# Copyright (c) 2008, Casey Duncan (casey dot duncan at gmail dot com)
# see LICENSE.txt for details
"""Noise functions for procedural generation of content

Contains native code implementations of Perlin improved noise (with
fBm capabilities) and Perlin simplex noise. Also contains a fast
"fake noise" implementation in GLSL for execution in shaders.

Copyright (c) 2008, Casey Duncan (casey dot duncan at gmail dot com)
"""
__version__ = "1.2.1"

from math import floor, fmod, sqrt
from random import randint

# 3D Gradient vectors
# fmt: off
_GRAD3 = (
    (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),
    (1, 1, 0), (0, -1, 1), (-1, 1, 0), (0, -1, -1),
)
# fmt: on

# 4D Gradient vectors
# fmt: off
_GRAD4 = (
    (0, 1, 1, 1), (0, 1, 1, -1), (0, 1, -1, 1), (0, 1, -1, -1),
    (0, -1, 1, 1), (0, -1, 1, -1), (0, -1, -1, 1), (0, -1, -1, -1),
    (1, 0, 1, 1), (1, 0, 1, -1), (1, 0, -1, 1), (1, 0, -1, -1),
    (-1, 0, 1, 1), (-1, 0, 1, -1), (-1, 0, -1, 1), (-1, 0, -1, -1),
    (1, 1, 0, 1), (1, 1, 0, -1), (1, -1, 0, 1), (1, -1, 0, -1),
    (-1, 1, 0, 1), (-1, 1, 0, -1), (-1, -1, 0, 1), (-1, -1, 0, -1),
    (1, 1, 1, 0), (1, 1, -1, 0), (1, -1, 1, 0), (1, -1, -1, 0),
    (-1, 1, 1, 0), (-1, 1, -1, 0), (-1, -1, 1, 0), (-1, -1, -1, 0)
)
# fmt: on

# A lookup table to traverse the simplex around a given point in 4D. 
# Details can be found where this table is used, in the 4D noise method.
# fmt: off
_SIMPLEX = (
    (0, 1, 2, 3), (0, 1, 3, 2), (0, 0, 0, 0), (0, 2, 3, 1), (0, 0, 0, 0),
    (0, 0, 0, 0), (0, 0, 0, 0), (1, 2, 3, 0), (0, 2, 1, 3), (0, 0, 0, 0),
    (0, 3, 1, 2), (0, 3, 2, 1), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0),
    (1, 3, 2, 0), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0),
    (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0), (1, 2, 0, 3),
    (0, 0, 0, 0), (1, 3, 0, 2), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0),
    (2, 3, 0, 1), (2, 3, 1, 0), (1, 0, 2, 3), (1, 0, 3, 2), (0, 0, 0, 0),
    (0, 0, 0, 0), (0, 0, 0, 0), (2, 0, 3, 1), (0, 0, 0, 0), (2, 1, 3, 0),
    (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0),
    (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0), (2, 0, 1, 3), (0, 0, 0, 0),
    (0, 0, 0, 0), (0, 0, 0, 0), (3, 0, 1, 2), (3, 0, 2, 1), (0, 0, 0, 0),
    (3, 1, 2, 0), (2, 1, 0, 3), (0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 0, 0),
    (3, 1, 0, 2), (0, 0, 0, 0), (3, 2, 0, 1), (3, 2, 1, 0)
)
# fmt: on
# Simplex skew constants
_F2 = 0.5 * (sqrt(3.0) - 1.0)
_G2 = (3.0 - sqrt(3.0)) / 6.0
_F3 = 1.0 / 3.0
_G3 = 1.0 / 6.0

# fmt: off
_permutation = (
    151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225,
    140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247,
    120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57,
    177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74,
    165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122,
    60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54,
    65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169,
    200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3,
    64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85,
    212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170,
    213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43,
    172, 9, 129, 22, 39, 253, 9, 98, 108, 110, 79, 113, 224, 232, 178, 185,
    112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191,
    179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31,
    181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150,
    254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195,
    78, 66, 215, 61, 156, 180
)
# fmt: on


class BaseNoise:
    """Noise abstract base class"""
    period = len(_permutation)
    # Double permutation array so we don't need to wrap
    permutation = _permutation * 2

    def __init__(self, period=None, permutation_table=None):
        """Initialize the noise generator. With no arguments, the default
        period and permutation table are used (256). The default permutation
        table generates the exact same noise pattern each time.

        An integer period can be specified, to generate a random permutation
        table with period elements. The period determines the (integer)
        interval that the noise repeats, which is useful for creating tiled
        textures.  period should be a power-of-two, though this is not
        enforced. Note that the speed of the noise algorithm is independent of
        the period size, though larger periods mean a larger table, which
        consume more memory.

