Changeset 2121


Ignore:
Timestamp:
Dec 6, 2007, 11:45:55 PM (12 years ago)
Author:
Sam Hocevar
Message:
  • A lot more non-rectangular tiles. With a few nice results.
Location:
www/study
Files:
16 added
4 deleted
10 edited
8 copied

Legend:

Unmodified
Added
Removed
  • www/study/fig2-5-3.svg

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  • www/study/fig2-6-1.svg

    r2120 r2121  
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  • www/study/fig2-6-2.svg

    r2120 r2121  
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  • www/study/part2.html

    r2115 r2121  
    4040
    4141<p> Observe the following patterns. From a certain distance or assuming small
    42 enough pixels, they look like shades of gray despite being made of only black
     42enough pixels, they look like shades of grey despite being made of only black
    4343and white pixels: </p>
    4444
     
    5757
    5858<p> This looks promising. Let’s try immediately on Lenna: we will use the
    59 5-colour thresholding picture and replace the 0.25, 0.5 and 0.75 gray values
     595-colour thresholding picture and replace the 0.25, 0.5 and 0.75 grey values
    6060with the above patterns: </p>
    6161
     
    7575
    7676<p> If your screen’s quality is not very good, you might experience slightly
    77 different shades of gray for the following patterns, despite being made of 50%
     77different shades of grey for the following patterns, despite being made of 50%
    7878black and 50% white pixels: </p>
    7979
     
    8787eye and don't create artifacts is a crucial element of a dithering
    8888algorithm. Here is another example of two patterns that approximate to
    89 the same shade of gray but may look slightly different from a distance: </p>
     89the same shade of grey but may look slightly different from a distance: </p>
    9090
    9191<p style="text-align: center;">
     
    109109thresholded with a value of 0.8, and so on, resulting in the image seen
    110110in 2.1. Here is a sample of what happens to groups of 4 even-coloured pixels
    111 of various gray values: </p>
     111of various grey values: </p>
    112112
    113113<p style="text-align: center;">
     
    264264</p>
    265265
    266 <p> Just like Bayer matrices, these tiles can be used to recursively create
    267 bigger patterns: </p>
    268 
    269 <p style="text-align: center;">
    270   <img src="fig2-5-3.png" width="270" height="240"
     266<p style="text-align: center;">
     267  <img src="fig2-5-3.png" width="270" height="210"
     268       class="matrix" alt="square dither tile" />
     269  <img src="out2-5-3.png" width="256" height="256"
     270       class="inline" alt="square dithering" />
     271  <img src="grad2-5-3.png" width="32" height="256"
     272       class="inline" alt="square dithering gradient" />
     273</p>
     274
     275<p style="text-align: center;">
     276  <img src="fig2-5-4.png" width="240" height="210"
     277       class="matrix" alt="hex2 dither tile" />
     278  <img src="out2-5-4.png" width="256" height="256"
     279       class="inline" alt="hex2 dithering" />
     280  <img src="grad2-5-4.png" width="32" height="256"
     281       class="inline" alt="hex2 dithering gradient" />
     282</p>
     283
     284<h3> 2.6. Recursive generation of dither matrices </h3>
     285
     286<p> Just like Bayer matrices, non-rectangular tiles can be used to recursively
     287create bigger patterns, giving finer results. The amount of shades of grey
     288that can be rendered using a given tile is the number of cells in the tile
     289plus one: </p>
     290
     291<p style="text-align: center;">
     292  <img src="fig2-6-1.png" width="270" height="240"
    271293       class="matrix" alt="4-wise cross dither tile" />
    272   <img src="out2-5-3.png" width="256" height="256"
     294  <img src="out2-6-1.png" width="256" height="256"
    273295       class="inline" alt="4-wise cross dithering" />
    274   <img src="grad2-5-3.png" width="32" height="256"
     296  <img src="grad2-6-1.png" width="32" height="256"
    275297       class="inline" alt="4-wise cross dithering gradient" />
    276298</p>
    277299
    278300<p style="text-align: center;">
    279   <img src="fig2-5-4.png" width="270" height="240"
     301  <img src="fig2-6-2.png" width="270" height="240"
    280302       class="matrix" alt="3-wise hex dither tile" />
    281   <img src="out2-5-4.png" width="256" height="256"
     303  <img src="out2-6-2.png" width="256" height="256"
    282304       class="inline" alt="3-wise hex dithering" />
    283   <img src="grad2-5-4.png" width="32" height="256"
     305  <img src="grad2-6-2.png" width="32" height="256"
    284306       class="inline" alt="3-wise hex dithering gradient" />
     307</p>
     308
     309<p style="text-align: center;">
     310  <img src="fig2-6-3.png" width="300" height="250"
     311       class="matrix" alt="4-wise square dither tile" />
     312  <img src="out2-6-3.png" width="256" height="256"
     313       class="inline" alt="4-wise square dithering" />
     314  <img src="grad2-6-3.png" width="32" height="256"
     315       class="inline" alt="4-wise square dithering gradient" />
     316</p>
     317
     318<p> Victor Ostromoukhov created a method called <b>CombiScreen</b> allowing
     319for unlimited recursive tile creation. </p>
     320
     321<p> This example shows a tile resembling a Davis-Knuth dragon curve. Though
     322the tile itself is beautiful, the results are not very different from a
     323classic Bayer dither matrix: </p>
     324
     325<p style="text-align: center;">
     326  <img src="fig2-6-4.png" width="325" height="250"
     327       class="matrix" alt="twin dragon dither tile" />
     328  <img src="out2-6-4.png" width="256" height="256"
     329       class="inline" alt="twin dragon dithering" />
     330  <img src="grad2-6-4.png" width="32" height="256"
     331       class="inline" alt="twin dragon dithering gradient" />
     332</p>
     333
     334<p> Here are two consecutive iterations of the hexagonal tiling shown
     335above: </p>
     336
     337<p style="text-align: center;">
     338  <img src="fig2-6-5.png" width="240" height="210"
     339       class="matrix" alt="3-way hex2 dither tile" />
     340  <img src="out2-6-5.png" width="256" height="256"
     341       class="inline" alt="3-way hex2 dithering" />
     342  <img src="grad2-6-5.png" width="32" height="256"
     343       class="inline" alt="3-way hex2 dithering gradient" />
     344</p>
     345
     346<p style="text-align: center;">
     347  <img src="fig2-6-6.png" width="280" height="240"
     348       class="matrix" alt="9-way hex2 dither tile" />
     349  <img src="out2-6-6.png" width="256" height="256"
     350       class="inline" alt="9-way hex2 dithering" />
     351  <img src="grad2-6-6.png" width="32" height="256"
     352       class="inline" alt="9-way hex2 dithering gradient" />
    285353</p>
    286354
  • www/study/study.py

