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+// SimplexNoise.h
+
+// Declares and implements the simplex noise, using a template parameter for the underlying datatype
+
+/*
+Note:
+This code has been adapted from the public domain code by Stefan Gustavson, available at
+http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
+*/
+
+#include <random>
+
+
+
+
+
+template<typename Datatype>
+class cSimplexNoise
+{
+public:
+ cSimplexNoise(int a_Seed)
+ {
+ // Based on the seed, initialize the permutation table, using a simple LCG and swapping
+
+ // Initialize with sorted sequence:
+ for (size_t i = 0; i < ARRAYCOUNT(m_Perm) / 2; i++)
+ {
+ m_Perm[i] = static_cast<int>(i);
+ }
+
+ // Use swaps to randomize:
+ std::linear_congruential_engine<unsigned, 48271, 0, 2147483647> lcg(a_Seed);
+ for (size_t i = 0; i < 2000; i++)
+ {
+ std::swap(m_Perm[lcg() % (ARRAYCOUNT(m_Perm) / 2)], m_Perm[lcg() % (ARRAYCOUNT(m_Perm) / 2)]);
+ }
+
+ // Copy to the upper half of the buffer (to avoid the need for modulo when accessing neighbors):
+ for (size_t i = ARRAYCOUNT(m_Perm) / 2; i < ARRAYCOUNT(m_Perm); i++)
+ {
+ m_Perm[i] = m_Perm[i - ARRAYCOUNT(m_Perm) / 2];
+ }
+
+ // Copy to the "modulo 12" table to optimize away four modulo ops per value calculation:
+ for (size_t i = 0; i < ARRAYCOUNT(m_Perm); i++)
+ {
+ m_PermMod12[i] = m_Perm[i] % 12;
+ }
+ }
+
+
+
+ /** Returns a dot product of an int vector with a Datatype vector. */
+ inline Datatype dot(const int * g, const Datatype x, const Datatype y, const Datatype z)
+ {
+ return g[0] * x + g[1] * y + g[2] * z;
+ }
+
+
+
+ /** Returns a dot product of two Datatype vectors. */
+ inline Datatype dot(const Datatype * g, const Datatype x, const Datatype y, const Datatype z)
+ {
+ return g[0] * x + g[1] * y + g[2] * z;
+ }
+
+
+
+ /** Returns the floor of the specified value, already type-cast to proper int type. */
+ inline int datafloor(const Datatype a_Val)
+ {
+ return (a_Val > 0) ? static_cast<int>(a_Val) : static_cast<int>(a_Val - 1); // This is faster than std::floor()
+ }
+
+
+ /** Returns a single noise value based on the 3D coords. */
+ Datatype GetValueAt3D(const Datatype a_X, const Datatype a_Y, const Datatype a_Z)
+ {
+ // The gradients are the midpoints of the vertices of a cube.
+ static const Datatype grad3[12][3] = {
+ {1, 1, 0}, {-1, 1, 0}, {1, -1, 0}, {-1, -1, 0},
+ {1, 0, 1}, {-1, 0, 1}, {1, 0, -1}, {-1, 0, -1},
+ {0, 1, 1}, { 0, -1, 1}, {0, 1, -1}, { 0, -1, -1}
+ };
+
+ // Skew factors:
+ static const Datatype F3 = static_cast<Datatype>(1.0 / 3.0);
+ static const Datatype G3 = static_cast<Datatype>(1.0 / 6.0);
+
+ // Noise contributions from the four corners:
+ Datatype n0, n1, n2, n3;
+
+ // Skew the input space to determine which simplex cell we're in
+ Datatype s = (a_X + a_Y + a_Z) * F3;
+ int i = datafloor(a_X + s);
+ int j = datafloor(a_Y + s);
+ int k = datafloor(a_Z + s);
+
+ // Unskew back into the XYZ space to calculate the distances from cell origin:
+ Datatype t = (i + j + k) * G3;
+ Datatype X0 = i - t;
+ Datatype Y0 = j - t;
+ Datatype Z0 = k - t;
+ Datatype x0 = a_X - X0;
+ Datatype y0 = a_Y - Y0;
+ Datatype z0 = a_Z - Z0;
+
+ // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
+ // Determine which simplex we are in.
+ int i1, j1, k1; // Offsets for second corner of simplex in IJK coords
+ int i2, j2, k2; // Offsets for third corner of simplex in IJK coords
+ if (x0 >= y0)
+ {
+ if (y0 >= z0)
+ {
+ // X Y Z order
+ i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
+ }
+ else if (x0 >= z0)
+ {
+ // X Z Y order
+ i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1;
+ }
+ else
+ {
+ // Z X Y order
+ i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1;
+ }
+ }
+ else
+ {
+ if (y0 < z0)
+ {
+ // Z Y X order
+ i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1;
+ }
+ else if (x0 < z0)
+ {
+ // Y Z X order
+ i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1;
+ }
+ else
+ {
+ // Y X Z order
+ i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
+ }
+ }
+
+ // A step of (1, 0, 0) in IJK means a step of (1 - c, -c, -c) in XYZ,
+ // a step of (0, 1, 0) in IJK means a step of (-c, 1 - c, -c) in XYZ, and
+ // a step of (0, 0, 1) in IJK means a step of (-c, -c, 1 - c) in XYZ, where c = G3 = 1 / 6.
