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Copyright (c) 2008, Casey Duncan (casey dot duncan at gmail dot com) z1.2.1)floorfmodsqrt)randint)rrrr)rr r)r r r)rrr)r rr)rrr )r rr )rrrrr r)rrr rr r rr r r ) )rrrr)rrrr )rrr r)rrr r )rr rr)rr rr )rr r r)rr r r )rrrr)rrrr )rrr r)rrr r )r rrr)r rrr )r rr r)r rr r )rrrr)rrrr )rr rr)rr rr )r rrr)r rrr )r r rr)r r rr )rrrr)rrr r)rr rr)rr r r)r rrr)r rr r)r r rr)r r r r)@)rr)rrrr rrrr)rr rrrrr)rr rr)rr rrr)rrrr )rrr rrrr)rrr rrrrrrrrr)rr rrr)rrrr rrr)r rrr)r rrr)rrr r)rrrr rrr)r rrrr)r rrrrrrrrrrr)r rrrrrr)rrrr )rrr rr)rrr r)r rrrrrr)rrrr r)rr rr)rr rr?@?g@gUUUUUU?gUUUUUU?([Z _`5$gEc% xKr>^u# 9!X8W}DJG0MSoz<i\)7.(f6A?rPILYtVdmr@4|{&v~RU;/:*wr ,Fe+ 'rblnOqpha" Q3k1jTsy2-]rCHNB=c:eZdZdZeeZedzZddZddZ y) BaseNoisezNoise abstract base classr Nc| | td||j|y|$t|dz|_t ||_yy)aInitialize the noise generator. With no arguments, the default period and permutation table are used (256). The default permutation table generates the exact same noise pattern each time. An integer period can be specified, to generate a random permutation table with period elements. The period determines the (integer) interval that the noise repeats, which is useful for creating tiled textures. period should be a power-of-two, though this is not enforced. Note that the speed of the noise algorithm is independent of the period size, though larger periods mean a larger table, which consume more memory. A permutation table consisting of an iterable sequence of whole numbers can be specified directly. This should have a power-of-two length. Typical permutation tables are a sequence of unique integers in the range [0,period) in random order, though other arrangements could prove useful, they will not be "pure" simplex noise. The largest element in the sequence must be no larger than period-1. period and permutation_table may not be specified together. Nz8Can specify either period or permutation_table, not bothr ) ValueError randomizetuple permutationlenperiod)selfrpermutation_tables V/var/www/html/public_html/myphp/venv/lib/python3.12/site-packages/ezdxf/math/perlin.py__init__zBaseNoise.__init__^s_,  "3"?J    NN6 "  *$%67!;D /0DK+c|||_tt|j}|jdz }t|D]}td|}||||c||<||<!t |dz|_y)zRandomize the permutation table used by the noise functions. This makes them generate a different noise pattern for the same inputs. Nrrr )rlistrangerrr)rrperm perm_rightijs rrzBaseNoise.randomize~s~   DKE$++&'[[1_ d 0A:&A#AwQ DGT!W 0!;?r)NNN) __name__ __module__ __qualname____doc__r _permutationrrrrrrrrXs$#  F"K1@ +rrceZdZdZdZdZy) SimplexNoiseaPerlin 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." cD||ztz}t||z}t||z}||ztz}|||z z }|||z z }||kDrd} d} nd} d} || z tz} || z tz} |tdzzdz } |tdzzdz }|j}t ||j z}t ||j z}||||zdz}||| z||| zzdz}||dz||dzzdz}d|dzz |dzz }|dkDr!t |}|dz|d|z|d|zzz}nd }d| dzz | dzz }|dkDr#t |}||dz|d| z|d| zzzz }d| dzz |dzz }|dkDr#t |}||dz|d| z|d|zzzz }|d zS) z2D 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). rr@rrrr rgQ@)_F2r_G2rintr_GRAD3)rxysr!r"tx0y0i1j1x1y1x2y2riijjgi0gi1gi2ttgnoises rnoise2zSimplexNoise.noise2s.UcM !a%L !a%L UcM !a%[ !a%[ 7BBBB "Ws] "Ws] sNS  #)^c ! Vdkk ! Vdkk !2R=!B&27T"r']*+b026DaL()B.27]R1W $ 6s A!Gqtby1Q4"945EE 27]R1W $ 6s A R1W!r AaD2I 56 6E 27]R1W $ 6s A R1W!r AaD2I 56 6Et|rc>||z|ztz}t||z}t||z}t||z}||z|ztz}|||z z } |||z z } |||z z } | | k\r1| | k\r d} d} d}d}d}d}nO| | k\r d} d} d}d}d}d}n=d} d} d}d}d}d}n0| | kr d} d} d}d}d}d}n| | kr d} d} d}d}d}d}n d} d} d}d}d}d}| | z tz}| | z tz}| |z tz}| |z dtzz}| |z dtzz}| |z dtzz}| dz dtzz}| dz dtzz}| dz dtzz}|j}t ||j z}t ||j z}t ||j z}||||||zzdz}||| z||| z|||zzzdz} |||z|||z|||zzzdz}!||dz||dz||dzzzdz}"d}#d| d zz | d zz | d zz }$|$dkDr*t |}%|$d z|%d| z|%d| zz|%d | zzz}#nd}#d|d zz |d zz |d zz }$|$dkDr,t | }%|#|$d z|%d|z|%d|zz|%d |zzzz }#d|d zz |d zz |d zz }$|$dkDr,t |!}%|#|$d z|%d|z|%d|zz|%d |zzzz }#d|d zz |d zz |d zz }$|$dkDr,t |"}%|#|$d z|%d|z|%d|zz|%d |zzzz }#|#d zS) z3D 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). rrr-rrrr.g333333?r rg@@)_F3r_G3rr1rr2)&rr3r4zr5r!r"kr6r7r8z0r9r:k1i2j2k2r;r<z1r=r>z2x3y3z3rr?r@kkrArBrCgi3rFrDrEs& rnoise3zSimplexNoise.noise3ssUQY#  !a%L !a%L !a%L UQY#  !a%[ !a%[ !a%[ 8RxrBwb"Ws] "Ws] "Ws] "WsSy  "WsSy  "WsSy  #Xc ! #Xc ! #Xc ! Vdkk ! Vdkk ! Vdkk !2R$r(]++,r127T"r'DbM"9::;b@27T"r'DbM"9::;b@26Da$rAv,!67782= 27]R1W $rQw . 6s A!Gqtby1Q4"94qtby@AEE 27]R1W $rQw . 6s A R1W!r AaD2I 5!r AB BE 27]R1W $rQw . 6s A R1W!r AaD2I 5!r AB BE 27]R1W $rQw . 6s A R1W!r AaD2I 5!r AB BEt|rN)r$r%r&r'rGrYr)rrr+r+s67rmrr+c||||z zzSr#r))r6abs rlerpr]Qs qAE{?rcNt|dz}||dz||dzz||dzzS)Nrrrr )r2)hashr3r4rKrEs rgrad3r`Us8tbyA qt8a!A$h QqT ))rceZdZdZddZy) TileableNoisezTileable implementation of Perlin "improved" noise. This is based on the reference implementation published here: http://mrl.nyu.edu/~perlin/noise/ cdttt||}ttt||}ttt||}|dz|z} |dz|z} |dz|z} |r||z }||z }||z }| |z } | |z } | |z } |t|z}|t|z}|t|z}|dz||dzdz zdzz} |dz||dzdz zdzz} |dz||dzdz zdzz}|j}||}|||z}||| z}|| }|||z}||| z}t |t | t | t |||z|||t |||z|dz ||t | t |||z||dz |t |||z|dz |dz |t | t | t ||| z|||dz t ||| z|dz ||dz t | t ||| z||dz |dz t ||| z|dz |dz |dz S)zTileable 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. rrr1rr.)r1rrrr]r`)rr3r4rKrepeatbaser!r"rLr?r@rWfxfyfzrAAAABBBABBs rrYzTileableNoise.noise3as U1Xv& ' U1Xv& ' U1Xv& '!ev !ev !ev   IA IA IA $JB $JB $JB U1X  U1X  U1X  !VqAEBJ'", - !VqAEBJ'", - !VqAEBJ'", - G !a%[ !b&\ H !a%[ !b&\  $rAv,1a0$rAv,Aq!4 $rAv,1q5!4$rAv,Aq1ua8  $rBw-Aq1u5$rBw-Q1q59 $rBw-AE1q59$rBw-QAq1u=   rN)r.)r$r%r&r'rYr)rrrbrbZs  B rrbN)r' __version__mathrrrrandomrr2_GRAD4_SIMPLEXr/r0rIrJr(rr+r]r`rb_simplexrGsnoise2rYsnoise3 _tileabletnoise3r)rrrys ""   " T#Y_ T#Y# ,1+1+hB9BJ* I II X > // // O   r