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layout: post title: 几种颜色映射方案的解析式 categories:

科 tags:
颜色

2016年09月02日 21:43:51 初稿
2017年02月23日 20:30:43 补充代码

在做三维数据的填色表面图时, 需要使用颜色映射方案, 将一定范围内的数值映射成一定的颜色来显示. 可用的颜色映射方案很多很多, 但并不是所有的方案都适合用来展示数据. 我前面有篇博文数据展示：请选择好的颜色映射方案对此有些说明, 可做参考.

在这篇博文中, 我首先推荐一篇有关颜色设计的资料Good Colour Maps: How to Design Them, 供需要使用颜色映射的人参考.

传统的颜色映射方案, 给出的都是一定范围内的离散数据, 使用中有时需要进行插值, 不是很方便在程序中使用. 一种解决办法是将其拟合成解析表达式. 拟合时, 我们一般使用比较简单的函数, 如高斯函数, 二次, 三次函数等. 下面我给出一些常用颜色映射方案解析表达式的拟合结果.

下面是几种常见常用的颜色映射图, 大家可根据自己的需要来选.

网络资料

gnuplot所用的颜色映射公式

* there are 37 available rgb color mapping formulae:
         0: 0               1: 0.5             2: 1
         3: x               4: x^2             5: x^3
         6: x^4             7: sqrt(x)         8: sqrt(sqrt(x))
         9: sin(90x)       10: cos(90x)       11: |x-0.5|
        12: (2x-1)^2       13: sin(180x)      14: |cos(180x)|
        15: sin(360x)      16: cos(360x)      17: |sin(360x)|
        18: |cos(360x)|    19: |sin(720x)|    20: |cos(720x)|
        21: 3x             22: 3x-1           23: 3x-2
        24: |3x-1|         25: |3x-2|         26: (3x-1)/2
        27: (3x-2)/2       28: |(3x-1)/2|     29: |(3x-2)/2|
        30: x/0.32-0.78125 31: 2*x-0.84       32: 4x;1;-2x+1.84;x/0.08-11.5
        33: |2*x - 0.5|    34: 2*x            35: 2*x - 0.5
        36: 2*x - 1
      * negative numbers mean inverted=negative colour component
      * thus the ranges in `set pm3d rgbformulae` are -36..36

代码

下面是几种颜色映射方案拟合的gnuplot代码.

<table class="highlighttable"><th colspan="2" style="text-align:left">cmFit.gpl</th><tr><td><div class="linenodiv" style="background-color: #f0f0f0; padding-right: 10px"><pre style="line-height: 125%"> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 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0.679074903 0.993301037 0.247058824 0.244580000 0.577690000 0.315230000 0.231674 0.318106 0.544834 1.000000000 0.976300 0.983100 0.053800 0.246093750 0.547531240 0.684028574 0.994386177 0.250980392 0.245560000 0.581850000 0.304390000 0.229739 0.322361 0.545706 N/A N/A N/A N/A 0.250000000 0.552953156 0.688929332 0.995375608 0.254901961 0.246300000 0.586030000 0.293360000 0.227802 0.326594 0.546532 N/A N/A N/A N/A 0.253906250 0.558374965 0.693776492 0.996269227 0.258823529 0.246800000 0.590190000 0.282140000 0.225863 0.330805 0.547314 N/A N/A N/A N/A 0.257812500 0.563795935 0.698569369 0.997066945 0.262745098 0.247070000 0.594380000 0.270670000 0.223925 0.334994 0.548053 N/A N/A N/A N/A 0.261718750 0.569215322 0.703307287 0.997768685 0.266666667 0.247140000 0.598560000 0.258960000 0.221989 0.339161 0.548752 N/A N/A N/A N/A 0.265625000 0.574632379 0.707989572 0.998374390 0.270588235 0.247030000 0.602750000 0.246960000 0.220057 0.343307 0.549413 N/A N/A N/A N/A 0.269531250 0.580046354 0.712615557 0.998884016 0.274509804 0.246790000 0.606930000 0.234730000 0.218130 0.347432 0.550038 N/A N/A N/A N/A 0.273437500 0.585456486 0.717184578 0.999297533 0.278431373 0.246470000 0.611090000 0.222160000 0.216210 0.351535 0.550627 N/A N/A N/A N/A 0.277343750 0.590862011 0.721695979 