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noise: support n-dimensional noise

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This commit is contained in:
Danny Robson 2015-10-06 15:45:26 +11:00
parent 29c6c50fda
commit e80e445645
39 changed files with 711 additions and 500 deletions
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4
Makefile.am
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@ -158,6 +158,10 @@ UTIL_FILES = \
noise/basis/perlin.ipp \
noise/basis/runtime.cpp \
noise/basis/runtime.hpp \
noise/basis/type/distance.cpp \
noise/basis/type/distance.hpp \
noise/basis/type/gradient.hpp \
noise/basis/type/gradient.cpp \
noise/basis/value.hpp \
noise/basis/value.ipp \
noise/basis/worley.hpp \

13
noise/basis/constant.cpp
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@ -19,14 +19,17 @@
using util::noise::basis::constant;
//-----------------------------------------------------------------------------
template <typename T>
constant<T>::constant (seed_t _seed):
///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
constant<S,T>::constant (seed_t _seed):
seed (_seed),
value (42)
{ ; }
///////////////////////////////////////////////////////////////////////////////
template struct util::noise::basis::constant<float>;
template struct util::noise::basis::constant<double>;
template struct util::noise::basis::constant<2,float>;
template struct util::noise::basis::constant<2,double>;
template struct util::noise::basis::constant<3,float>;
template struct util::noise::basis::constant<3,double>;

5
noise/basis/constant.hpp
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@ -22,12 +22,13 @@
#include <cstdint>
namespace util { namespace noise { namespace basis {
template <typename T>
template <size_t S, typename T>
struct constant {
using seed_t = uint64_t;
constant (seed_t);
T operator() (util::point<2,T>) const;
T operator() (point<S,T>) const;
seed_t seed;
T value;

4
noise/basis/constant.ipp
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@ -20,9 +20,9 @@
#define __UTIL_NOISE_BASIS_CONSTANT_IPP
namespace util { namespace noise { namespace basis {
template <typename T>
template <size_t S, typename T>
T
constant<T>::operator() (util::point<2,T>) const
constant<S,T>::operator() (point<S,T>) const
{
return value;
}

20
noise/basis/expgrad.hpp
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@ -24,10 +24,22 @@
#include "../../point.hpp"
#include "../../range.hpp"
///////////////////////////////////////////////////////////////////////////////
// modifies a standard uniforma gradient generator to follow an exponential
// distribution, base^(-t*exp)
//
//
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});
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
lerp_t<T> L // axis interpolation function
>
struct expgrad : public gradient<S,T,L> {
explicit expgrad (seed_t seed,
T base = (T)1.02,
T exponent = T{256});
T base (void) const;
T base (T);
@ -36,7 +48,7 @@ namespace util { namespace noise { namespace basis {
T exponent (T);
protected:
vector<2,T> generate (point<2,intmax_t>) const;
vector<S,T> generate (pointi<S>) const;
T m_base;
T m_exponent;

15
noise/basis/expgrad.ipp
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@ -24,21 +24,22 @@
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),
template <size_t S, typename T, util::noise::lerp_t<T> L
>
expgrad<S,T,L>::expgrad (seed_t _seed, T _base, T _exponent):
gradient<S,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
template <size_t S, typename T, util::noise::lerp_t<T> L>
vector<S,T>
expgrad<S,T,L>::generate (pointi<S> 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);
return factor * gradient<S,T,L>::generate (p);
}
} } }

8
noise/basis/gradient.hpp
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@ -24,7 +24,11 @@
namespace util { namespace noise { namespace basis {
/// Perlin: interpolated value across each grid space
template <typename T, lerp_t<T> L>
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
lerp_t<T> L // axis interpolation function
>
struct gradient {
gradient (seed_t);
@ -32,7 +36,7 @@ namespace util { namespace noise { namespace basis {
seed_t seed (seed_t);
protected:
vector<2,T> generate (point<2,intmax_t>) const;
vector<S,T> generate (pointi<S>) const;
seed_t m_seed;
};

20
noise/basis/gradient.ipp
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@ -23,36 +23,36 @@
namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T, util::noise::lerp_t<T> L>
gradient<T,L>::gradient (seed_t _seed):
template <size_t S, typename T, util::noise::lerp_t<T> L>
gradient<S,T,L>::gradient (seed_t _seed):
m_seed (_seed)
{ ; }
//-------------------------------------------------------------------------
template <typename T, lerp_t<T> L>
template <size_t S, typename T, lerp_t<T> L>
seed_t
gradient<T,L>::seed (void) const
gradient<S,T,L>::seed (void) const
{
return m_seed;
}
//-------------------------------------------------------------------------
template <typename T, lerp_t<T> L>
template <size_t S, typename T, lerp_t<T> L>
seed_t
gradient<T,L>::seed (seed_t _seed)
gradient<S,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
template <size_t S, typename T, util::noise::lerp_t<T> L>
vector<S,T>
gradient<S,T,L>::generate (pointi<S> p) const
{
return noise::rand<2,T> (m_seed, p);
return noise::rand<vector,T> (m_seed, p);
}
} } }

12
noise/basis/patch.hpp
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@ -17,16 +17,19 @@
#ifndef __UTIL_NOISE_BASIS_PATCH_HPP
#define __UTIL_NOISE_BASIS_PATCH_HPP
#include "./type/distance.hpp"
#include "../fwd.hpp"
#include "../../point.hpp"
namespace util { namespace noise { namespace basis {
template <typename T>
struct patch {
template <size_t S, typename T>
struct patch : public type::distance<S,2> {
patch (seed_t, T width = 0);
range<T> bounds (void) const;
T operator() (point2<T>) const;
T operator() (point<S,T>) const;
seed_t seed (void) const;
seed_t seed (seed_t);
@ -35,9 +38,6 @@ namespace util { namespace noise { namespace basis {
T width (T);
private:
point2<T> centroid (util::point2i) const;
T generate (util::point2i) const;
static constexpr T THRESHOLD = 1 - T(0.999);
T m_width;

