What's New
About the Project
NIST
Need Help?Viewing DLMF Interactive 3D Graphics

About Color Map

Surface visualizations in the DLMF represent functions of the form z=f(x,y) by the height z or the magnitude, |z|, for complex functions, over the x×y plane. We use color to augment these vizualizations, either to reinforce the recognition of the height, or to convey an extra dimension to represent the phase of complex valued functions.

§ Height Mapping

To provide an easily interpreted encoding of surface heights, a rainbow-like mapping of height to color is used. The following figure illustrates the piece-wise linear mapping of the height to each of the color components red, green and blue, written as R, G, B.

\begin{pspicture}(-14.226364pt,-14.226364pt)(122.346848pt,56.905502pt){\psline%
(0.0pt,0.0pt)(0.0pt,31.298019pt)}\rput[r](-2.845261pt,0.0pt){0} {\psline(-2.84%
5261pt,0.0pt)(0.0pt,0.0pt)}\rput[r](-2.845261pt,28.452744pt){1} {\psline(-2.84%
5261pt,28.452744pt)(0.0pt,28.452744pt)}\rput(0.0pt,-0.853577pt){
{\psline{->}(0.0pt,0.0pt)(119.501572pt,0.0pt)}{\psline(0.0pt,0.0pt)(0.0pt,-5.6%
90536pt)}\rput[t](0.0pt,-5.690536pt){$z_{\mbox{\scriptsize min}}$}
{\psline(28.452744pt,0.0pt)(28.452744pt,-2.845261pt)}{\psline(56.905502pt,0.0%
pt)(56.905502pt,-5.690536pt)}{\psline(85.358261pt,0.0pt)(85.358261pt,-2.845261%
pt)}{\psline(113.81102pt,0.0pt)(113.81102pt,-5.690536pt)}\rput[t](113.81102pt,%
-5.690536pt){$z_{\mbox{\scriptsize max}}$}
}
{\psset{linecolor=red}\psline(0.0pt,0.0pt)(28.452744pt,0.0pt)(56.905502pt,0.0%
pt)(85.358261pt,28.452744pt)(113.81102pt,28.452744pt)}{\psset{linecolor=green}%
\psline(0.0pt,0.0pt)(28.452744pt,28.452744pt)(56.905502pt,28.452744pt)(85.3582%
61pt,28.452744pt)(113.81102pt,0.0pt)}{\psset{linecolor=blue}\psline(0.0pt,28.4%
52744pt)(28.452744pt,28.452744pt)(56.905502pt,0.0pt)(85.358261pt,0.0pt)(113.81%
102pt,0.0pt)}{\psset{linestyle=none, fillstyle=gradient, gradangle=90, gradmid%
point=1}
{\psset{gradbegin=blue, gradend=cyan}\psframe(0.0pt,31.298019pt)(28.452744pt,5%
6.905502pt)}{\psset{gradbegin=cyan, gradend=green}\psframe(28.452744pt,31.2980%
19pt)(56.905502pt,56.905502pt)}{\psset{gradbegin=green, gradend=yellow}%
\psframe(56.905502pt,31.298019pt)(85.358261pt,56.905502pt)}{\psset{gradbegin=%
yellow, gradend=red}\psframe(85.358261pt,31.298019pt)(113.81102pt,56.905502pt)%
}}
\end{pspicture}
Figure 1: Mapping of height to color

Mathematically, we scale the height to h lying in the interval [0,4] and the components are computed as follows

R, G, B={0, h, 1if 0h<10, 1, 2-hif 1h<2h-2, 1, 0if 2h<31, 4-h, 0if 3h4

§ Phase Mappings

By painting the surfaces with a color that encodes the phase, phf, both the magnitude and phase of complex valued functions can be displayed. We offer two options for encoding the phase.

§ Four Color Phase Mapping

The four color scheme quickly indicates in which quadrant z lies: the colors blue, green, red and yellow are used to indicate the first, second, third and fourth quadrants, respectively. As a mnemonic, the colors are sorted alphabetically.

