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invGH (std::pow (gain, H))
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{
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CHECK_NEQ (octaves, 0);
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CHECK_NEQ (frequency, 0);
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@ -48,6 +52,7 @@ namespace util { namespace noise { namespace fractal {
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template <typename T, typename B>
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fbm<T,B>::fbm ():
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fbm<T,B> (DEFAULT_OCTAVES,
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DEFAULT_H,
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DEFAULT_FREQUENCY,
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DEFAULT_LACUNARITY,
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DEFAULT_AMPLITUDE,
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@ -63,13 +68,13 @@ namespace util { namespace noise { namespace fractal {
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{
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T total = 0;
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T f = frequency;
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T a = amplitude;
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T a = invAH;
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for (size_t i = 0; i < octaves; ++i) {
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total += basis (p * f) * a;
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f *= lacunarity;
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a *= gain;
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a *= invGH;
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}
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return total;
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@ -45,6 +45,10 @@ namespace util { namespace noise { namespace fractal {
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B basis;
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constexpr T operator() (util::point<2,T>) const;
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private:
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T invAH;
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T invGH;
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};
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} } }
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@ -29,7 +29,9 @@ namespace util { namespace noise { namespace fractal {
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lacunarity (2),
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offset (0.7f),
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amplitude (1),
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gain (1)
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gain (1/lacunarity),
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invAH (std::pow (amplitude, -H)),
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invGH (std::pow (gain, H))
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{ ; }
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@ -38,20 +40,19 @@ namespace util { namespace noise { namespace fractal {
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constexpr T
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hetero<T,B>::operator() (util::point<2,T> p) const
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{
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T exponents[octaves];
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for (size_t i = 0; i < octaves; ++i)
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exponents[i] = std::pow (std::pow (lacunarity, float (i)), -H);
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T result = 0;
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T increment = 0;
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T scale = invAH;
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p *= frequency;
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result = basis (p) + offset;
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T result = (basis (p) + offset) * scale;
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p *= lacunarity;
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for (size_t i = 0; i < octaves; ++i) {
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T increment = 0;
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for (size_t i = 1; i < octaves; ++i) {
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scale *= invGH;
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increment = basis (p) + offset;
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increment *= exponents[i];
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increment *= scale;
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increment *= result;
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result += increment;
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@ -23,6 +23,7 @@
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namespace util { namespace noise { namespace fractal {
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///////////////////////////////////////////////////////////////////////
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/// Musgrave's "Hybrid MultiFractal"
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template <typename T, typename B>
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struct hmf {
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using seed_t = uint64_t;
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@ -44,7 +45,11 @@ namespace util { namespace noise { namespace fractal {
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B basis;
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constexpr T operator() (util::point<2,T>) const;
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constexpr T operator() (point<2,T>) const;
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private:
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T invAH;
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T invGH;
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};
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} } }
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@ -22,6 +22,7 @@
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namespace util { namespace noise { namespace fractal {
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//-------------------------------------------------------------------------
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// H should be fairly low due to the decreasing weight parameter in eval
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template <typename T, typename B>
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hmf<T,B>::hmf ():
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H (0.25f),
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@ -30,7 +31,9 @@ namespace util { namespace noise { namespace fractal {
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lacunarity (2),
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offset (0.7f),
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amplitude (1),
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gain (1)
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gain (1 / lacunarity),
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invAH (std::pow (amplitude, -H)),
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invGH (std::pow (gain, H))
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{ ; }
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@ -39,9 +42,7 @@ namespace util { namespace noise { namespace fractal {
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constexpr T
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hmf<T,B>::operator() (util::point<2,T> p) const
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{
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T exponents[octaves];
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for (size_t i = 0; i < octaves; ++i)
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exponents[i] = std::pow (std::pow (lacunarity, float (i)), -H);
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T scale = invAH;
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T result = 0;
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T signal = 0;
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@ -50,13 +51,13 @@ namespace util { namespace noise { namespace fractal {
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p *= frequency;
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for (size_t i = 0; i < octaves; ++i) {
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signal = (basis (p) + offset) * exponents[i];
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result += weight * signal;
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signal = (basis (p) + offset) * scale;
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result += signal * weight;
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weight *= gain * signal;
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if (weight > 1)
