simplex_noise.hpp

#ifndef PASTELGFX_SIMPLEX_NOISE_HPP
#define PASTELGFX_SIMPLEX_NOISE_HPP

#include "pastel/gfx/noise/simplex_noise.h"
#include "pastel/gfx/noise/gradientfield.h"
#include "pastel/gfx/noise/perlin_noise.h"

namespace Pastel
{

    template <typename Real>
    Real simplexNoise(const NoDeduction<Real>& position)
    {
        return perlinNoise<Real>(position);
    }

    template <typename Real, int N>
    Real simplexNoise(const Vector<Real, N>& x)
    {
        integer n = x.size();
        Real c = std::sqrt((Real)(n + 1));
        Real d = std::sqrt((Real)n / (n + 1));
        Real s = (c - 1) / n;
        Real q = s / c;
        Real dInv = inverse(d);

        // Transform the point to the integer
        // cube simplicial partitioning.

        const Vector<Real, N> u = d * (x + s * sum(x));

        // Find out in which integer cube we are.

        Vector<integer, N> p = floor(u);
        Vector<Real, N> f = u - Vector<Real, N>(p);

        // In that cube, find out in which
        // simplex we are in.

        using Pair = std::pair<Real, integer>;

        std::vector<Pair> orderSet;
        orderSet.reserve(n);
        for (integer i = 0;i < n;++i)
        {
            orderSet.emplace_back(f[i], i);
        }

        auto greater = [&](const Pair& left, const Pair& right)
        {
            if (left.first != right.first)
            {
                return left.first > right.first;
            }
            return left.second > right.second;
        };

        std::sort(orderSet.begin(), orderSet.end(), greater);

        // Map the min vertex back to the transformed simplex space
        // (out of the scalings along [1, ..., 1], this one maximizes
        // the regularity of the resulting simplices).

        Vector<Real, N> simplexMin =
            (Vector<Real, N>(p) - q * sum(p)) * dInv;
        f = x - simplexMin;

        // Sum the contributions from the surrounding
        // simplex vertices weighted with a symmetric
        // attenuation function.

        Real r2Inv = std::pow((Real)4 / 3, (Real)(n - 1));

        Real value = 0;
        for (integer i = 0;i < n;++i)
        {

            const Real attenuation = 1 - dot(f) * r2Inv;

            if (attenuation > 0)
            {
                Real vertexValue = gradientField<Real, N>()(p, f);

                value += square(square(attenuation)) * vertexValue;
            }

            integer axis = orderSet[i].second;

            f += q * dInv;
            f[axis] -= dInv;
            ++p[axis];
        }
        {
            const Real attenuation = 1 - dot(f) * r2Inv;

            if (attenuation > 0)
            {
                Real vertexValue = gradientField<Real, N>()(p, f);

                value += square(square(attenuation)) * vertexValue;
            }
        }

        return (value * 2 + 1) / 2;
    }

}

#endif