        A permutation table consisting of an iterable sequence of whole
        numbers can be specified directly. This should have a power-of-two
        length. Typical permutation tables are a sequence of unique integers in
        the range [0,period) in random order, though other arrangements could
        prove useful, they will not be "pure" simplex noise. The largest
        element in the sequence must be no larger than period-1.

        period and permutation_table may not be specified together.
        """
        if period is not None and permutation_table is not None:
            raise ValueError(
                "Can specify either period or permutation_table, not both"
            )
        if period is not None:
            self.randomize(period)
        elif permutation_table is not None:
            self.permutation = tuple(permutation_table) * 2
            self.period = len(permutation_table)

    def randomize(self, period=None):
        """Randomize the permutation table used by the noise functions. This
        makes them generate a different noise pattern for the same inputs.
        """
        if period is not None:
            self.period = period
        perm = list(range(self.period))
        perm_right = self.period - 1
        for i in list(perm):
            j = randint(0, perm_right)
            perm[i], perm[j] = perm[j], perm[i]
        self.permutation = tuple(perm) * 2


class SimplexNoise(BaseNoise):
    """Perlin simplex noise generator

    Adapted from Stefan Gustavson's Java implementation described here:

    http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf

    To summarize:

    "In 2001, Ken Perlin presented 'simplex noise', a replacement for his classic
    noise algorithm.  Classic 'Perlin noise' won him an academy award and has
    become an ubiquitous procedural primitive for computer graphics over the
    years, but in hindsight it has quite a few limitations.  Ken Perlin himself
    designed simplex noise specifically to overcome those limitations, and he
    spent a lot of good thinking on it. Therefore, it is a better idea than his
    original algorithm. A few of the more prominent advantages are:

    * Simplex noise has a lower computational complexity and requires fewer
      multiplications.
    * Simplex noise scales to higher dimensions (4D, 5D and up) with much less
      computational cost, the complexity is O(N) for N dimensions instead of
      the O(2^N) of classic Noise.
    * Simplex noise has no noticeable directional artifacts.  Simplex noise has
      a well-defined and continuous gradient everywhere that can be computed
      quite cheaply.
    * Simplex noise is easy to implement in hardware."
    """

    def noise2(self, x, y):
        """2D Perlin simplex noise.

        Return a floating point value from -1 to 1 for the given x, y coordinate.
        The same value is always returned for a given x, y pair unless the
        permutation table changes (see randomize above).
        """
        # Skew input space to determine which simplex (triangle) we are in
        s = (x + y) * _F2
        i = floor(x + s)
        j = floor(y + s)
        t = (i + j) * _G2
        x0 = x - (i - t)  # "Unskewed" distances from cell origin
        y0 = y - (j - t)

        if x0 > y0:
            i1 = 1
            j1 = 0  # Lower triangle, XY order: (0,0)->(1,0)->(1,1)
        else:
            i1 = 0
            j1 = 1  # Upper triangle, YX order: (0,0)->(0,1)->(1,1)

        x1 = x0 - i1 + _G2  # Offsets for middle corner in (x,y) unskewed coords
        y1 = y0 - j1 + _G2
        x2 = (
            x0 + _G2 * 2.0 - 1.0
        )  # Offsets for last corner in (x,y) unskewed coords
        y2 = y0 + _G2 * 2.0 - 1.0

        # Determine hashed gradient indices of the three simplex corners
        perm = self.permutation
        ii = int(i) % self.period
        jj = int(j) % self.period
        gi0 = perm[ii + perm[jj]] % 12
        gi1 = perm[ii + i1 + perm[jj + j1]] % 12
        gi2 = perm[ii + 1 + perm[jj + 1]] % 12

        # Calculate the contribution from the three corners
        tt = 0.5 - x0 ** 2 - y0 ** 2
        if tt > 0:
            g = _GRAD3[gi0]
            noise = tt ** 4 * (g[0] * x0 + g[1] * y0)
        else:
            noise = 0.0

        tt = 0.5 - x1 ** 2 - y1 ** 2
        if tt > 0:
            g = _GRAD3[gi1]
            noise += tt ** 4 * (g[0] * x1 + g[1] * y1)

        tt = 0.5 - x2 ** 2 - y2 ** 2
        if tt > 0:
            g = _GRAD3[gi2]
            noise += tt ** 4 * (g[0] * x2 + g[1] * y2)

        return noise * 70.0  # scale noise to [-1, 1]

    def noise3(self, x, y, z):
        """3D Perlin simplex noise.

        Return a floating point value from -1 to 1 for the given x, y, z coordinate.
        The same value is always returned for a given x, y, z pair unless the
        permutation table changes (see randomize above).
        """
        # Skew the input space to determine which simplex cell we're in
        s = (x + y + z) * _F3
        i = floor(x + s)
        j = floor(y + s)
        k = floor(z + s)
        t = (i + j + k) * _G3
        x0 = x - (i - t)  # "Unskewed" distances from cell origin
        y0 = y - (j - t)
        z0 = z - (k - t)