0.999614929 0.282352941 0.246150000 0.615230000 0.209360000 0.214298 0.355619 0.551184 N/A N/A N/A N/A 0.281250000 0.596262162 0.726149107 0.999836203 0.286274510 0.245950000 0.619360000 0.196320000 0.212395 0.359683 0.551710 N/A N/A N/A N/A 0.285156250 0.601656165 0.730543315 0.999961374 0.290196078 0.246000000 0.623420000 0.183040000 0.210503 0.363727 0.552206 N/A N/A N/A N/A 0.289062500 0.607043242 0.734877964 0.999990472 0.294117647 0.246440000 0.627420000 0.169690000 0.208623 0.367752 0.552675 N/A N/A N/A N/A 0.292968750 0.612422610 0.739152418 0.999923544 0.298039216 0.247480000 0.631350000 0.156300000 0.206756 0.371758 0.553117 N/A N/A N/A N/A 0.296875000 0.617793485 0.743366047 0.999760652 0.301960784 0.249250000 0.635180000 0.142990000 0.204903 0.375746 0.553533 N/A N/A N/A N/A 0.300781250 0.623155076 0.747518228 0.999501871 0.305882353 0.251960000 0.638900000 0.130010000 0.203063 0.379716 0.553925 N/A N/A N/A N/A 0.304687500 0.628506592 0.751608345 0.999147293 0.309803922 0.255700000 0.642490000 0.117410000 0.201239 0.383670 0.554294 N/A N/A N/A N/A 0.308593750 0.633847237 0.755635786 0.998697024 0.313725490 0.260570000 0.645940000 0.105570000 0.199430 0.387607 0.554642 N/A N/A N/A N/A 0.312500000 0.639176211 0.759599947 0.998151185 0.317647059 0.266590000 0.649260000 0.094696000 0.197636 0.391528 0.554969 N/A N/A N/A N/A 0.316406250 0.644492714 0.763500228 0.997509910 0.321568627 0.273720000 0.652420000 0.084904000 0.195860 0.395433 0.555276 N/A N/A N/A N/A 0.320312500 0.649795942 0.767336039 0.996773351 0.325490196 0.281820000 0.655450000 0.076489000 0.194100 0.399323 0.555565 N/A N/A N/A N/A 0.324218750 0.655085089 0.771106793 0.995941671 0.329411765 0.290780000 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0.158480000 0.208030 0.718701 0.472873 N/A N/A N/A N/A 0.664062500 0.968530150 0.724553162 0.616403502 0.670588235 0.990720000 0.754110000 0.156340000 0.214000 0.722114 0.469588 N/A N/A N/A N/A 0.667968750 0.968994435 0.719665383 0.610228525 0.674509804 0.991460000 0.748850000 0.154140000 0.220124 0.725509 0.466226 N/A N/A N/A N/A 0.671875000 0.969367729 0.714712956 0.604054002 0.678431373 0.992140000 0.743560000 0.151960000 0.226397 0.728888 0.462789 N/A N/A N/A N/A 0.675781250 0.969650186 0.709696378 0.597880686 0.682352941 0.992790000 0.738250000 0.149810000 0.232815 0.732247 0.459277 N/A N/A N/A N/A 0.679687500 0.969841963 0.704616143 0.591709328 0.686274510 0.993400000 0.732930000 0.147600000 0.239374 0.735588 0.455688 N/A N/A N/A N/A 0.683593750 0.969943224 0.699472746 0.585540669 0.690196078 0.993980000 0.727590000 0.145430000 0.246070 0.738910 0.452024 N/A N/A N/A N/A 0.687500000 0.969954137 0.694266682 0.579375448 0.694117647 0.994540000 0.722240000 0.143200000 0.252899 0.742211 0.448284 N/A N/A N/A N/A 0.691406250 0.969874878 0.688998447 0.573214394 0.698039216 0.995090000 0.716890000 0.141030000 0.259857 0.745492 0.444467 N/A N/A N/A N/A 0.695312500 0.969705626 0.683668532 0.567058232 0.701960784 0.995620000 0.711520000 0.138800000 0.266941 0.748751 0.440573 N/A N/A N/A N/A 0.699218750 0.969446570 0.678277431 0.560907681 