\begin{pspicture}(-42.679123pt,-42.679123pt)(42.679123pt,42.679123pt){
{\psline{<->}(-42.679123pt,0.0pt)(42.679123pt,0.0pt)}\rput[t](36.988571pt,0.0%
pt){$+1$}
\rput[t](-36.988571pt,0.0pt){$-1$}
{\psline{<->}(0.0pt,-42.679123pt)(0.0pt,42.679123pt)}\rput[l](0.0pt,36.988571%
pt){$+\iunit$}
\rput[l](0.0pt,-36.988571pt){$-\iunit$}
}
{\psset{fillstyle=solid, linestyle=none}
{\psset{fillcolor=blue}\pswedge(0.0pt,0.0pt){28.452744pt}{0.0}{90.0}}
{\psset{fillcolor=green}\pswedge(0.0pt,0.0pt){28.452744pt}{90.0}{180.0}}
{\psset{fillcolor=red}\pswedge(0.0pt,0.0pt){28.452744pt}{180.0}{270.0}}
{\psset{fillcolor=yellow}\pswedge(0.0pt,0.0pt){28.452744pt}{270.0}{360.0}}}
\end{pspicture}
Figure 2: Four-color map

§ Continuous Phase Mapping

For the continuous phase mapping, we map the phase continuously onto the hue, as both are periodic. In doing this, however, we would like to place the mathematically significant phase values, specifically the multiples of π/2 correponding to the real and imaginary axes, at more immediately recognizable colors.