        # For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        # Determine which simplex we are in.
        if x0 >= y0:
            if y0 >= z0:
                i1 = 1
                j1 = 0
                k1 = 0
                i2 = 1
                j2 = 1
                k2 = 0
            elif x0 >= z0:
                i1 = 1
                j1 = 0
                k1 = 0
                i2 = 1
                j2 = 0
                k2 = 1
            else:
                i1 = 0
                j1 = 0
                k1 = 1
                i2 = 1
                j2 = 0
                k2 = 1
        else:  # x0 < y0
            if y0 < z0:
                i1 = 0
                j1 = 0
                k1 = 1
                i2 = 0
                j2 = 1
                k2 = 1
            elif x0 < z0:
                i1 = 0
                j1 = 1
                k1 = 0
                i2 = 0
                j2 = 1
                k2 = 1
            else:
                i1 = 0
                j1 = 1
                k1 = 0
                i2 = 1
                j2 = 1
                k2 = 0

        # Offsets for remaining corners
        x1 = x0 - i1 + _G3
        y1 = y0 - j1 + _G3
        z1 = z0 - k1 + _G3
        x2 = x0 - i2 + 2.0 * _G3
        y2 = y0 - j2 + 2.0 * _G3
        z2 = z0 - k2 + 2.0 * _G3
        x3 = x0 - 1.0 + 3.0 * _G3
        y3 = y0 - 1.0 + 3.0 * _G3
        z3 = z0 - 1.0 + 3.0 * _G3

        # Calculate the hashed gradient indices of the four simplex corners
        perm = self.permutation
        ii = int(i) % self.period
        jj = int(j) % self.period
        kk = int(k) % self.period
        gi0 = perm[ii + perm[jj + perm[kk]]] % 12
        gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12
        gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12
        gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12

        # Calculate the contribution from the four corners
        noise = 0.0
        tt = 0.6 - x0 ** 2 - y0 ** 2 - z0 ** 2
        if tt > 0:
            g = _GRAD3[gi0]
            noise = tt ** 4 * (g[0] * x0 + g[1] * y0 + g[2] * z0)
        else:
            noise = 0.0

        tt = 0.6 - x1 ** 2 - y1 ** 2 - z1 ** 2
        if tt > 0:
            g = _GRAD3[gi1]
            noise += tt ** 4 * (g[0] * x1 + g[1] * y1 + g[2] * z1)

        tt = 0.6 - x2 ** 2 - y2 ** 2 - z2 ** 2
        if tt > 0:
            g = _GRAD3[gi2]
            noise += tt ** 4 * (g[0] * x2 + g[1] * y2 + g[2] * z2)

        tt = 0.6 - x3 ** 2 - y3 ** 2 - z3 ** 2
        if tt > 0:
            g = _GRAD3[gi3]
            noise += tt ** 4 * (g[0] * x3 + g[1] * y3 + g[2] * z3)

        return noise * 32.0


def lerp(t, a, b):
    return a + t * (b - a)


def grad3(hash, x, y, z):
    g = _GRAD3[hash % 16]
    return x * g[0] + y * g[1] + z * g[2]


class TileableNoise(BaseNoise):
    """Tileable implementation of Perlin "improved" noise. This
    is based on the reference implementation published here:

    http://mrl.nyu.edu/~perlin/noise/
    """

    def noise3(self, x, y, z, repeat, base=0.0):
        """Tileable 3D noise.

        repeat specifies the integer interval in each dimension
        when the noise pattern repeats.

        base allows a different texture to be generated for
        the same repeat interval.
        """
        i = int(fmod(floor(x), repeat))
        j = int(fmod(floor(y), repeat))
        k = int(fmod(floor(z), repeat))
        ii = (i + 1) % repeat
        jj = (j + 1) % repeat
        kk = (k + 1) % repeat
        if base:
            i += base
            j += base
            k += base
            ii += base
            jj += base
            kk += base

        x -= floor(x)
        y -= floor(y)
        z -= floor(z)
        fx = x ** 3 * (x * (x * 6 - 15) + 10)
        fy = y ** 3 * (y * (y * 6 - 15) + 10)
        fz = z ** 3 * (z * (z * 6 - 15) + 10)

        perm = self.permutation
        A = perm[i]
        AA = perm[A + j]
        AB = perm[A + jj]
        B = perm[ii]
        BA = perm[B + j]
        BB = perm[B + jj]

        return lerp(
            fz,
            lerp(
                fy,
                lerp(
                    fx,
                    grad3(perm[AA + k], x, y, z),
                    grad3(perm[BA + k], x - 1, y, z),
                ),
                lerp(
                    fx,
                    grad3(perm[AB + k], x, y - 1, z),
                    grad3(perm[BB + k], x - 1, y - 1, z),
                ),
            ),
            lerp(
                fy,
                lerp(
                    fx,
                    grad3(perm[AA + kk], x, y, z - 1),
                    grad3(perm[BA + kk], x - 1, y, z - 1),
                ),
                lerp(
                    fx,
                    grad3(perm[AB + kk], x, y - 1, z - 1),
                    grad3(perm[BB + kk], x - 1, y - 1, z - 1),
                ),
            ),
        )


_simplex = SimplexNoise()
snoise2 = _simplex.noise2
snoise3 = _simplex.noise3
_tileable = TileableNoise()
tnoise3 = _tileable.noise3