0.705882353 0.996130000 0.706140000 0.136590000 0.274149 0.751988 0.436601 N/A N/A N/A N/A 0.703125000 0.969097901 0.672825633 0.554763452 0.709803922 0.996620000 0.700750000 0.134440000 0.281477 0.755203 0.432552 N/A N/A N/A N/A 0.707031250 0.968659818 0.667313624 0.548626250 0.713725490 0.997100000 0.695340000 0.132230000 0.288921 0.758394 0.428426 N/A N/A N/A N/A 0.710937500 0.968132528 0.661741889 0.542496774 0.717647059 0.997550000 0.689930000 0.130060000 0.296479 0.761561 0.424223 N/A N/A N/A N/A 0.714843750 0.967516241 0.656110908 0.536375716 0.721568627 0.998000000 0.684500000 0.127830000 0.304148 0.764704 0.419943 N/A N/A N/A N/A 0.718750000 0.966811177 0.650421156 0.530263762 0.725490196 0.998420000 0.679060000 0.125640000 0.311925 0.767822 0.415586 N/A N/A N/A N/A 0.722656250 0.966017559 0.644673104 0.524161591 0.729411765 0.998830000 0.673610000 0.123400000 0.319809 0.770914 0.411152 N/A N/A N/A N/A 0.726562500 0.965135621 0.638867216 0.518069875 0.733333333 0.999220000 0.668150000 0.121190000 0.327796 0.773980 0.406640 N/A N/A N/A N/A 0.730468750 0.964165599 0.633003950 0.511989279 0.737254902 0.999590000 0.662670000 0.119040000 0.335885 0.777018 0.402049 N/A N/A N/A N/A 0.734375000 0.963107739 0.627083758 0.505920462 0.741176471 0.999940000 0.657170000 0.116820000 0.344074 0.780029 0.397381 N/A N/A N/A N/A 0.738281250 0.961962293 0.621107082 0.499864075 0.745098039 1.000000000 0.651660000 0.114580000 0.352360 0.783011 0.392636 N/A N/A N/A N/A 0.742187500 0.960729521 0.615074355 0.493820764 0.749019608 1.000000000 0.646130000 0.112440000 0.360741 0.785964 0.387814 N/A N/A N/A N/A 0.746093750 0.959409687 0.608986000 0.487791167 0.752941176 1.000000000 0.640590000 0.110240000 0.369214 0.788888 0.382914 N/A N/A N/A N/A 0.750000000 0.958003065 0.602842431 0.481775914 0.756862745 1.000000000 0.635030000 0.107970000 0.377779 0.791781 0.377939 N/A N/A N/A N/A 0.753906250 0.956509936 0.596644046 0.475775629 0.760784314 1.000000000 0.629450000 0.105800000 0.386433 0.794644 0.372886 N/A N/A N/A N/A 0.757812500 0.954930586 0.590391232 0.469790930 0.764705882 1.000000000 0.623860000 0.103600000 0.395174 0.797475 0.367757 N/A N/A N/A N/A 0.761718750 0.953265310 0.584084361 0.463822426 0.768627451 1.000000000 0.618250000 0.101350000 0.404001 0.800275 0.362552 N/A N/A N/A N/A 0.765625000 0.951514411 0.577723790 0.457870719 0.772549020 1.000000000 0.612610000 0.099135000 0.412913 0.803041 0.357269 N/A N/A N/A N/A 0.769531250 0.949678196 0.571309856 0.451936407 0.776470588 1.000000000 0.606970000 0.096882000 0.421908 0.805774 0.351910 N/A N/A N/A N/A 0.773437500 0.947756983 0.564842879 0.446020077 0.780392157 1.000000000 0.601300000 0.094743000 0.430983 0.808473 0.346476 N/A N/A N/A N/A 0.777343750 0.945751096 0.558323158 0.440122312 0.784313725 1.000000000 0.595610000 0.092465000 0.440137 0.811138 0.340967 N/A N/A N/A N/A 0.781250000 0.943660866 0.551750968 0.434243684 0.788235294 1.000000000 0.589890000 0.090257000 0.449368 0.813768 0.335384 N/A N/A N/A N/A 0.785156250 0.941486631 0.545126562 0.428384763 0.792156863 1.000000000 0.584160000 0.088032000 