112
noise/basis/patch.ipp
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@ -26,8 +26,8 @@
namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T>
patch<T>::patch (seed_t _seed, T _width):
template <size_t S, typename T>
patch<S,T>::patch (seed_t _seed, T _width):
m_width (_width),
m_power (exactly_zero (_width)
? std::numeric_limits<T>::infinity ()
@ -37,58 +37,56 @@ namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T>
template <size_t S, typename T>
range<T>
patch<T>::bounds (void) const
patch<S,T>::bounds (void) const
{
return { T{0}, T{1} };
}
///////////////////////////////////////////////////////////////////////////
template <typename T>
template <size_t S, typename T>
T
patch<T>::operator () (point2<T> p) const
patch<S,T>::operator () (point<S,T> p) const
{
static const size_t COUNT = type::distance<S,2>::OFFSET_SIZE;
// extract integer and fractional parts. be careful to always round down
auto p_int = floor (p).template cast<intmax_t> ();
auto p_rem = (p - p_int).template as<point> ();
static const util::vector2i OFFSETS[] = {
{ 0, -2 },
{ -1, -1 }, { 0, -1 }, { 1, -1 },
{ -2, 0 }, { -1, 0 }, { 0, 0 }, { 1, 0 }, { 2, 0 },
{ -1, 1 }, { 0, 1 }, { 1, 1 },
{ 0, 2 },
};
static const size_t COUNT = elems (OFFSETS);
// find the distances to each neighbour's centroid
util::point2<T> centres[COUNT];
for (size_t i = 0; i < COUNT; ++i)
centres[i] = centroid (p_int + OFFSETS[i]) + OFFSETS[i];
// find the distances to each neighbour's centroid.
util::point<S,T> centres[COUNT];
std::transform (std::begin (this->OFFSETS),
std::end (this->OFFSETS),
std::begin (centres),
[this,p_int] (auto i) { return (noise::rand<point,T> (m_seed, p_int + i) + 1) / 2 + i; });
T distances[COUNT];
for (size_t i = 0; i < COUNT; ++i)
distances[i] = std::sqrt (util::distance2 (p_rem, centres[i]));
std::transform (std::begin (centres),
std::end (centres),
std::begin (distances),
[p_rem] (auto i) { return util::distance (p_rem, i); });
// sort the distances, using indices so we can use 'offsets' to generate values
// sort the distances using indices so we can reuse indices into
// 'OFFSETS' to generate the random patch values
unsigned indices[COUNT];
std::iota (std::begin (indices), std::end (indices), 0);
std::sort (std::begin (indices),
std::end (indices),
std::end (indices),
[&] (auto a, auto b) {
return distances[a] < distances[b];
});
// calculate normalisation constants for the 9 nearest points. the
// setup normalisation for the distances to the nearest points. the
// neighbourhood size is implicitly specified by the 1.5 unit maximum
// distance.
constexpr auto MAX_DISTANCE = 2.1213203435596424f; // std::hypot (1.5f, 1.5f);
const auto lo = distances[indices[0]];
const auto hi = std::min (distances[indices[COUNT-1]], MAX_DISTANCE);
const size_t hi_off = pow(3,S);
const auto lo = distances[indices[0 ]];
const auto hi = distances[indices[hi_off]];
T out = 0.f;
T sumw = 0.f;
@ -96,11 +94,15 @@ namespace util { namespace noise { namespace basis {
// sum the weight values of each neighbour. weight by a function of
// the distance. we use an power function which allows a known width
// to blend.
for (size_t i = 0; i < COUNT && distances[indices[i]] <= MAX_DISTANCE; ++i)
for (size_t i = 0; i < hi_off; ++i)
{
auto v = generate (p_int + OFFSETS[indices[i]]);
auto v = util::noise::rand<T> (
m_seed,
p_int + this->OFFSETS[indices[i]]
);
auto d = (distances[indices[i]] - lo) / (hi - lo);
auto w = std::pow (1-d, m_power);
auto w = std::pow (1 - d, m_power);
sumw += w;
out += v * w;
@ -111,36 +113,36 @@ namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T>
template <size_t S, typename T>
seed_t
patch<T>::seed (void) const
patch<S,T>::seed (void) const
{
return m_seed;
}
//-------------------------------------------------------------------------
template <typename T>
template <size_t S, typename T>
seed_t
patch<T>::seed (util::noise::seed_t _seed)
patch<S,T>::seed (util::noise::seed_t _seed)
{
return m_seed = _seed;
}
///////////////////////////////////////////////////////////////////////////
template <typename T>
template <size_t S, typename T>
T
patch<T>::width (void) const
patch<S,T>::width (void) const
{
return m_width;
}
//-------------------------------------------------------------------------
template <typename T>
template <size_t S, typename T>
T
patch<T>::width (T _width)
patch<S,T>::width (T _width)
{
m_width = _width;
m_power = exactly_zero (_width)
@ -149,36 +151,4 @@ namespace util { namespace noise { namespace basis {
return m_width;
}
///////////////////////////////////////////////////////////////////////////
template <typename T>
util::point2<T>
patch<T>::centroid (util::point2i p) const
{
using util::hash::murmur2::mix;
auto u = mix (m_seed, mix (uint64_t (p.x), uint64_t (p.y)));
auto v = mix (u, m_seed);
auto r = util::point<2,T> {
(u & 0xffff) / T{0xffff},
(v & 0xffff) / T{0xffff}
};
CHECK_LIMIT (r, T{0}, T{1});
return r;
}
//-------------------------------------------------------------------------
template <typename T>
T
patch<T>::generate (util::point2i p) const
{
using util::hash::murmur2::mix;
auto u = mix (m_seed, mix (uint64_t (p.x), uint64_t (p.y)));
return (u & 0xffff) / T{0xffff};
}
} } }

8
noise/basis/perlin.hpp
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@ -19,6 +19,7 @@
#define __UTIL_NOISE_BASIS_PERLIN_HPP
#include "./gradient.hpp"
#include "./type/gradient.hpp"
#include "../fwd.hpp"
#include "../../point.hpp"
@ -27,18 +28,21 @@
namespace util { namespace noise { namespace basis {
/// Perlin: interpolated value across each grid space
template <
size_t S, // point point dimensionality
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)
size_t,
typename,
lerp_t<T>
> class G = gradient
>
struct perlin : public G<T,L> {
struct perlin : public G<S,T,L>, public type::gradient<S> {
perlin (seed_t);
range<T> bounds (void) const;
T operator() (point<2,T>) const;
T operator() (point<S,T>) const;
};
} } }

49
noise/basis/perlin.ipp
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@ -20,19 +20,21 @@
#define __UTIL_NOISE_BASIS_PERLIN_IPP
#include "../rand.hpp"
#include "../../types.hpp"
namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T, util::noise::lerp_t<T> L, template <typename,lerp_t<T>> class G>
perlin<T,L,G>::perlin (seed_t _seed):
G<T,L> (_seed)
template <size_t S, typename T, util::noise::lerp_t<T> L, template <size_t,typename,lerp_t<T>> class G>
perlin<S,T,L,G>::perlin (seed_t _seed):
G<S,T,L> (_seed)
{ ; }
//-------------------------------------------------------------------------
template <typename T, util::noise::lerp_t<T> L, template <typename,lerp_t<T>> class G>
template <size_t S, typename T, util::noise::lerp_t<T> L, template <size_t,typename,lerp_t<T>> class G>
util::range<T>
perlin<T,L,G>::bounds (void) const
perlin<S,T,L,G>::bounds (void) const
{
return {
-std::sqrt (T{2}) / 2,
@ -42,37 +44,38 @@ namespace util { namespace noise { namespace basis {
//-------------------------------------------------------------------------
template <typename T, util::noise::lerp_t<T> L, template <typename,lerp_t<T>> class G>
template <size_t S, typename T, util::noise::lerp_t<T> L, template <size_t,typename,lerp_t<T>> class G>
T
perlin<T,L,G>::operator() (util::point<2,T> p) const
perlin<S,T,L,G>::operator() (util::point<S,T> p) const
{
// extract integer and fractional parts. be careful to always round down
auto p_int = floor (p).template cast<intmax_t> ();
auto p_rem = p - p_int;
// generate the corner positions
auto p0 = p_int + util::vector<2,intmax_t> { 0, 0 };
auto p1 = p_int + util::vector<2,intmax_t> { 1, 0 };
auto p2 = p_int + util::vector<2,intmax_t> { 0, 1 };
auto p3 = p_int + util::vector<2,intmax_t> { 1, 1 };
pointi<S> p_[pow(2,S)];
std::transform (std::begin (this->CORNERS), std::end (this->CORNERS),
std::begin (p_),
[p_int] (auto i) { return i + p_int; });
// generate the corner gradients
auto g0 = G<T,L>::generate (p0);
auto g1 = G<T,L>::generate (p1);
auto g2 = G<T,L>::generate (p2);
auto g3 = G<T,L>::generate (p3);
vector<S,T> g_[pow(2,S)];
std::transform (std::begin (p_), std::end (p_),
std::begin (g_),
[this] (auto i) { return this->generate (i); });
// compute the dot products
T v0 = dot (g0, p - p0);
T v1 = dot (g1, p - p1);
T v2 = dot (g2, p - p2);
T v3 = dot (g3, p - p3);
T v_[pow(2,S)];
for (size_t i = 0; i < elems (v_); ++i)
v_[i] = dot (g_[i], p - p_[i]);
// interpolate the results
auto L0 = L (v0, v1, p_rem.x);
auto L1 = L (v2, v3, p_rem.x);
auto L_ = L (L0, L1, p_rem.y);
T l_[pow(2,S)];
std::copy (std::begin (v_), std::end (v_), std::begin (l_));
return L_;
for (size_t i = S; i; --i)
for (size_t j = 0; j < std::pow(2,i); j += 2)
l_[j / 2] = L (l_[j], l_[j+1], p_rem[S-i]);
return l_[0];
}
} } }