\begin{pspicture}(-19.916916pt,-19.916916pt)(19.916916pt,19.916916pt)
\definecolor{temp}{hsb}{0.0,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{0.0}{3.6}}
\definecolor{temp}{hsb}{0.01,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{3.6}{7.2}}
\definecolor{temp}{hsb}{0.02,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{7.2}{10.8}}
\definecolor{temp}{hsb}{0.03,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{10.8}{14.4}}
\definecolor{temp}{hsb}{0.04,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{14.4}{18.0}}
\definecolor{temp}{hsb}{0.05,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{18.0}{21.6}}
\definecolor{temp}{hsb}{0.06,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{21.6}{25.2}}
\definecolor{temp}{hsb}{0.07,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{25.2}{28.8}}
\definecolor{temp}{hsb}{0.08,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{28.8}{32.4}}
\definecolor{temp}{hsb}{0.09,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{32.4}{36.0}}
\definecolor{temp}{hsb}{0.1,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{36.0}{39.6}}
\definecolor{temp}{hsb}{0.11,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{39.6}{43.2}}
\definecolor{temp}{hsb}{0.12,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{43.2}{46.8}}
\definecolor{temp}{hsb}{0.13,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{46.8}{50.4}}
\definecolor{temp}{hsb}{0.14,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{50.4}{54.0}}
\definecolor{temp}{hsb}{0.15,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{54.0}{57.6}}
\definecolor{temp}{hsb}{0.16,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{57.6}{61.2}}
\definecolor{temp}{hsb}{0.17,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{61.2}{64.8}}
\definecolor{temp}{hsb}{0.18,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{64.8}{68.4}}
\definecolor{temp}{hsb}{0.19,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{68.4}{72.0}}
\definecolor{temp}{hsb}{0.2,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{72.0}{75.6}}
\definecolor{temp}{hsb}{0.21,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{75.6}{79.2}}
\definecolor{temp}{hsb}{0.22,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{79.2}{82.8}}
\definecolor{temp}{hsb}{0.23,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{82.8}{86.4}}
\definecolor{temp}{hsb}{0.24,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{86.4}{90.0}}
\definecolor{temp}{hsb}{0.25,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{90.0}{93.6}}
\definecolor{temp}{hsb}{0.26,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{93.6}{97.2}}
\definecolor{temp}{hsb}{0.27,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{97.2}{100.8}}
\definecolor{temp}{hsb}{0.28,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{100.8}{104.4}}
\definecolor{temp}{hsb}{0.29,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{104.4}{108.0}}
\definecolor{temp}{hsb}{0.3,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{108.0}{111.6}}
\definecolor{temp}{hsb}{0.31,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{111.6}{115.2}}
\definecolor{temp}{hsb}{0.32,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{115.2}{118.8}}
\definecolor{temp}{hsb}{0.33,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{118.8}{122.4}}
\definecolor{temp}{hsb}{0.34,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{122.4}{126.0}}
\definecolor{temp}{hsb}{0.35,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{126.0}{129.6}}
\definecolor{temp}{hsb}{0.36,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{129.6}{133.2}}
\definecolor{temp}{hsb}{0.37,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{133.2}{136.8}}
\definecolor{temp}{hsb}{0.38,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{136.8}{140.4}}
\definecolor{temp}{hsb}{0.39,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{140.4}{144.0}}
\definecolor{temp}{hsb}{0.4,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{144.0}{147.6}}
\definecolor{temp}{hsb}{0.41,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{147.6}{151.2}}
\definecolor{temp}{hsb}{0.42,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{151.2}{154.8}}
\definecolor{temp}{hsb}{0.43,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{154.8}{158.4}}
\definecolor{temp}{hsb}{0.44,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{158.4}{162.0}}
\definecolor{temp}{hsb}{0.45,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{162.0}{165.6}}
\definecolor{temp}{hsb}{0.46,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{165.6}{169.2}}
\definecolor{temp}{hsb}{0.47,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{169.2}{172.8}}
\definecolor{temp}{hsb}{0.48,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{172.8}{176.4}}
\definecolor{temp}{hsb}{0.49,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{176.4}{180.0}}
\definecolor{temp}{hsb}{0.5,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{180.0}{183.6}}
\definecolor{temp}{hsb}{0.51,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{183.6}{187.2}}
\definecolor{temp}{hsb}{0.52,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{187.2}{190.8}}
\definecolor{temp}{hsb}{0.53,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{190.8}{194.4}}
\definecolor{temp}{hsb}{0.54,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{194.4}{198.0}}
\definecolor{temp}{hsb}{0.55,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{198.0}{201.6}}
\definecolor{temp}{hsb}{0.56,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{201.6}{205.2}}
\definecolor{temp}{hsb}{0.57,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{205.2}{208.8}}
\definecolor{temp}{hsb}{0.58,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{208.8}{212.4}}
\definecolor{temp}{hsb}{0.59,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{212.4}{216.0}}
\definecolor{temp}{hsb}{0.6,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{216.0}{219.6}}
\definecolor{temp}{hsb}{0.61,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{219.6}{223.2}}
\definecolor{temp}{hsb}{0.62,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{223.2}{226.8}}
\definecolor{temp}{hsb}{0.63,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{226.8}{230.4}}
\definecolor{temp}{hsb}{0.64,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{230.4}{234.0}}
\definecolor{temp}{hsb}{0.65,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{234.0}{237.6}}
\definecolor{temp}{hsb}{0.66,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{237.6}{241.2}}
\definecolor{temp}{hsb}{0.67,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{241.2}{244.8}}
\definecolor{temp}{hsb}{0.68,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{244.8}{248.4}}
\definecolor{temp}{hsb}{0.69,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{248.4}{252.0}}
\definecolor{temp}{hsb}{0.7,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{252.0}{255.6}}
\definecolor{temp}{hsb}{0.71,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{255.6}{259.2}}
\definecolor{temp}{hsb}{0.72,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{259.2}{262.8}}
\definecolor{temp}{hsb}{0.73,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{262.8}{266.4}}
\definecolor{temp}{hsb}{0.74,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{266.4}{270.0}}
\definecolor{temp}{hsb}{0.75,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{270.0}{273.6}}
\definecolor{temp}{hsb}{0.76,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{273.6}{277.2}}
\definecolor{temp}{hsb}{0.77,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{277.2}{280.8}}
\definecolor{temp}{hsb}{0.78,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{280.8}{284.4}}
\definecolor{temp}{hsb}{0.79,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{284.4}{288.0}}
\definecolor{temp}{hsb}{0.8,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{288.0}{291.6}}
\definecolor{temp}{hsb}{0.81,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{291.6}{295.2}}
\definecolor{temp}{hsb}{0.82,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{295.2}{298.8}}
\definecolor{temp}{hsb}{0.83,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{298.8}{302.4}}
\definecolor{temp}{hsb}{0.84,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{302.4}{306.0}}
\definecolor{temp}{hsb}{0.85,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{306.0}{309.6}}
\definecolor{temp}{hsb}{0.86,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{309.6}{313.2}}
\definecolor{temp}{hsb}{0.87,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{313.2}{316.8}}
\definecolor{temp}{hsb}{0.88,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{316.8}{320.4}}
\definecolor{temp}{hsb}{0.89,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{320.4}{324.0}}
\definecolor{temp}{hsb}{0.9,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{324.0}{327.6}}
\definecolor{temp}{hsb}{0.91,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{327.6}{331.2}}
\definecolor{temp}{hsb}{0.92,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{331.2}{334.8}}
\definecolor{temp}{hsb}{0.93,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{334.8}{338.4}}
\definecolor{temp}{hsb}{0.94,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{338.4}{342.0}}
\definecolor{temp}{hsb}{0.95,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{342.0}{345.6}}
\definecolor{temp}{hsb}{0.96,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{345.6}{349.2}}
\definecolor{temp}{hsb}{0.97,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{349.2}{352.8}}
\definecolor{temp}{hsb}{0.98,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{352.8}{356.4}}
\definecolor{temp}{hsb}{0.99,1,1}
{\psset{fillstyle=solid, fillcolor=temp, linestyle=none}\pswedge(0.0pt,0.0pt){%
19.916916pt}{356.4}{360.0}}
\ignorespaces\end{pspicture}