0.458674 0.816363 0.329727 N/A N/A N/A N/A 0.789062500 0.939228739 0.538450165 0.422546107 0.796078431 1.000000000 0.578400000 0.085726000 0.468053 0.818921 0.323998 N/A N/A N/A N/A 0.792968750 0.936887543 0.531721972 0.416728270 0.800000000 1.000000000 0.572630000 0.083542000 0.477504 0.821444 0.318195 N/A N/A N/A N/A 0.796875000 0.934463404 0.524942147 0.410931798 0.803921569 1.000000000 0.566820000 0.081316000 0.487026 0.823929 0.312321 N/A N/A N/A N/A 0.800781250 0.931956691 0.518110821 0.405157230 0.807843137 1.000000000 0.560980000 0.079004000 0.496615 0.826376 0.306377 N/A N/A N/A N/A 0.804687500 0.929367782 0.511228087 0.399405096 0.811764706 1.000000000 0.555130000 0.076745000 0.506271 0.828786 0.300362 N/A N/A N/A N/A 0.808593750 0.926697060 0.504293997 0.393675922 0.815686275 1.000000000 0.549250000 0.074530000 0.515992 0.831158 0.294279 N/A N/A N/A N/A 0.812500000 0.923944917 0.497308560 0.387970225 0.819607843 1.000000000 0.543330000 0.072245000 0.525776 0.833491 0.288127 N/A N/A N/A N/A 0.816406250 0.921111753 0.490271735 0.382288516 0.823529412 1.000000000 0.537390000 0.070004000 0.535621 0.835785 0.281908 N/A N/A N/A N/A 0.820312500 0.918197974 0.483183431 0.376631297 0.827450980 1.000000000 0.531410000 0.067732000 0.545524 0.838039 0.275626 N/A N/A N/A N/A 0.824218750 0.915203996 0.476043498 0.370999065 0.831372549 1.000000000 0.525410000 0.065424000 0.555484 0.840254 0.269281 N/A N/A N/A N/A 0.828125000 0.912130241 0.468851724 0.365392310 0.835294118 1.000000000 0.519370000 0.063180000 0.565498 0.842430 0.262877 N/A N/A N/A N/A 0.832031250 0.908977139 0.461607831 0.359811513 0.839215686 1.000000000 0.513300000 0.060810000 0.575563 0.844566 0.256415 N/A N/A N/A N/A 0.835937500 0.905745128 0.454311462 0.354257151 0.843137255 1.000000000 0.507180000 0.058502000 0.585678 0.846661 0.249897 N/A N/A N/A N/A 0.839843750 0.902434654 0.446962183 0.348729691 0.847058824 1.000000000 0.501040000 0.056232000 0.595839 0.848717 0.243329 N/A N/A N/A N/A 0.843750000 0.899046170 0.439559467 0.343229596 0.850980392 1.000000000 0.494860000 0.053826000 0.606045 0.850733 0.236712 N/A N/A N/A N/A 0.847656250 0.895580136 0.432102690 0.337757320 0.854901961 1.000000000 0.488630000 0.051494000 0.616293 0.852709 0.230052 N/A N/A N/A N/A 0.851562500 0.892037022 0.424591118 0.332313313 0.858823529 1.000000000 0.482360000 0.049242000 0.626579 0.854645 0.223353 N/A N/A N/A N/A 0.855468750 0.888417303 0.417023898 0.326898016 0.862745098 1.000000000 0.476050000 0.046828000 0.636902 0.856542 0.216620 N/A N/A N/A N/A 0.859375000 0.884721464 0.409400045 0.321511863 0.866666667 1.000000000 0.469690000 0.044447000 0.647257 0.858400 0.209861 N/A N/A N/A N/A 0.863281250 0.880949996 0.401718425 0.316155284 0.870588235 1.000000000 0.463270000 0.042093000 0.657642 0.860219 0.203082 N/A N/A N/A N/A 0.867187500 0.877103399 0.393977745 0.310828702 0.874509804 1.000000000 0.456810000 0.039648000 0.668054 0.861999 0.196293 N/A N/A N/A N/A 0.871093750 0.873182178 0.386176527 0.305532531 0.878431373 1.000000000 0.450310000 0.037261000 0.678489 0.863742 0.189503 N/A N/A N/A N/A 