2
noise/basis/runtime.cpp
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@ -17,4 +17,4 @@
#include "runtime.hpp"
template struct util::noise::basis::runtime<float>;
template struct util::noise::basis::runtime<2,float>;

8
noise/basis/runtime.hpp
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@ -25,7 +25,7 @@
#include <memory>
namespace util { namespace noise { namespace basis {
template <typename T>
template <size_t S, typename T>
struct runtime {
public:
runtime (seed_t) {}
@ -34,7 +34,7 @@ namespace util { namespace noise { namespace basis {
runtime& operator= (const runtime&) = delete;
// basis functions
T operator () (util::point<2,T> p) const { return (*m_child) (p); }
T operator () (util::point<S,T> p) const { return (*m_child) (p); }
range<T> bounds (void) const { return m_child->bounds (); }
seed_t seed (void) const { return m_child->seed (); }
@ -43,7 +43,7 @@ namespace util { namespace noise { namespace basis {
private:
struct base {
virtual ~base () = default;
virtual T operator() (util::point<2,T>) const = 0;
virtual T operator() (util::point<S,T>) const = 0;
virtual range<T> bounds (void) const = 0;
virtual seed_t seed (void) const = 0;
virtual seed_t seed (seed_t) = 0;
@ -53,7 +53,7 @@ namespace util { namespace noise { namespace basis {
struct child : public base {
template <typename ...Args>
child (seed_t _seed, Args&& ...args): data (_seed, std::forward<Args> (args)...) { }
virtual T operator() (util::point<2,T> p) const override { return data (p); }
virtual T operator() (util::point<S,T> p) const override { return data (p); }
virtual range<T> bounds (void) const override { return data.bounds (); }
virtual seed_t seed (void) const override { return data.seed (); }
virtual seed_t seed (seed_t _seed) override { return data.seed (_seed); }

43
noise/basis/type/distance.cpp Normal file
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@ -0,0 +1,43 @@
#include "./distance.hpp"
#include "../../../extent.hpp"
///////////////////////////////////////////////////////////////////////////////
template <size_t S, size_t R>
static const std::array<util::vectori<S>, util::pow(R*2+1,S)>
generate (void)
{
static const util::extent_range<
S,typename util::vectori<S>::value_type
> area (util::extent<S,typename util::vectori<S>::value_type> {R*2+1});
std::array<
util::vectori<S>,
util::pow(R*2+1,S)
> out;
std::transform (area.begin (), area.end (),
out.begin (),
[] (auto i) { return i.template as<util::vector> () - R; });
return out;
}
///////////////////////////////////////////////////////////////////////////////
template <size_t S, size_t R>
const std::array<
util::vectori<S>,
util::pow(R*2+1,S)
>
util::noise::basis::type::distance<S,R>::OFFSETS = generate<S,R> ();
//-----------------------------------------------------------------------------
template struct util::noise::basis::type::distance<1,1>;
template struct util::noise::basis::type::distance<2,1>;
template struct util::noise::basis::type::distance<3,1>;
template struct util::noise::basis::type::distance<1,2>;
template struct util::noise::basis::type::distance<2,2>;
template struct util::noise::basis::type::distance<3,2>;

22
noise/basis/type/distance.hpp Normal file
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@ -0,0 +1,22 @@
#ifndef __UTIL_NOISE_BASIS_TYPE_HPP
#define __UTIL_NOISE_BASIS_TYPE_HPP
#include "../../../vector.hpp"
#include "../../../maths.hpp"
#include <array>
namespace util { namespace noise { namespace basis { namespace type {
template <size_t S, size_t R>
struct distance {
protected:
static constexpr size_t OFFSET_SIZE = util::pow(R*2+1,S);
static const std::array<
vectori<S>, util::pow(R*2+1,S)
> OFFSETS;
};
} } } }
#endif

44
noise/basis/type/gradient.cpp Normal file
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@ -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 2015 Danny Robson <danny@nerdcruft.net>
*/
#include "./gradient.hpp"
///////////////////////////////////////////////////////////////////////////////
template <size_t S>
static std::array<util::vectori<S>,util::pow(2,S)>
generate (void)
{
std::array<util::vectori<S>,util::pow(2,S)> out;
for (size_t i = 0; i < util::pow(2,S); ++i)
for (size_t s = 0; s < S; ++s)
out[i][s] = (i >> s) & 1;
return out;
}
///////////////////////////////////////////////////////////////////////////////
template <size_t S>
const std::array<util::vectori<S>,util::pow(2,S)>
util::noise::basis::type::gradient<S>::CORNERS = generate<S> ();
//-----------------------------------------------------------------------------
template struct util::noise::basis::type::gradient<1>;
template struct util::noise::basis::type::gradient<2>;
template struct util::noise::basis::type::gradient<3>;
template struct util::noise::basis::type::gradient<4>;

36
noise/basis/type/gradient.hpp Normal file
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@ -0,0 +1,36 @@
/*
* 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_TYPE_GRADIENT_HPP
#define __UTIL_NOISE_BASIS_TYPE_GRADIENT_HPP
#include "../../../point.hpp"
#include "../../../maths.hpp"
#include <array>
///////////////////////////////////////////////////////////////////////////////
namespace util { namespace noise { namespace basis { namespace type {
template <size_t S>
struct gradient {
protected:
static const std::array<vectori<S>,util::pow(2,S)> CORNERS;
};
} } } }
#endif

