Task: Perlin noise







Python: import math

def perlin_noise(x, y, z):
    X = math.floor(x) & 255                  
    Y = math.floor(y) & 255                  
    Z = math.floor(z) & 255
    x -= math.floor(x)                                
    y -= math.floor(y)                                
    z -= math.floor(z)
    u = fade(x)                                
    v = fade(y)                                
    w = fade(z)
    A = p[X  ]+Y; AA = p[A]+Z; AB = p[A+1]+Z      
    B = p[X+1]+Y; BA = p[B]+Z; BB = p[B+1]+Z      
 
    return lerp(w, lerp(v, lerp(u, grad(p[AA  ], x  , y  , z   ),  
                                   grad(p[BA  ], x-1, y  , z   )), 
                           lerp(u, grad(p[AB  ], x  , y-1, z   ),  
                                   grad(p[BB  ], x-1, y-1, z   ))),
                   lerp(v, lerp(u, grad(p[AA+1], x  , y  , z-1 ),  
                                   grad(p[BA+1], x-1, y  , z-1 )), 
                           lerp(u, grad(p[AB+1], x  , y-1, z-1 ),
                                   grad(p[BB+1], x-1, y-1, z-1 ))))
                                   
def fade(t): 
    return t ** 3 * (t * (t * 6 - 15) + 10)
    
def lerp(t, a, b):
    return a + t * (b - a)
    
def grad(hash, x, y, z):
    h = hash & 15                      
    u = x if h<8 else y                
    v = y if h<4 else (x if h in (12, 14) else z)
    return (u if (h&1) == 0 else -u) + (v if (h&2) == 0 else -v)

p = [None] * 512
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, 19,98,108,110,79,113,224,232,178,185, 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]
for i in range(256):
    p[256+i] = p[i] = permutation[i]

if __name__ == '__main__':
    print("%1.17f" % perlin_noise(3.14, 42, 7))




Fortran: PROGRAM PERLIN
IMPLICIT NONE
INTEGER :: i
INTEGER, DIMENSION(0:511) :: p
INTEGER, DIMENSION(0:255), PARAMETER :: 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, 19,98,108,110,79,113,224,232,178,185, 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/)

DO i=0, 255
    p(i) = permutation(i)
    p(256+i) = permutation(i)
END DO

WRITE(*,"(F19.17)") NOISE(3.14d0, 42d0, 7d0)

CONTAINS

DOUBLE PRECISION FUNCTION NOISE(x_in, y_in, z_in)
    DOUBLE PRECISION, INTENT(IN) :: x_in, y_in, z_in
    DOUBLE PRECISION :: x, y, z
    INTEGER :: xx, yy, zz, a, aa, ab, b, ba, bb
    DOUBLE PRECISION :: u, v, w

    x = x_in
    y = y_in
    z = z_in

    xx = IAND(FLOOR(x), 255)
    yy = IAND(FLOOR(y), 255)
    zz = IAND(FLOOR(z), 255)

    x = x - FLOOR(x)
    y = y - FLOOR(y)
    z = z - FLOOR(z)

    u = FADE(x)
    v = FADE(y)
    w = FADE(z)

    a  = p(xx)   + yy
    aa = p(a)    + zz
    ab = p(a+1)  + zz
    b  = p(xx+1) + yy
    ba = p(b)    + zz
    bb = p(b+1)  + zz

    NOISE = LERP(w, LERP(v, LERP(u, GRAD(p(aa),   x,   y,   z),     &
                                    GRAD(p(ba),   x-1, y,   z)),    &
                            LERP(u, GRAD(p(ab),   x,   y-1, z),     &
                                    GRAD(p(bb),   x-1, y-1, z))),   &
                    LERP(v, LERP(u, GRAD(p(aa+1), x,   y,   z-1),   &
                                    GRAD(p(ba+1), x-1, y,   z-1)),  &
                            LERP(u, GRAD(p(ab+1), x,   y-1, z-1),   &
                                    GRAD(p(bb+1), x-1, y-1, z-1))))
END FUNCTION


DOUBLE PRECISION FUNCTION FADE(t)
    DOUBLE PRECISION, INTENT(IN) :: t

    FADE = t ** 3 * (t * ( t * 6 - 15) + 10)
END FUNCTION


DOUBLE PRECISION FUNCTION LERP(t, a, b)
    DOUBLE PRECISION, INTENT(IN) :: t, a, b

    LERP = a + t * (b - a)
END FUNCTION


DOUBLE PRECISION FUNCTION GRAD(hash, x, y, z)
    INTEGER, INTENT(IN) :: hash
    DOUBLE PRECISION, INTENT(IN) :: x, y, z
    INTEGER :: h
    DOUBLE PRECISION :: u, v

    h = IAND(hash, 15)

    u = MERGE(x, y, h < 8)

    v = MERGE(y, MERGE(x, z, h == 12 .OR. h == 14), h < 4)

    GRAD = MERGE(u, -u, IAND(h, 1) == 0) + MERGE(v, -v, IAND(h, 2) == 0)
END FUNCTION


END PROGRAM