0.875000000 0.869186849 0.378313092 0.300267182 0.882352941 1.000000000 0.443740000 0.034882000 0.688944 0.865448 0.182725 N/A N/A N/A N/A 0.878906250 0.865117934 0.370385535 0.295033059 0.886274510 1.000000000 0.437120000 0.032495000 0.699415 0.867117 0.175971 N/A N/A N/A N/A 0.882812500 0.860975962 0.362391695 0.289830559 0.890196078 1.000000000 0.430430000 0.030303000 0.709898 0.868751 0.169257 N/A N/A N/A N/A 0.886718750 0.856761470 0.354329127 0.284660075 0.894117647 1.000000000 0.423670000 0.028180000 0.720391 0.870350 0.162603 N/A N/A N/A N/A 0.890625000 0.852475004 0.346195061 0.279521991 0.898039216 1.000000000 0.416860000 0.026121000 0.730889 0.871916 0.156029 N/A N/A N/A N/A 0.894531250 0.848117114 0.337986361 0.274416690 0.901960784 1.000000000 0.409970000 0.024126000 0.741388 0.873449 0.149561 N/A N/A N/A N/A 0.898437500 0.843688361 0.329699471 0.269344545 0.905882353 1.000000000 0.402990000 0.022194000 0.751884 0.874951 0.143228 N/A N/A N/A N/A 0.902343750 0.839189312 0.321330360 0.264305927 0.909803922 1.000000000 0.395950000 0.020325000 0.762373 0.876424 0.137064 N/A N/A N/A N/A 0.906250000 0.834620542 0.312874446 0.259301199 0.913725490 1.000000000 0.388820000 0.018517000 0.772852 0.877868 0.131109 N/A N/A N/A N/A 0.910156250 0.829982631 0.304326513 0.254330723 0.917647059 0.999940000 0.381590000 0.016771000 0.783315 0.879285 0.125405 N/A N/A N/A N/A 0.914062500 0.825276170 0.295680611 0.249394851 0.921568627 0.999610000 0.374280000 0.015085000 0.793760 0.880678 0.120005 N/A N/A N/A N/A 0.917968750 0.820501754 0.286929926 0.244493934 0.925490196 0.999270000 0.366850000 0.013457000 0.804182 0.882046 0.114965 N/A N/A N/A N/A 0.921875000 0.815659988 0.278066636 0.239628318 0.929411765 0.998920000 0.359320000 0.011916000 0.814576 0.883393 0.110347 N/A N/A N/A N/A 0.925781250 0.810751482 0.269081721 0.234798343 0.933333333 0.998550000 0.351670000 0.010169000 0.824940 0.884720 0.106217 N/A N/A N/A N/A 0.929687500 0.805776855 0.259964733 0.230004348 0.937254902 0.998170000 0.343900000 0.008743700 0.835270 0.886029 0.102646 N/A N/A N/A N/A 0.933593750 0.800736732 0.250703507 0.225246666 0.941176471 0.997780000 0.336000000 0.007354100 0.845561 0.887322 0.099702 N/A N/A N/A N/A 0.937500000 0.795631745 0.241283790 0.220525627 0.945098039 0.997380000 0.327960000 0.006019900 0.855810 0.888601 0.097452 N/A N/A N/A N/A 0.941406250 0.790462533 0.231688768 0.215841558 0.949019608 0.996960000 0.319760000 0.004742900 0.866013 0.889868 0.095953 N/A N/A N/A N/A 0.945312500 0.785229744 0.221898442 0.211194782 0.952941176 0.996530000 0.311380000 0.003521700 0.876168 0.891125 0.095250 N/A N/A N/A N/A 0.949218750 0.779934029 0.211888813 0.206585620 0.956862745 0.996090000 0.302820000 0.002355700 0.886271 0.892374 0.095374 N/A N/A N/A N/A 0.953125000 0.774576051 0.201630762 0.202014392 0.960784314 0.995630000 0.294070000 0.001244500 0.896320 0.893616 0.096335 N/A N/A N/A N/A 0.957031250 0.769156474 0.191088518 0.197481414 0.964705882 0.995170000 0.285100000 0.000187420 0.906311 0.894855 0.098125 N/A N/A N/A N/A 0.960937500 0.763675975 0.180217488 0.192987001 