9
noise/basis/value.hpp
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@ -18,18 +18,21 @@
#ifndef __UTIL_NOISE_BASIS_VALUE_HPP
#define __UTIL_NOISE_BASIS_VALUE_HPP
#include "./type/gradient.hpp"
#include "../fwd.hpp"
#include "../../range.hpp"
#include "../../point.hpp"
namespace util { namespace noise { namespace basis {
/// Single value per grid space
template <typename T, lerp_t<T>>
struct value {
template <size_t S, typename T, lerp_t<T>>
struct value : public type::gradient<S> {
value (seed_t);
range<T> bounds (void) const;
T operator() (util::point<2,T>) const;
T operator() (util::point<S,T>) const;
seed_t seed (void) const;
seed_t seed (seed_t);

50
noise/basis/value.ipp
View File

@ -20,68 +20,72 @@
#define __UTIL_NOISE_BASIS_VALIE_IPP
#include "../rand.hpp"
#include "../../types.hpp"
namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T, util::noise::lerp_t<T> L>
value<T,L>::value (seed_t _seed):
template <size_t S, typename T, util::noise::lerp_t<T> L>
value<S,T,L>::value (seed_t _seed):
m_seed (_seed)
{ ; }
//-------------------------------------------------------------------------
template <typename T, util::noise::lerp_t<T> L>
template <size_t S, typename T, util::noise::lerp_t<T> L>
util::range<T>
value<T,L>::bounds (void) const
value<S,T,L>::bounds (void) const
{
return { -1, 1 };
}
//-------------------------------------------------------------------------
template <typename T, lerp_t<T> L>
template <size_t S, typename T, lerp_t<T> L>
seed_t
value<T,L>::seed (void) const
value<S,T,L>::seed (void) const
{
return m_seed;
}
//-------------------------------------------------------------------------
template <typename T, lerp_t<T> L>
template <size_t S, typename T, lerp_t<T> L>
seed_t
value<T,L>::seed (seed_t _seed)
value<S,T,L>::seed (seed_t _seed)
{
return m_seed = _seed;
}
//-------------------------------------------------------------------------
template <typename T, util::noise::lerp_t<T> L>
template <size_t S, typename T, util::noise::lerp_t<T> L>
T
value<T,L>::operator() (util::point<2,T> p) const
value<S,T,L>::operator() (util::point<S,T> p) const
{
// extract integer and fractional parts. be careful to always round down
auto p_int = floor (p).template cast<intmax_t> ();
auto p_rem = p - p_int;
// generate the corner points
auto p0 = p_int + util::vector<2,intmax_t> { 0, 0 };
auto p1 = p_int + util::vector<2,intmax_t> { 1, 0 };
auto p2 = p_int + util::vector<2,intmax_t> { 0, 1 };
auto p3 = p_int + util::vector<2,intmax_t> { 1, 1 };
std::array<pointi<S>,pow(2,S)> p_;
std::transform (std::begin (this->CORNERS), std::end (this->CORNERS),
std::begin (p_),
[p_int] (auto i) { return p_int + i; });
// Generate the four corner values
T g0 = noise::rand<float> (m_seed, p0);
T g1 = noise::rand<float> (m_seed, p1);
T g2 = noise::rand<float> (m_seed, p2);
T g3 = noise::rand<float> (m_seed, p3);
// Generate the corner values
std::array<T,pow(2,S)> g_;
std::transform (std::begin (p_), std::end (p_),
std::begin (g_),
[this] (auto i) { return noise::rand<float> (m_seed, i); });
// Interpolate on one dimension, then the other.
auto l0 = L (g0, g1, p_rem.x);
auto l1 = L (g2, g3, p_rem.x);
auto l_ = L (l0, l1, p_rem.y);
T l_[pow(2,S)];
std::copy (std::begin (g_), std::end (g_), std::begin (l_));
return l_;
for (size_t i = S; i; --i)
for (size_t j = 0; j < std::pow(2,i); j += 2)
l_[j / 2] = L (l_[j], l_[j+1], p_rem[S-i]);
return l_[0];
}
} } }

12
noise/basis/worley.hpp
View File

@ -18,23 +18,27 @@
#ifndef __UTIL_NOISE_BASIS_WORLEY_HPP
#define __UTIL_NOISE_BASIS_WORLEY_HPP
#include "./type/distance.hpp"
#include "../fwd.hpp"
#include "../../point.hpp"
#include "../../range.hpp"
namespace util { namespace noise { namespace basis {
template <typename T, size_t F = 0>
struct worley {
template <size_t S, typename T, size_t F = 0>
struct worley : public type::distance<S,1> {
worley (seed_t);
range<T> bounds (void) const;
T operator() (util::point<2,T>) const;
T operator() (util::point<S,T>) const;
seed_t seed (void) const;
seed_t seed (seed_t);
private:
point<2,T> generate (point<2,intmax_t>) const;
point<S,T> generate (point<S,intmax_t>) const;
seed_t m_seed;
};
} } }

64
noise/basis/worley.ipp
View File

@ -25,67 +25,58 @@
namespace util { namespace noise { namespace basis {
///////////////////////////////////////////////////////////////////////////
template <typename T, size_t F>
worley<T,F>::worley (seed_t _seed):
template <size_t S, typename T, size_t F>
worley<S,T,F>::worley (seed_t _seed):
m_seed (_seed)
{ ; }
//-------------------------------------------------------------------------
template <typename T, size_t F>
template <size_t S, typename T, size_t F>
util::range<T>
worley<T,F>::bounds (void) const
worley<S,T,F>::bounds (void) const
{
return { 0.0, 1.5 };
}
//-------------------------------------------------------------------------
template <typename T, size_t F>
template <size_t S, typename T, size_t F>
seed_t
worley<T,F>::seed (void) const
worley<S,T,F>::seed (void) const
{
return m_seed;
}
//-------------------------------------------------------------------------
template <typename T, size_t F>
template <size_t S, typename T, size_t F>
seed_t
worley<T,F>::seed (seed_t _seed)
worley<S,T,F>::seed (seed_t _seed)
{
return m_seed = _seed;
}
//-------------------------------------------------------------------------
template <typename T, size_t F>
template <size_t S, typename T, size_t F>
T
worley<T,F>::operator() (util::point<2,T> p) const
worley<S,T,F>::operator() (point<S,T> p) const
{
// extract integer and fractional parts. be careful to always round down
auto p_int = floor (p).template cast<intmax_t> ();
auto p_rem = (p - p_int).template as<point> ();
// setup an array of distances
constexpr size_t RADIUS = 1;
constexpr size_t COUNT = pow2 (RADIUS * 2 + 1);
T distances[COUNT] = { std::numeric_limits<T>::quiet_NaN () };
T *cursor = distances;
constexpr size_t COUNT = type::distance<S,1>::OFFSET_SIZE;
T distances[COUNT];
// record the distances to each candidate point
for (signed y_off = -signed(RADIUS); y_off <= signed(RADIUS) ; ++y_off) {
for (signed x_off = -signed(RADIUS); x_off <= signed(RADIUS); ++x_off) {
auto off = vector<2,intmax_t> {x_off, y_off};
auto pos = generate (p_int + off);
CHECK_LIMIT (pos.x, T{0}, T{1});
CHECK_LIMIT (pos.y, T{0}, T{1});
*cursor = distance2 (pos + off, p_rem);
cursor++;
}
}
std::transform (std::begin (this->OFFSETS), std::end (this->OFFSETS),
distances,
[p_int,p_rem,this] (auto i) {
auto q = this->generate (p_int + i);
return distance2 (q + i, p_rem);
});
// find the f'th lowest value
static_assert (F < COUNT, "worley order must be less than search radius");
@ -96,21 +87,10 @@ namespace util { namespace noise { namespace basis {
//////////////////////////////////////////////////////////////////////////
template <typename T, size_t F>
point<2,T>
worley<T,F>::generate (point<2,intmax_t> p) const
template <size_t S, typename T, size_t F>
point<S,T>
worley<S,T,F>::generate (point<S,intmax_t> p) const
{
using util::hash::murmur2::mix;
auto u = mix (m_seed, mix (uint64_t (p.x), uint64_t (p.y)));
auto v = mix (u, m_seed);
auto r = util::point<2,T> {
(u & 0xffff) / T{0xffff},
(v & 0xffff) / T{0xffff}
};
CHECK_LIMIT (r, T{0}, T{1});
return r;
return (noise::rand<util::point,T> (m_seed, p) + 1) / 2;
}
} } }

