I'm reading through this explanation of Perlin noise which describes a hash function that is calculates random points for all x, y coordinates.
If the x, y coordinate hashes are generated randomly which are eventually used for computing the gradient's and such, why couldn't I just generate random numbers on the fly?
Is it simply a question of optimization that we use a permutation on hash maps to find our random values? The only reason I could think of is that permutations through our hash map some how generates a smoothening effect but I fail to see how.
Just for clarification, I'm refering to this section in the code:
private static readonly int[] p = { 151,160,137,91,90,15, // Hash lookup table as defined by Ken Perlin. This is a randomly
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, // arranged array of all numbers from 0-255 inclusive.
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
};
int aaa, aba, aab, abb, baa, bba, bab, bbb;
aaa = p[p[p[ xi ]+ yi ]+ zi ];
aba = p[p[p[ xi ]+inc(yi)]+ zi ];
aab = p[p[p[ xi ]+ yi ]+inc(zi)];
abb = p[p[p[ xi ]+inc(yi)]+inc(zi)];
baa = p[p[p[inc(xi)]+ yi ]+ zi ];
bba = p[p[p[inc(xi)]+inc(yi)]+ zi ];
bab = p[p[p[inc(xi)]+ yi ]+inc(zi)];
bbb = p[p[p[inc(xi)]+inc(yi)]+inc(zi)];
Why don't we just initialize the values as follows?
aaa = random(255)
aab = random(255)
// ...