0.968627451 0.994690000 0.275910000 0.000000000 0.916242 0.896091 0.100717 N/A N/A N/A N/A 0.964843750 0.758135232 0.168961101 0.188531467 0.972549020 0.994200000 0.266420000 0.000000000 0.926106 0.897330 0.104071 N/A N/A N/A N/A 0.968750000 0.752534934 0.157246067 0.184115123 0.976470588 0.993690000 0.256640000 0.000000000 0.935904 0.898570 0.108131 N/A N/A N/A N/A 0.972656250 0.746875773 0.144974956 0.179738284 0.980392157 0.993180000 0.246520000 0.000000000 0.945636 0.899815 0.112838 N/A N/A N/A N/A 0.976562500 0.741158452 0.132014017 0.175401259 0.984313725 0.992650000 0.236050000 0.000000000 0.955300 0.901065 0.118128 N/A N/A N/A N/A 0.980468750 0.735383675 0.118171900 0.171104363 0.988235294 0.992110000 0.225110000 0.000000000 0.964894 0.902323 0.123941 N/A N/A N/A N/A 0.984375000 0.729552157 0.103159409 0.166847907 0.992156863 0.991550000 0.213700000 0.000000000 0.974417 0.903590 0.130215 N/A N/A N/A N/A 0.988281250 0.723664618 0.086504694 0.162632207 0.996078431 0.990990000 0.201690000 0.000000000 0.983868 0.904867 0.136897 N/A N/A N/A N/A 0.992187500 0.717721782 0.067344036 0.158457578 1.000000000 0.990410000 0.189030000 0.000000000 0.993248 0.906157 0.143936 N/A N/A N/A N/A 0.996093750 0.711724383 0.043755173 0.154324339 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 1.000000000 0.705673158 0.015556160 0.150232812 EOD f(x)=y0+a1*x+a2*x**2+a3*x**3 g(x)=Y0+A*exp( -.5*(x-x0)**2/w**2 ) # Raibow fit [.137254902:.309803922] f(x) $data u 1:2 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.309803922:.623529412] f(x) $data u 1:2 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.623529412:.741176471] f(x) $data u 1:2 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.917647059:] f(x) $data u 1:2 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [0:.611764706] f(x) $data u 1:3 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.611764706:1] f(x) $data u 1:3 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [0:.345098039] f(x) $data u 1:4 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.345098039:.623529412] f(x) $data u 1:4 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.623529412:.964705882] f(x) $data u 1:4 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) # Viridis fit [0:.55] f(x) $data u 1:5 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.55:] f(x) $data u 1:5 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [0:.55] f(x) $data u 1:6 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.55:] f(x) $data u 1:6 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [0:.55] f(x) $data u 1:7 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.55:.9] f(x) $data u 1:7 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.9:] f(x) $data u 1:7 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) # Parula fit [0:.15] f(x) $data u 8:9 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.15:.39] f(x) $data u 8:9 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.39:.86] f(x) $data u 8:9 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.86:] f(x) $data u 8:9 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [0:.80] f(x) $data