6
noise/fractal/base.hpp
View File

@ -32,7 +32,11 @@ namespace util { namespace noise { namespace fractal {
/// lacunarity: per octave frequency scaling factor
/// amplitude: maximum absolute value of the noise
/// gain: per octave amplitude scaling factor. typically 1/f.
template <typename T, typename B>
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
typename B // noise basis function
>
struct base {
using seed_t = uint64_t;

84
noise/fractal/base.ipp
View File

@ -23,14 +23,14 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
base<T,B>::base (seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
template <size_t S, typename T, typename B>
base<S,T,B>::base (seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
// literals
m_octaves (_octaves),
m_H (_H),
@ -51,27 +51,27 @@ namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
template <size_t S, typename T, typename B>
unsigned
base<T,B>::octaves (unsigned _octaves)
base<S,T,B>::octaves (unsigned _octaves)
{
return m_octaves = _octaves;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr unsigned
base<T,B>::octaves (void) const
base<S,T,B>::octaves (void) const
{
return m_octaves;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
base<T,B>::H (T _h)
base<S,T,B>::H (T _h)
{
m_H = _h;
m_invAH = std::pow (m_amplitude, -m_H);
@ -81,63 +81,63 @@ namespace util { namespace noise { namespace fractal {
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr T
base<T,B>::H (void) const
base<S,T,B>::H (void) const
{
return m_H;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
base<T,B>::frequency (T _frequency)
base<S,T,B>::frequency (T _frequency)
{
return m_frequency = _frequency;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr T
base<T,B>::frequency (void) const
base<S,T,B>::frequency (void) const
{
return m_frequency;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
base<T,B>::lacunarity (T _lacunarity)
base<S,T,B>::lacunarity (T _lacunarity)
{
return m_lacunarity = _lacunarity;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr T
base<T,B>::lacunarity (void) const
base<S,T,B>::lacunarity (void) const
{
return m_lacunarity;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr T
base<T,B>::amplitude (void) const
base<S,T,B>::amplitude (void) const
{
return m_amplitude;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
base<T,B>::amplitude (T _amplitude)
base<S,T,B>::amplitude (T _amplitude)
{
m_amplitude = _amplitude;
m_invAH = std::pow (m_amplitude, -m_H);
@ -146,18 +146,18 @@ namespace util { namespace noise { namespace fractal {
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr T
base<T,B>::gain (void) const
base<S,T,B>::gain (void) const
{
return m_gain;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
base<T,B>::gain (T _gain)
base<S,T,B>::gain (T _gain)
{
m_gain = _gain;
m_invGH = std::pow (_gain, m_H);
@ -166,36 +166,36 @@ namespace util { namespace noise { namespace fractal {
//-------------------------------------------------------------------------
template <typename T, typename B>
typename base<T,B>::seed_t
base<T,B>::seed (seed_t _seed)
template <size_t S, typename T, typename B>
typename base<S,T,B>::seed_t
base<S,T,B>::seed (seed_t _seed)
{
return m_basis.seed (_seed);
}
//-------------------------------------------------------------------------
template <typename T, typename B>
typename base<T,B>::seed_t
base<T,B>::seed (void) const
template <size_t S, typename T, typename B>
typename base<S,T,B>::seed_t
base<S,T,B>::seed (void) const
{
return m_basis.seed ();
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
const B&
base<T,B>::basis (void) const
base<S,T,B>::basis (void) const
{
return m_basis;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
B&
base<T,B>::basis (void)
base<S,T,B>::basis (void)
{
return m_basis;
}

12
noise/fractal/fbm.hpp
View File

@ -33,9 +33,13 @@ namespace util { namespace noise { namespace fractal {
/// lacunarity: per octave frequency scaling factor
/// amplitude: maximum absolute value of the noise
/// gain: per octave amplitude scaling factor. typically 1/f.
template <typename T, typename B>
struct fbm : public base<T,B> {
using seed_t = typename base<T,B>::seed_t;
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
typename B // generating basis function
>
struct fbm : public base<S,T,B> {
using seed_t = typename base<S,T,B>::seed_t;
static constexpr unsigned DEFAULT_OCTAVES = 8;
static constexpr T DEFAULT_H = 1;
@ -53,7 +57,7 @@ namespace util { namespace noise { namespace fractal {
T gain);
fbm (seed_t);
T operator() (util::point<2,T>) const;
T operator() (point<S,T>) const;
};
} } }

54
noise/fractal/fbm.ipp
View File

@ -23,41 +23,41 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
fbm<T,B>::fbm (seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
base<T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain)
template <size_t S, typename T, typename B>
fbm<S,T,B>::fbm (seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
base<S,T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain)
{ ; }
//-------------------------------------------------------------------------
template <typename T, typename B>
fbm<T,B>::fbm (seed_t _seed):
fbm<T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN)
template <size_t S, typename T, typename B>
fbm<S,T,B>::fbm (seed_t _seed):
fbm<S,T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN)
{ ; }
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
fbm<T,B>::operator() (util::point<2,T> p) const
fbm<S,T,B>::operator() (point<S,T> p) const
{
T total = 0;
T scale = this->m_invAH;
@ -67,7 +67,7 @@ namespace util { namespace noise { namespace fractal {
for (size_t i = 0; i < this->m_octaves; ++i) {
total += this->m_basis (p) * scale;
p += T{1};
p += PI<float>;
p *= this->m_lacunarity;
scale *= this->m_invGH;
}

12
noise/fractal/hetero.hpp
View File

@ -25,9 +25,13 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////
/// Heterogeneous procedural terrain fucntion: stats by altitude method
template <typename T, typename B>
struct hetero : public base<T,B> {
using seed_t = typename base<T,B>::seed_t;
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
typename B // generating basis function
>
struct hetero : public base<S,T,B> {
using seed_t = typename base<S,T,B>::seed_t;
static constexpr unsigned DEFAULT_OCTAVES = 6;
static constexpr T DEFAULT_H = T(0.75);
@ -59,7 +63,7 @@ namespace util { namespace noise { namespace fractal {
constexpr T offset (void) const;
T offset (T);
T operator() (util::point<2,T>) const;
T operator() (point<S,T>) const;
private:
T m_offset;