+ Datatype x1 = x0 - i1 + G3; // Offsets for second corner in XYZ coords
+ Datatype y1 = y0 - j1 + G3;
+ Datatype z1 = z0 - k1 + G3;
+ Datatype x2 = x0 - i2 + static_cast<Datatype>(2) * G3; // Offsets for third corner in XYZ coords
+ Datatype y2 = y0 - j2 + static_cast<Datatype>(2) * G3;
+ Datatype z2 = z0 - k2 + static_cast<Datatype>(2) * G3;
+ Datatype x3 = x0 - static_cast<Datatype>(1) + static_cast<Datatype>(3) * G3; // Offsets for last corner in XYZ coords
+ Datatype y3 = y0 - static_cast<Datatype>(1) + static_cast<Datatype>(3) * G3;
+ Datatype z3 = z0 - static_cast<Datatype>(1) + static_cast<Datatype>(3) * G3;
+
+ // Work out the hashed gradient indices of the four simplex corners
+ int ii = i & 255;
+ int jj = j & 255;
+ int kk = k & 255;
+ int gi0 = m_PermMod12[ii + m_Perm[jj + m_Perm[kk]]];
+ int gi1 = m_PermMod12[ii + i1 + m_Perm[jj + j1 + m_Perm[kk + k1]]];
+ int gi2 = m_PermMod12[ii + i2 + m_Perm[jj + j2 + m_Perm[kk + k2]]];
+ int gi3 = m_PermMod12[ii + 1 + m_Perm[jj + 1 + m_Perm[kk + 1]]];
+
+ // Calculate the contribution from the four corners
+ Datatype t0 = static_cast<Datatype>(0.6) - x0 * x0 - y0 * y0 - z0 * z0;
+ if (t0 < 0)
+ {
+ n0 = 0.0;
+ }
+ else
+ {
+ t0 *= t0;
+ n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
+ }
+
+ Datatype t1 = static_cast<Datatype>(0.6) - x1 * x1 - y1 * y1 - z1 * z1;
+ if (t1 < 0)
+ {
+ n1 = 0.0;
+ }
+ else
+ {
+ t1 *= t1;
+ n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
+ }
+
+ Datatype t2 = static_cast<Datatype>(0.6) - x2 * x2 - y2 * y2 - z2 * z2;
+ if (t2 < 0)
+ {
+ n2 = 0.0;
+ }
+ else
+ {
+ t2 *= t2;
+ n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
+ }
+
+ Datatype t3 = static_cast<Datatype>(0.6) - x3 * x3 - y3 * y3 - z3 * z3;
+ if (t3 < 0)
+ {
+ n3 = 0.0;
+ }
+ else
+ {
+ t3 *= t3;
+ n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
+ }
+
+ // Add contributions from each corner to get the final noise value.
+ // The result is scaled to stay just inside [-1, 1]
+ return static_cast<Datatype>(32) * (n0 + n1 + n2 + n3);
+ }
+
+
+
+
+ /** Generates the 3D version of the SImplex noise.
+ a_Out is the 3D array into which the noise is output. Organized as [x + a_SizeX * y + a_SizeX * a_SizeY * z].
+ a_SizeX, a_SizeY, a_SizeZ are the dimensions of the a_Out array.
+ a_Start and a_End are the coords of the 3D array in the noise-space. */
+ void Generate3D(
+ Datatype * a_Out,
+ int a_SizeX, int a_SizeY, int a_SizeZ,
+ Datatype a_StartX, Datatype a_EndX,
+ Datatype a_StartY, Datatype a_EndY,
+ Datatype a_StartZ, Datatype a_EndZ
+ )
+ {
+ Datatype * out = a_Out;
+ for (int z = 0; z < a_SizeZ; ++z)
+ {
+ Datatype nz = a_StartZ + z * (a_EndZ - a_StartZ) / a_SizeZ;
+ for (int y = 0; y < a_SizeY; ++y)
+ {
+ Datatype ny = a_StartY + y * (a_EndY - a_StartY) / a_SizeY;
+ for (int x = 0; x < a_SizeX; ++x)
+ {
+ Datatype nx = a_StartX + x * (a_EndX - a_StartX) / a_SizeX;
+ *out = GetValueAt3D(nx, ny, nz);
+ ++out;
+ } // for x
+ } // for y
+ } // for z
+ }
+
+protected:
+ /** The permutation table, initialized by the seed. */
+ int m_Perm[512];
+
+ /** A copy of the permutation table, with each item modulo 12, to avoid 4 modulo operations per value calculation. */
+ int m_PermMod12[512];
+};
+
+
+
+