u 8:10 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.80:] f(x) $data u 8:10 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [:.15] f(x) $data u 8:11 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.15:.39] f(x) $data u 8:11 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.39:.70] f(x) $data u 8:11 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.70:] f(x) $data u 8:11 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) # Diverging-CoolWarm fit [:.5] f(x) $data u 12:13 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.5:1] f(x) $data u 12:13 via y0,a1,a2,a3; print sprintf("r=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [:.5] f(x) $data u 12:14 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.5:1] f(x) $data u 12:14 via y0,a1,a2,a3; print sprintf("g=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [:.5] f(x) $data u 12:15 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) fit [.5:1] f(x) $data u 12:15 via y0,a1,a2,a3; print sprintf("b=Cubic(%12.6f,%12.6f,%12.6f,%12.6f)\n",y0,a1,a2,a3) Y0=1E-3 fit g(x) $data u 12:13 via Y0,A,x0,w; print sprintf("r=Gauss(%12.6f,%12.6f,%12.6f,%12.6f)\n",Y0,A,x0,w) fit g(x) $data u 12:15 via Y0,A,x0,w; print sprintf("b=Gauss(%12.6f,%12.6f,%12.6f,%12.6f)\n",Y0,A,x0,w) fit [:.5] g(x) $data u 12:14 via Y0,A,x0,w; print sprintf("g=Gauss(%12.6f,%12.6f,%12.6f,%12.6f)\n",Y0,A,x0,w) Y0=1; A=-1; x0=2; w=0.5 fit [.5:] g(x) $data u 12:14 via Y0,A,x0,w; print sprintf("g=Gauss(%12.6f,%12.6f,%12.6f,%12.6f)\n",Y0,A,x0,w) p [] [0:1] $data u 12:14 w p pt 7, g(x) w l lw 2 </pre></div> </td></tr></table>

下面是绘制这些颜色映射方案的python代码

<table class="highlighttable"><th colspan="2" style="text-align:left">cm.py</th><tr><td><div class="linenodiv" style="background-color: #f0f0f0; padding-right: 10px"><pre style="line-height: 125%"> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116</pre></div></td><td class="code"><div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"># coding: utf-8 import math def Cubic(y0, a1, a2, a3, x): return y0+a1*x+a2*x*x+a3*x*x*x def Gauss(y0, A, x0, w, x): return y0+A*math.exp(-.5*(x-x0)**2/w**2) def RGB(V, Vmin=0, Vmax=1, Vcnt=0.5, cm=8): x=(V-Vmin)/(Vmax-Vmin) if V<Vcnt: x=0.5*(V-Vmin)/(Vcnt-Vmin) else: x=0.5*(V-Vcnt)/(Vmax-Vcnt)+0.5 if cm==1: # Rainbow http://stackoverflow.com/questions/7706339 r=1; g=1; b=1 if x<0.25: r = 0; g = 4*x elif x<0.50: r = 0; b = 2-4*x elif x<0.75: r = 4*x-2; b = 0 else: g = 4-4*x; b = 0 elif cm==2: # Rainbow gnuplot_33/13/10 r=abs(2*x-0.5) g=math.sin(math.pi*x) b=math.cos(.5*math.pi*x) elif cm==3: # Rainbow gnuplot_26/13/10 r=(3*x-1)/2 g=math.sin(math.pi*x) b=math.cos(.5*math.pi*x) elif cm==4: # Rainbow gnuplot_22/13/-31 r=3*x-1 g=math.sin(math.pi*x) b=0.84-2*x elif cm==5: # Rainbow rainbow_bgyr_35-85_c72_n256 if x<.137254902: r=0 elif x<.309803922: r=Cubic( -1.782709, 22.937070, -86.635448, 109.222171, x) elif x<.623529412: r=Cubic( -0.765706, 3.908358, -2.385836, 0.911563, x) elif x<.741176471: r=Cubic(-18.069920, 81.220268, -115.432390, 54.731649, x) elif x<.917647059: r=1 else : r=Cubic( 0.688335, 