96
noise/fractal/hetero.ipp
View File

@ -21,82 +21,82 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
hetero<T,B>::hetero(seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
hetero<T,B> (_seed,
template <size_t S, typename T, typename B>
hetero<S,T,B>::hetero(seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
hetero<S,T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain,
-this->basis ().bounds ().min + this->basis ().bounds ().magnitude () / T{2})
{ ; }
//-------------------------------------------------------------------------
template <size_t S, typename T, typename B>
hetero<S,T,B>::hetero(seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain,
T _offset):
base<S,T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain,
-this->basis ().bounds ().min + this->basis ().bounds ().magnitude () / T{2})
{ ; }
//-------------------------------------------------------------------------
template <typename T, typename B>
hetero<T,B>::hetero(seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain,
T _offset):
base<T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain),
_gain),
m_offset (_offset)
{ ; }
//-------------------------------------------------------------------------
template <typename T, typename B>
hetero<T,B>::hetero (seed_t _seed):
hetero<T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN,
DEFAULT_OFFSET)
template <size_t S, typename T, typename B>
hetero<S,T,B>::hetero (seed_t _seed):
hetero<S,T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN,
DEFAULT_OFFSET)
{ ; }
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
template <size_t S, typename T, typename B>
constexpr T
hetero<T,B>::offset (void) const
hetero<S,T,B>::offset (void) const
{
return m_offset;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
hetero<T,B>::offset (T _offset)
hetero<S,T,B>::offset (T _offset)
{
return m_offset = _offset;
}
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
hetero<T,B>::operator() (util::point<2,T> p) const
hetero<S,T,B>::operator() (point<S,T> p) const
{
T scale = this->m_invAH;
@ -115,7 +115,7 @@ namespace util { namespace noise { namespace fractal {
result += increment;
p += T{1};
p += PI<T>;
p *= this->m_lacunarity;
}

12
noise/fractal/hmf.hpp
View File

@ -24,9 +24,13 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////
/// Musgrave's "Hybrid MultiFractal"
template <typename T, typename B>
struct hmf : public base<T,B> {
using seed_t = typename base<T,B>::seed_t;
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
typename B // generating basis function
>
struct hmf : public base<S,T,B> {
using seed_t = typename base<S,T,B>::seed_t;
// H should be fairly low due to the decreasing weight parameter in eval
static constexpr unsigned DEFAULT_OCTAVES = 6;
@ -48,7 +52,7 @@ namespace util { namespace noise { namespace fractal {
hmf (seed_t);
T operator() (point<2,T>) const;
T operator() (point<S,T>) const;
private:
T m_offset;

58
noise/fractal/hmf.ipp
View File

@ -22,44 +22,44 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
hmf<T,B>::hmf (seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain,
T _offset):
base<T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain),
template <size_t S, typename T, typename B>
hmf<S,T,B>::hmf (seed_t _seed,
unsigned _octaves,
T _H,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain,
T _offset):
base<S,T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain),
m_offset (_offset)
{ ; }
//-------------------------------------------------------------------------
template <typename T, typename B>
hmf<T,B>::hmf (seed_t _seed):
hmf<T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN,
DEFAULT_OFFSET)
template <size_t S, typename T, typename B>
hmf<S,T,B>::hmf (seed_t _seed):
hmf<S,T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN,
DEFAULT_OFFSET)
{ ; }
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
hmf<T,B>::operator() (util::point<2,T> p) const
hmf<S,T,B>::operator() (point<S,T> p) const
{
T scale = this->m_invAH;
@ -77,7 +77,7 @@ namespace util { namespace noise { namespace fractal {
weight = min (weight, T{1});
scale *= this->m_invGH;
p += T{1};
p += PI<T>;
p *= this->m_lacunarity;
}

12
noise/fractal/rmf.hpp
View File

@ -32,9 +32,13 @@ namespace util { namespace noise { namespace fractal {
/// lacunarity: incremental octave frequency scaling factor
/// amplitude: value scaling factor for the base octave
/// gain: incremental octave value scaling factor
template <typename T, typename B>
struct rmf : public base<T,B> {
using seed_t = typename base<T,B>::seed_t;
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
typename B // generating basis function
>
struct rmf : public base<S,T,B> {
using seed_t = typename base<S,T,B>::seed_t;
static constexpr unsigned DEFAULT_OCTAVES = 5;
static constexpr T DEFAULT_H = 1;
@ -55,7 +59,7 @@ namespace util { namespace noise { namespace fractal {
rmf (seed_t);
T operator() (util::point<2,T>) const;
T operator() (point<S,T>) const;
T offset (void) const;
T offset (T);

66
noise/fractal/rmf.ipp
View File

@ -22,46 +22,46 @@
namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
rmf<T,B>::rmf (seed_t _seed,
unsigned _octaves,
T _H,
T _offset,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
base<T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain),
template <size_t S, typename T, typename B>
rmf<S,T,B>::rmf (seed_t _seed,
unsigned _octaves,
T _H,
T _offset,
T _frequency,
T _lacunarity,
T _amplitude,
T _gain):
base<S,T,B> (_seed,
_octaves,
_H,
_frequency,
_lacunarity,
_amplitude,
_gain),
m_offset (_offset)
{ ; }
//-------------------------------------------------------------------------
template <typename T, typename B>
rmf<T,B>::rmf (seed_t _seed):
rmf<T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN,
DEFAULT_OFFSET)
template <size_t S, typename T, typename B>
rmf<S,T,B>::rmf (seed_t _seed):
rmf<S,T,B> (_seed,
DEFAULT_OCTAVES,
DEFAULT_H,
DEFAULT_FREQUENCY,
DEFAULT_LACUNARITY,
DEFAULT_AMPLITUDE,
DEFAULT_GAIN,
DEFAULT_OFFSET)
{ ; }
///////////////////////////////////////////////////////////////////////////
// we use the name 'amplitude' instead of musgrave's 'gain'.
// assumes basis distribution [-1,1] and offset ~= 1
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
rmf<T,B>::operator() (util::point<2,T> p) const
rmf<S,T,B>::operator() (point<S,T> p) const
{
T scale = this->m_invAH;
@ -92,7 +92,7 @@ namespace util { namespace noise { namespace fractal {
scale *= this->m_invGH;
p += T{1};
p += PI<T>;
p *= this->m_lacunarity;
}
@ -101,18 +101,18 @@ namespace util { namespace noise { namespace fractal {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
rmf<T,B>::offset (void) const
rmf<S,T,B>::offset (void) const
{
return m_offset;
}
//-------------------------------------------------------------------------
template <typename T, typename B>
template <size_t S, typename T, typename B>
T
rmf<T,B>::offset (T _offset)
rmf<S,T,B>::offset (T _offset)
{
return m_offset = _offset;
}

5
noise/fractal/runtime.cpp
View File

@ -17,4 +17,7 @@
#include "runtime.hpp"
#include "../basis/runtime.hpp"
template struct util::noise::fractal::runtime<float,util::noise::basis::runtime<float>>;
template struct util::noise::fractal::runtime<
2,float,
util::noise::basis::runtime<2,float>
>;