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weight = 1;
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weight *= signal;
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weight = min (weight, T{1});
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scale *= invGH;
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p *= lacunarity;
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}
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@ -25,19 +25,27 @@ namespace util { namespace noise { namespace fractal {
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/// Rigid Multifractal summation, based on Musgrave's algorithm
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///
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/// octaves: count of layers to be summed
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/// H: hurst parameter (~roughness)
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/// offset: TODO
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/// frequency: point scaling factor for the base octave
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/// lacunarity: per octave frequency scaling factor
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/// lacunarity: incremental octave frequency scaling factor
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/// amplitude: value scaling factor for the base octave
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/// gain: incremental octave value scaling factor
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template <typename T, typename B>
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struct rmf {
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using seed_t = uint64_t;
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static constexpr unsigned DEFAULT_OCTAVES = 5;
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static constexpr T DEFAULT_FREQUENCY = T(1);
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static constexpr T DEFAULT_H = 1;
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static constexpr T DEFAULT_OFFSET = 1;
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static constexpr T DEFAULT_FREQUENCY = 1;
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static constexpr T DEFAULT_LACUNARITY = 2;
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static constexpr T DEFAULT_AMPLITUDE = 1;
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static constexpr T DEFAULT_GAIN = 2;
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static constexpr T DEFAULT_AMPLITUDE = 2;
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static constexpr T DEFAULT_GAIN = 1 / DEFAULT_LACUNARITY;
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rmf (unsigned octaves,
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T H,
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T offset,
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T frequency,
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T lacunarity,
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T amplitude,
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@ -46,7 +54,10 @@ namespace util { namespace noise { namespace fractal {
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rmf ();
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seed_t seed;
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unsigned octaves;
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T H;
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T offset;
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T frequency;
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T lacunarity;
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@ -55,7 +66,12 @@ namespace util { namespace noise { namespace fractal {
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T gain;
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B basis;
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constexpr T operator() (util::point<2,T>) const;
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private:
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T invAH;
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T invGH;
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};
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} } }
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@ -24,6 +24,8 @@ namespace util { namespace noise { namespace fractal {
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///////////////////////////////////////////////////////////////////////////
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template <typename T, typename B>
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rmf<T,B>::rmf (unsigned _octaves,
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T _H,
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T _offset,
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T _frequency,
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T _lacunarity,
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T _amplitude,
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@ -31,11 +33,15 @@ namespace util { namespace noise { namespace fractal {
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seed_t _seed):
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seed (_seed),
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octaves (_octaves),
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H (_H),
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offset (_offset),
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frequency (_frequency),
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lacunarity (_lacunarity),
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amplitude (_amplitude),
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gain (_gain),
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basis (_seed)
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basis (_seed),
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invAH (std::pow (amplitude, -H)),
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invGH (std::pow (gain, H))
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{ ; }
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@ -43,6 +49,8 @@ namespace util { namespace noise { namespace fractal {
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template <typename T, typename B>
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rmf<T,B>::rmf ():
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rmf<T,B> (DEFAULT_OCTAVES,
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DEFAULT_H,
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DEFAULT_OFFSET,
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DEFAULT_FREQUENCY,
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DEFAULT_LACUNARITY,
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DEFAULT_AMPLITUDE,
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@ -52,16 +60,13 @@ namespace util { namespace noise { namespace fractal {
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//-------------------------------------------------------------------------
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// we use the name 'amplitude' instead of musgrave's 'gain'.
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// assumes basis distribution [-1,1] and offset ~= 1
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template <typename T, typename B>
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constexpr T
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rmf<T,B>::operator() (util::point<2,T> p) const
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{
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const T offset = 1;
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const T H = 1.f;
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T exponents[octaves];
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for (size_t i = 0; i < octaves; ++i)
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exponents[i] = std::pow (std::pow (lacunarity, float (i)), -H);
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T scale = invAH;
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T signal = 0;
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T result = 0;
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@ -82,12 +87,13 @@ namespace util { namespace noise { namespace fractal {
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signal *= weight;
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// contribute to the weight
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weight = signal * gain;
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weight = signal * amplitude;
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weight = limit (weight, 0, 1);
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// record and continue
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result += signal * exponents[i];
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result += signal * scale;
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scale *= invGH;
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p *= lacunarity;
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}
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