    r2120 r2121  
    497497# Output 2.5.1: cross pattern
    498498# Output 2.5.2: hex pattern
    499 # Output 2.5.3: 4-wise cross pattern
    500 # Output 2.5.4: 3-wise hex pattern
     499# Output 2.5.3: square pattern
    501500def test25x(src, mat, vec):
    502501    # 1. count non-zero pixels
     
    546545    test25x(lenna256bw, mat, vec).save("out2-5-2.png")
    547546    test25x(gradient256bw, mat, vec).save("grad2-5-2.png")
     547    mat = [[ 0,  0,  0,  8,  0],
     548           [ 0,  3,  7, 10,  9],
     549           [ 4,  1,  2,  6,  0],
     550           [ 0,  5,  0,  0,  0]]
     551    vec = [(2, 4), (3, 1)]
     552    test25x(lenna256bw, mat, vec).save("out2-5-3.png")
     553    test25x(gradient256bw, mat, vec).save("grad2-5-3.png")
     554    mat = [[ 0,  0,  3,  0],
     555           [ 1,  2,  4,  9],
     556           [ 6,  5,  8,  7],
     557           [ 0, 10,  0,  0]]
     558    vec = [(2, 2), (0, 5)]
     559    test25x(lenna256bw, mat, vec).save("out2-5-4.png")
     560    test25x(gradient256bw, mat, vec).save("grad2-5-4.png")
     561
     562# Output 2.6.1: 4-wise cross pattern
     563# Output 2.6.2: 3-wise hex pattern
     564# Output 2.6.3: 4-wise square pattern
     565if chapter(2):
    548566    mat = [[ 0,  0,  0, 19,  0,  0],
    549567           [ 0, 17, 15,  3,  7,  0],
     
    553571           [ 0,  0, 12,  0,  0,  0]]
    554572    vec = [(4, -2), (2, 4)]
    555     test25x(lenna256bw, mat, vec).save("out2-5-3.png")
    556     test25x(gradient256bw, mat, vec).save("grad2-5-3.png")
     573    test25x(lenna256bw, mat, vec).save("out2-6-1.png")
     574    test25x(gradient256bw, mat, vec).save("grad2-6-1.png")
    557575    mat = [[ 0, 13,  7,  0,  0,  0,  0],
    558576           [19,  1, 16, 10, 15,  9,  0],
     
