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c42f/TurboColormap.ipynb

Created August 21, 2019 13:44
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Recomputing the polynomial approximation for the Turbo colormap
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TurboColormap.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using Colors\n",
"using ColorSchemes\n",
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"turbocolormap (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Direct translation of \n",
"# https://gist.github.com/mikhailov-work/0d177465a8151eb6ede1768d51d476c7\n",
"# something seems wrong...\n",
"function turbocolormap(x)\n",
" kRedVec4 = [-0.05195877, 5.18000081, -30.94853351, 81.96403246]\n",
" kGreenVec4 = [0.16207513, 0.17712472, 15.24091500, -36.50657960]\n",
" kBlueVec4 = [0.55305649, 3.00913185, -5.46192616, -11.11819092]\n",
" kRedVec2 = [-86.53476570, 30.23299484]\n",
" kGreenVec2 = [25.95549545, -5.02738237]\n",
" kBlueVec2 = [27.81927491, -14.87899417]\n",
" x = clamp(x, 0.0, 1.0)\n",
" v4 = [1.0, x, x^2, x^3] \n",
" v4zw = [v4[3], v4[4]]\n",
" v2 = v4zw * v4[3]\n",
" return RGB(\n",
" dot(v4, kRedVec4) + dot(v2, kRedVec2),\n",
" dot(v4, kGreenVec4) + dot(v2, kGreenVec2),\n",
" dot(v4, kBlueVec4) + dot(v2, kBlueVec2)\n",
" )\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
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"text/plain": [
"ColorScheme(RGB{Float64}[RGB{Float64}(0.18995,0.07176,0.23217), RGB{Float64}(0.19483,0.08339,0.26149), RGB{Float64}(0.19956,0.09498,0.29024), RGB{Float64}(0.20415,0.10652,0.31844), RGB{Float64}(0.2086,0.11802,0.34607), RGB{Float64}(0.21291,0.12947,0.37314), RGB{Float64}(0.21708,0.14087,0.39964), RGB{Float64}(0.22111,0.15223,0.42558), RGB{Float64}(0.225,0.16354,0.45096), RGB{Float64}(0.22875,0.17481,0.47578) … RGB{Float64}(0.5955,0.05399,0.00453), RGB{Float64}(0.58336,0.04931,0.00486), RGB{Float64}(0.57103,0.04474,0.00529), RGB{Float64}(0.55852,0.04028,0.00579), RGB{Float64}(0.54583,0.03593,0.00638), RGB{Float64}(0.53295,0.03169,0.00705), RGB{Float64}(0.51989,0.02756,0.0078), RGB{Float64}(0.50664,0.02354,0.00863), RGB{Float64}(0.49321,0.01963,0.00955), RGB{Float64}(0.4796,0.01583,0.01055)], \"general\", \"turbo, improved rainbow colormap, anton mikhailov\")"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# sampled version\n",
"colorschemes[:turbo]"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
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" RGB{Float64}(0.14028106393010037,0.09359521827486748,0.11921834836995292) \n",
" RGB{Float64}(0.1447567068016563,0.09579736953914444,0.1316435912733039) \n",
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" RGB{Float64}(0.1850607875932843,0.11832539947062834,0.24944940474982064) \n",
" ⋮ \n",
" RGB{Float64}(0.5666862067624792,0.04522412479296451,-0.020049866871783784) \n",
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Recreate the polynomial approximation\n",
"using Polynomials\n",
"\n",
"N = 5\n",
"\n",
"cs = colorschemes[:turbo].colors\n",
"t = LinRange(0,1,256)\n",
"\n",
"pr = polyfit(t, getproperty.(cs, :r), N)\n",
"pg = polyfit(t, getproperty.(cs, :g), N)\n",
"pb = polyfit(t, getproperty.(cs, :b), N)\n",
"\n",
"s = LinRange(0,1,1000)\n",
"\n",
"display(colorschemes[:turbo])\n",
"display(RGB.(polyval.(Ref(pr), s), polyval.(Ref(pg), s), polyval.(Ref(pb), s)))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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{
"data": {
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display.((pr,pg,pb));"
]
},
{
"cell_type": "code",
"execution_count": 12,
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"text/plain": [
"turbocolormap2 (generic function with 1 method)"
]
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"source": [
"# 5th order polynomial approximation.\n",
"# This looses some subtleties of the original, especially at the red end\n",
"\n",
"function turbocolormap2(x)\n",
" x = clamp(x, 0.0, 1.0)\n",
" RGB(\n",
" 0.13572137988692035 + x*(4.597363719627905 + x*(-42.327689751912274 + x*( 130.58871182451415 + x*(-150.56663492057857 + x*58.137453451135656)))),\n",
" 0.09140261235958302 + x*(2.1856173378635675 + x*( 4.805204796477784 + x*(-14.019450960349728 + x*( 4.210856355081685 + x*2.7747311504638876)))),\n",
" 0.10667330048674728 + x*(12.592563476453211 + x*(-60.10967551582361 + x*( 109.07449945380961 + x*( -88.50658250648611 + x*26.818260967511673)))),\n",
" )\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 14,
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"latex_user_defs": false,
"report_style_numbering": false,
"user_envs_cfg": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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