12
noise/fractal/runtime.hpp
View File

@ -25,7 +25,11 @@
#include <memory>
namespace util { namespace noise { namespace fractal {
template <typename T, typename B>
template <
size_t S, // probe point dimensionality
typename T, // probe point value_type
typename B // generating basis function
>
struct runtime {
public:
using seed_t = uint64_t;
@ -37,7 +41,7 @@ namespace util { namespace noise { namespace fractal {
runtime& operator= (const runtime&) = delete;
// basis functions
T operator () (util::point<2,T> p) const { return (*m_child) (p); }
T operator () (point<S,T> p) const { return (*m_child) (p); }
unsigned octaves (void) const { return m_child->octaves (); }
unsigned octaves (unsigned _octaves) { return m_child->octaves (_octaves); }
@ -67,7 +71,7 @@ namespace util { namespace noise { namespace fractal {
struct base {
virtual ~base () = default;
virtual T operator() (util::point<2,T>) = 0;
virtual T operator() (util::point<S,T>) = 0;
virtual unsigned octaves (void) const = 0;
virtual unsigned octaves (unsigned) = 0;
@ -116,7 +120,7 @@ namespace util { namespace noise { namespace fractal {
_gain)
{ ; }
T operator() (util::point<2,T> p) override { return data (p); }
T operator() (util::point<S,T> p) override { return data (p); }
unsigned octaves (void) const override { return data.octaves (); }
unsigned octaves (unsigned _octaves) override { return data.octaves (_octaves); }

23
noise/rand.hpp
View File

@ -19,13 +19,24 @@
namespace util { namespace noise {
/// generate a uniform random floating point in the range [-1, 1] from a seed and vector
template <typename T, typename V>
T
rand (uint64_t seed, V value);
template <
typename U,
size_t S,
typename T,
template <size_t,typename> class Q
>
U
rand (uint64_t seed, Q<S,T> value);
template <size_t N, typename T, typename V>
vector<N,T>
rand (uint64_t seed, V value);
template <
template <size_t,typename> class R,
typename U,
size_t S,
typename T,
template <size_t,typename> class Q
>
R<S,U>
rand (uint64_t seed, Q<S,T> value);
} }
#include "rand.ipp"

48
noise/rand.ipp
View File

@ -24,37 +24,53 @@
namespace util { namespace noise {
template <typename T, typename V>
T
rand (uint64_t seed, V value)
//-------------------------------------------------------------------------
template <
typename U,
size_t S,
typename T,
template <size_t,typename> class Q
>
U
rand (uint64_t seed, Q<S,T> query)
{
static_assert (std::is_integral<T>::value,
"mixing only works on integral types");
uint64_t accum = seed;
for (auto i: value)
for (auto i: query)
accum = hash::murmur2::mix (accum, i);
T out = (accum & 0xFFFF) / T{0xFFFF};
U result = (accum & 0xFFFF) / U{0xFFFF};
out *= 2;
out -= 1;
result *= 2;
result -= 1;
return out;
return result;
}
template <size_t N, typename T, typename V>
vector<N,T>
rand (uint64_t seed, V value)
//-------------------------------------------------------------------------
template <
template <size_t,typename> class R,
typename U,
size_t S,
typename T,
template <size_t,typename> class Q
>
R<S,U>
rand (uint64_t seed, Q<S,T> query)
{
uint64_t accum = seed;
for (auto i: value)
for (auto i: query)
accum = hash::murmur2::mix (accum, i);
vector<N,T> out;
for (auto &i: out) {
i = (accum & 0xFFFF) / T{0xFFFF};
R<S,U> result;
for (auto &i: result) {
i = (accum & 0xFFFF) / U{0xFFFF};
accum = hash::murmur2::mix (accum, seed);
}
return out * 2 - 1;
return result * 2 - 1;
}
} }

26
noise/turbulence.hpp
View File

@ -29,20 +29,36 @@ namespace util { namespace noise {
/// assumes the pertubation function is roughly symetrical around 0.
/// nothing will explode if it isn't, but you'll see strong directional
/// artefacts with higher scaling factors.
template <typename T, typename D, typename P>
template <
size_t S, // dimension
typename T, // value_type
typename D, // data fractal
typename P // pertubation fractal
>
struct turbulence {
static constexpr auto dimension = S;
using value_type = T;
using seed_t = uint64_t;
turbulence (seed_t, vector<2,T> scale);
turbulence (seed_t, vector<S,T> scale);
seed_t seed (seed_t);
seed_t seed (void) const;
constexpr T operator() (point<2,T>) const;
constexpr T operator() (point<S,T>) const;
D data;
P perturb[2];
vector<2,T> scale;
// XXX: use a union to defer initialization of pertubation fractals in
// the constructor. i know this is horrible, but there's no time to
// write the proper generator constructor to pass out the seeds.
union {
char _[0];
P perturb[S];
};
vector<S,T> scale;
};
} }

44
noise/turbulence.ipp
View File

@ -24,50 +24,48 @@
namespace util { namespace noise {
///////////////////////////////////////////////////////////////////////////
template <typename T, typename D, typename P>
turbulence<T,D,P>::turbulence (seed_t _seed,
vector<2,T> _scale):
template <size_t S, typename T, typename D, typename P>
turbulence<S,T,D,P>::turbulence (seed_t _seed,
vector<S,T> _scale):
data (_seed),
perturb {
hash::wang (_seed),
hash::wang (hash::wang (_seed))
},
scale (_scale)
{ ; }
{
for (auto &p: perturb)
new (&p) P (_seed = hash::wang (_seed));
}
////////////////////////////////////////////////////////////////////////////
template <typename T, typename D, typename P>
typename turbulence<T,D,P>::seed_t
turbulence<T,D,P>::seed (void) const
template <size_t S, typename T, typename D, typename P>
typename turbulence<S,T,D,P>::seed_t
turbulence<S,T,D,P>::seed (void) const
{
return data.seed ();
}
//-------------------------------------------------------------------------
template <typename T, typename D, typename P>
typename turbulence<T,D,P>::seed_t
turbulence<T,D,P>::seed (seed_t _seed)
template <size_t S, typename T, typename D, typename P>
typename turbulence<S,T,D,P>::seed_t
turbulence<S,T,D,P>::seed (seed_t _seed)
{
auto ret = _seed;
data.seed (_seed);
data.seed (_seed); _seed = hash::wang (_seed);
perturb[0].seed (_seed); _seed = hash::wang (_seed);
perturb[1].seed (_seed); _seed = hash::wang (_seed);
for (size_t i = 0; i < S; ++i)
perturb[i].seed (_seed = hash::wang (_seed));
return ret;
}
///////////////////////////////////////////////////////////////////////////
template <typename T, typename D, typename P>
template <size_t S, typename T, typename D, typename P>
constexpr T
turbulence<T,D,P>::operator() (point<2,T> p) const
turbulence<S,T,D,P>::operator() (point<S,T> p) const
{
vector<2,T> n = {
perturb[0] (p),
perturb[1] (p)
};
vector<S,T> n;
for (size_t i = 0; i < S; ++i)
n[i] = perturb[i] (p);
// scale by the data frequency so that we match scale
return data (p + n * scale / data.frequency ());