    562580           [ 0,  0, 23,  5,  0,  0,  0]]
    563581    vec = [(5, -1), (-1, 5)]
    564     test25x(lenna256bw, mat, vec).save("out2-5-4.png")
    565     test25x(gradient256bw, mat, vec).save("grad2-5-4.png")
     582    test25x(lenna256bw, mat, vec).save("out2-6-2.png")
     583    test25x(gradient256bw, mat, vec).save("grad2-6-2.png")
     584    mat = [[ 0,  0,  0,  0, 31,  0,  0,  0,  0],
     585           [ 0,  0, 11, 27, 39, 35,  0, 30,  0],
     586           [ 0, 15,  3,  7, 23, 10, 26, 38, 34],
     587           [ 0,  0, 19, 29, 14,  2,  6, 22,  0],
     588           [ 0,  9, 25, 37, 33, 18, 32,  0,  0],
     589           [13,  1,  5, 21, 12, 28, 40, 36,  0],
     590           [ 0, 17,  0, 16,  4,  8, 24,  0,  0],
     591           [ 0,  0,  0,  0, 20,  0,  0,  0,  0]]
     592    vec = [(6, 2), (-2, 6)]
     593    test25x(lenna256bw, mat, vec).save("out2-6-3.png")
     594    test25x(gradient256bw, mat, vec).save("grad2-6-3.png")
     595    mat = [[ 0,  0,  4, 36,  0,  0,  2, 34,  0,  0,  0,  0,  0],
     596           [ 0,  0,  0, 20, 52,  0,  0, 18, 50,  0,  0,  0,  0],
     597           [ 8, 40, 12, 44,  6, 38, 10, 42,  0,  0,  0,  0,  0],
     598           [ 0, 24, 56, 28, 60, 22, 54, 26, 58,  0,  0,  0,  0],
     599           [16, 48,  0,  0, 14, 46,  3, 35,  0,  0,  1, 33,  0],
     600           [ 0, 32, 64,  0,  0, 30, 62, 19, 51,  0,  0, 17, 49],
     601           [ 0,  0,  0,  0,  7, 39, 11, 43,  5, 37,  9, 41,  0],
     602           [ 0,  0,  0,  0,  0, 23, 55, 27, 59, 21, 53, 25, 57],
     603           [ 0,  0,  0,  0, 15, 47,  0,  0, 13, 45,  0,  0,  0],
     604           [ 0,  0,  0,  0,  0, 31, 63,  0,  0, 29, 61,  0,  0]]
     605    vec = [(8, 0), (0, 8)]
     606    test25x(lenna256bw, mat, vec).save("out2-6-4.png")
     607    test25x(gradient256bw, mat, vec).save("grad2-6-4.png")
     608    mat = [[  0,  0,  0,  0,  0,  0,  9,  0],
     609           [  0,  0,  7,  0,  3,  6, 12, 27],
     610           [  1,  4, 10, 25, 18, 15, 24, 21],
     611           [ 16, 13, 22, 19,  8, 30,  0,  0],
     612           [  0, 28,  2,  5, 11, 26,  0,  0],
     613           [  0,  0, 17, 14, 23, 20,  0,  0],
     614           [  0,  0,  0, 29,  0,  0,  0,  0]]
     615    vec = [(6, 1), (0, 5)]
     616    test25x(lenna256bw, mat, vec).save("out2-6-5.png")
     617    test25x(gradient256bw, mat, vec).save("grad2-6-5.png")
     618    mat = [[  0,  0,  0,  0,  0,  0, 25,  0,  0,  0,  0,  0,  0,  0],
     619           [  0,  0, 19,  0,  7, 16, 34, 79,  0,  0,  0,  0, 27,  0],
     620           [  1, 10, 28, 73, 52, 43, 70, 61, 21,  0,  9, 18, 36, 81],
     621           [ 46, 37, 64, 55, 22, 88,  3, 12, 30, 75, 54, 45, 72, 63],
     622           [  0, 82,  4, 13, 31, 76, 48, 39, 66, 57, 24, 90,  0,  0],
     623           [  0,  0, 49, 40, 67, 58, 26, 84,  6, 15, 33, 78,  0,  0],
     624           [  0,  0, 20, 85,  8, 17, 35, 80, 51, 42, 69, 60,  0,  0],
     625           [  2, 11, 29, 74, 53, 44, 71, 62,  0, 87,  0,  0,  0,  0],
     626           [ 47, 38, 65, 56, 23, 89,  0,  0,  0,  0,  0,  0,  0,  0],
     627           [  0, 83,  5, 14, 32, 77,  0,  0,  0,  0,  0,  0,  0,  0],
     628           [  0,  0, 50, 41, 68, 59,  0,  0,  0,  0,  0,  0,  0,  0],
     629           [  0,  0,  0, 86,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0]]
     630    test25x(lenna256bw, mat, vec).save("out2-6-6.png")
     631    test25x(gradient256bw, mat, vec).save("grad2-6-6.png")
    566632
    567633##############################################################################
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