0.804310, -0.553402, 0.051166, x) if x<.611764706 : g=Cubic( 0.221600, 2.096260, -2.989336, 1.865388, x) else : g=Cubic( 2.304104, -4.665514, 5.405245, -2.842239, x) if x<.345098039: b=Cubic( 0.964755, -3.046139, 3.252455, -6.730486, x) elif x<.623529412: b=Cubic( 0.034808, -0.485577, 2.123163, -1.570901, x) elif x<.964705882: b=Cubic( -0.692383, 4.166389, -6.037159, 2.550446, x) else : b=0 elif cm==6: # viridis python if x<.55: r=Cubic( 0.270292, 0.333180, -2.630394, 2.791978, x) else : r=Cubic( 3.693069, -15.201373, 19.879325, -7.377033, x) if x<.55: g=Cubic( 0.003646, 1.508667, -1.151450, 0.759940, x) else : g=Cubic( 0.042276, 0.851820, 0.720388, -0.711664, x) if x<.55: b=Cubic( 0.329096, 1.646430, -3.791185, 2.755424, x) elif x<.90: b=Cubic( -0.218020, 3.162757, -3.558470, 0.553676, x) else : b=Cubic(-19.388025, 82.308615, -108.295603, 45.520845, x) elif cm==7: # parula matlab if x<.15: r=Cubic( 0.198797, 1.970497, -41.589822, 123.449482, x) elif x<.39: r=Cubic( -0.907359, 10.573222, -36.564186, 39.903611, x) elif x<.86: r=Cubic( 1.054605, -8.205269, 17.972106, -9.889006, x) else : r=Cubic(-33.422658, 116.236961, -130.247319, 48.409917, x) if x<.8: g=Cubic( 0.163279, 1.805921, -1.371303, -0.029298, x) else : g=Cubic( 3.313963, -8.334822, 7.779816, -1.777729, x) if x<.15: b=Cubic( 0.532434, 2.273628, 23.667368, -156.366854, x) elif x<.39: b=Cubic( 1.229754, -3.907034, 13.494324, -16.649945, x) elif x<.70: b=Cubic( 0.011934, 6.277798, -14.821041, 9.471777, x) else : b=Cubic( -3.553961, 15.536741, -19.352350, 7.429805, x) elif cm==8: # Diverging-CoolWarm http://www.kennethmoreland.com/color-maps/ # r=Gauss( 0.009719, 0.957350, 0.684475, 0.405381, x) # b=Gauss( -0.058369, 1.059922, 0.287974, 0.397540, x) # g=Gauss( -0.704876, 1.571408, 0.517821, 0.546999, x) # if x>0.5: g=Gauss( 1.049701, -11.064245, 2.617332, 0.736066, x) r=Cubic( 0.231337, 1.075890, 1.311415, -1.847011, x) g=Cubic( 0.298328, 1.762637, -0.350029, -1.819830, x) b=Cubic( 0.751440, 1.685291, -2.782078, -0.283025, x) if x>0.5: r=Cubic( -0.671865, 5.184908, -4.640348, 0.831930, x) g=Cubic( 1.155680, -0.818882, 1.293472, -1.569916, x) b=Cubic( 1.148734, 0.728630, -3.447502, 1.721348, x) r=min(max(r,0), 1) g=min(max(g,0) ,1) b=min(max(b,0) ,1) return r, g, b Vmin=-0.008; Vmax=0.015; Vcnt=0; dV=0.0001; cm=8 Nbin=int((Vmax-Vmin)/dV)+1 # 颜色标尺 Nx=Nbin; Ny=70; w1=5; w2=3; w3=2 h1=20; h2=10; h3=5 file=open('ColorMap-'+str(cm)+'.ppm', 'w') file.write('P3\n#ppm\n'+str(Nx)+' '+str(Ny)+'\n255\n') for j in range(Ny): for i in range(Nx): if i>w1 and i<Nx-w1 and ( \ (abs(i-100*(i/100))<w1 and (j<h1 or j>Ny-h1)) \ or (abs(i- 50*(i/ 50))<w2 and (j<h2 or j>Ny-h2)) \ or (abs(i- 10*(i/ 10))<w3 and (j<h3 or j>Ny-h3)) ): r=0; g=0; b=0 else: V=Vmin+i*dV r, g, b=RGB(V, Vmin, Vmax, Vcnt, cm) file.write(str(int(r*255))+' '+str(int(g*255))+' '+str(int(b*255))+' ') file.write('\n') file.close() # 调色板 file=open('ColorMap-'+str(cm)+'.pal', 'w') for i in range(Nx): V=Vmin+i*dV r, g, b=RGB(V, Vmin, Vmax, Vcnt, cm) file.write("%10.6f %10.6f %10.6f %10.6f\n" % (V, r, g, b) ) file.close() </pre></div> </td></tr></table>