81
tools/noise.cpp
View File

@ -25,11 +25,13 @@
#include "region.hpp"
constexpr size_t S = 3;
///////////////////////////////////////////////////////////////////////////////
template struct util::noise::fractal::fbm<float, util::noise::basis::perlin<float,util::lerp::cubic>>;
template struct util::noise::fractal::hmf<float, util::noise::basis::value<float,util::lerp::cubic>>;
template struct util::noise::fractal::rmf<float, util::noise::basis::constant<float>>;
template struct util::noise::fractal::hetero<float, util::noise::basis::worley<float,2>>;
template struct util::noise::fractal::fbm<S,float, util::noise::basis::perlin<S,float,util::lerp::cubic>>;
template struct util::noise::fractal::hmf<S,float, util::noise::basis::value<S,float,util::lerp::cubic>>;
template struct util::noise::fractal::rmf<S,float, util::noise::basis::constant<S,float>>;
template struct util::noise::fractal::hetero<S,float, util::noise::basis::worley<S,float,S>>;
///////////////////////////////////////////////////////////////////////////////
@ -221,30 +223,30 @@ main (int argc, char **argv)
#endif
util::noise::turbulence<
float,
S,float,
util::noise::fractal::runtime<
float,
util::noise::basis::runtime<float>
S,float,
util::noise::basis::runtime<S,float>
>,
util::noise::fractal::fbm<
float,
S,float,
util::noise::basis::perlin<
float,
S,float,
util::lerp::cubic
>
>
> t (seed, { turbulence, turbulence });
> t (seed, util::vectorf<S> (turbulence));
auto &f = t.data;
switch (fractal) {
using namespace util::noise;
case FBM: f.reset<fractal::fbm <float,basis::runtime<float>>> (seed); break;
case HMF: f.reset<fractal::hmf <float,basis::runtime<float>>> (seed); break;
case RMF: f.reset<fractal::rmf <float,basis::runtime<float>>> (seed); break;
case FBM: f.reset<fractal::fbm<S,float,basis::runtime<S,float>>> (seed); break;
case HMF: f.reset<fractal::hmf<S,float,basis::runtime<S,float>>> (seed); break;
case RMF: f.reset<fractal::rmf<S,float,basis::runtime<S,float>>> (seed); break;
case HETERO: {
auto &child = f.reset<fractal::hetero<float,basis::runtime<float>>> (seed);
auto &child = f.reset<fractal::hetero<S,float,basis::runtime<S,float>>> (seed);
if (!std::isnan (offset))
child.offset (offset);
break;
@ -260,11 +262,11 @@ main (int argc, char **argv)
case PERLIN: {
switch (lerp) {
case LINEAR: b.reset<basis::perlin<float,util::lerp::linear>> (seed); break;
case CUBIC: b.reset<basis::perlin<float,util::lerp::cubic>> (seed); break;
case QUINTIC: b.reset<basis::perlin<float,util::lerp::quintic>> (seed); break;
case COSINE: b.reset<basis::perlin<float,util::lerp::cosine>> (seed); break;
case TRUNC: b.reset<basis::perlin<float,util::lerp::trunc>> (seed); break;
case LINEAR: b.reset<basis::perlin<S,float,util::lerp::linear>> (seed); break;
case CUBIC: b.reset<basis::perlin<S,float,util::lerp::cubic>> (seed); break;
case QUINTIC: b.reset<basis::perlin<S,float,util::lerp::quintic>> (seed); break;
case COSINE: b.reset<basis::perlin<S,float,util::lerp::cosine>> (seed); break;
case TRUNC: b.reset<basis::perlin<S,float,util::lerp::trunc>> (seed); break;
default:
unreachable ();
@ -274,11 +276,11 @@ main (int argc, char **argv)
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;
case LINEAR: b.reset<basis::perlin<S,float,util::lerp::linear,basis::expgrad>> (seed); break;
case CUBIC: b.reset<basis::perlin<S,float,util::lerp::cubic,basis::expgrad>> (seed); break;
case QUINTIC: b.reset<basis::perlin<S,float,util::lerp::quintic,basis::expgrad>> (seed); break;
case COSINE: b.reset<basis::perlin<S,float,util::lerp::cosine,basis::expgrad>> (seed); break;
case TRUNC: b.reset<basis::perlin<S,float,util::lerp::trunc,basis::expgrad>> (seed); break;
default:
unreachable ();
@ -288,11 +290,11 @@ main (int argc, char **argv)
case VALUE: {
switch (lerp) {
case LINEAR: b.reset<basis::value<float,util::lerp::linear>> (seed); break;
case CUBIC: b.reset<basis::value<float,util::lerp::cubic>> (seed); break;
case QUINTIC: b.reset<basis::value<float,util::lerp::quintic>> (seed); break;
case COSINE: b.reset<basis::value<float,util::lerp::cosine>> (seed); break;
case TRUNC: b.reset<basis::value<float,util::lerp::trunc>> (seed); break;
case LINEAR: b.reset<basis::value<S,float,util::lerp::linear>> (seed); break;
case CUBIC: b.reset<basis::value<S,float,util::lerp::cubic>> (seed); break;
case QUINTIC: b.reset<basis::value<S,float,util::lerp::quintic>> (seed); break;
case COSINE: b.reset<basis::value<S,float,util::lerp::cosine>> (seed); break;
case TRUNC: b.reset<basis::value<S,float,util::lerp::trunc>> (seed); break;
default:
unreachable ();
@ -301,12 +303,12 @@ main (int argc, char **argv)
}
case WORLEY: {
b.reset<util::noise::basis::worley<float>> (seed);
b.reset<util::noise::basis::worley<S,float>> (seed);
break;
}
case PATCH: {
b.reset<util::noise::basis::patch<float>> (seed, width);
b.reset<util::noise::basis::patch<S,float>> (seed, width);
break;
}
@ -322,9 +324,8 @@ main (int argc, char **argv)
if (!std::isnan (amplitude)) f.amplitude (amplitude);
if (!std::isnan (gain)) f.gain (gain);
t.perturb[0].frequency ( scale / res.w);
t.perturb[1].frequency ( scale / res.w);
for (auto &p: t.perturb)
p.frequency (scale / res.w);
util::image::buffer<float> img (res);
@ -336,8 +337,10 @@ main (int argc, char **argv)
{
for (size_t y = 0; y < res.h; ++y)
for (size_t x = 0; x < res.w; ++x)
img[{x, y}] = t (util::point2f {float (x), float (y)} + OFFSET);
for (size_t x = 0; x < res.w; ++x) {
util::point2f p (x, y);
img[{x, y}] = t ((p + OFFSET).redim<S> ());
}
}
// working on the assumption that all octave images are based on summation,
@ -350,8 +353,10 @@ main (int argc, char **argv)
auto prev = img.clone ();
for (size_t y = 0; y < res.h; ++y)
for (size_t x = 0; x < res.w; ++x)
prev[{x,y}] = t (util::point2f {float (x), float (y)} + OFFSET);
for (size_t x = 0; x < res.w; ++x) {
util::point2f p (x, y);
prev[{x,y}] = t ((p + OFFSET).redim<S> ());
}
CHECK_EQ (img.stride (), prev.stride ());
for (size_t i = 0; i < img.size (); ++i)