CMYK color wheel

The conventional CMYK color wheel (not to be confused with the traditional Artist’s color wheel) places the additive colors (red, green, blue) and the subtractive colors (yellow, cyan, magenta) at multiples of 60 degrees. In particular, the colors at 90 and 180 degrees are some vague greenish and purplish hues.

We therefore use a piecewise linear mapping as illustrated below, that takes phase 0 to red, π/2 to yellow, π to cyan and 3π/2 to blue.

\begin{pspicture}(-25.607468pt,-21.339554pt)(133.727951pt,101.007278pt){%
\psline(0.0pt,0.0pt)(0.0pt,86.780899pt)}{\psline(-2.845261pt,0.0pt)(0.0pt,0.0%
pt)}\rput[r](-2.845261pt,0.0pt){ 0}
{\psline(-2.845261pt,14.226364pt)(0.0pt,14.226364pt)}{\psline(-2.845261pt,28.4%
52744pt)(0.0pt,28.452744pt)}{\psline(-2.845261pt,42.679123pt)(0.0pt,42.679123%
pt)}\rput[r](-2.845261pt,42.679123pt){180}
{\psline(-2.845261pt,56.905502pt)(0.0pt,56.905502pt)}{\psline(-2.845261pt,71.1%
31882pt)(0.0pt,71.131882pt)}{\psline(-2.845261pt,85.358261pt)(0.0pt,85.358261%
pt)}\rput[r](-2.845261pt,85.358261pt){360}
\rput[b]{90.0}(-17.07164pt,42.679123pt){hue}
\rput(0.0pt,-0.426788pt){
{\psline{->}(0.0pt,0.0pt)(119.501572pt,0.0pt)}{\psline(0.0pt,0.0pt)(0.0pt,-4.2%
67899pt)}\rput[t](0.0pt,-4.267899pt){ 0}
{\psline(28.452744pt,0.0pt)(28.452744pt,-4.267899pt)}{\psline(56.905502pt,0.0%
pt)(56.905502pt,-4.267899pt)}\rput[t](56.905502pt,-4.267899pt){$\cpi$}
{\psline(85.358261pt,0.0pt)(85.358261pt,-4.267899pt)}{\psline(113.81102pt,0.0%
pt)(113.81102pt,-4.267899pt)}\rput[t](113.81102pt,-4.267899pt){$2\cpi$}
\rput[t](56.905502pt,-11.381088pt){phase}}
{\psline(0.0pt,0.0pt)(28.452744pt,14.226364pt)(56.905502pt,42.679123pt)(85.358%
261pt,56.905502pt)(113.81102pt,85.358261pt)}{\psset{linestyle=none, linewidth=%
0.0pt, fillstyle=solid}
\definecolor{temp}{hsb}{0.0,1,1}
{\psset{fillcolor=temp}\psframe(0.0pt,86.780899pt)(1.422623pt,99.584641pt)}{%
\psset{fillcolor=temp}\psframe(116.656296pt,0.0pt)(130.882675pt,0.711304pt)}
\definecolor{temp}{hsb}{0.00833,1,1}
{\psset{fillcolor=temp}\psframe(1.422623pt,86.780899pt)(2.845261pt,99.584641pt%
)}{\psset{fillcolor=temp}\psframe(116.656296pt,0.711304pt)(130.882675pt,1.4226%
23pt)}
\definecolor{temp}{hsb}{0.01666,1,1}
{\psset{fillcolor=temp}\psframe(2.845261pt,86.780899pt)(4.267899pt,99.584641pt%
)}{\psset{fillcolor=temp}\psframe(116.656296pt,1.422623pt)(130.882675pt,2.1339%
42pt)}
\definecolor{temp}{hsb}{0.02499,1,1}
{\psset{fillcolor=temp}\psframe(4.267899pt,86.780899pt)(5.690536pt,99.584641pt%
)}{\psset{fillcolor=temp}\psframe(116.656296pt,2.133942pt)(130.882675pt,2.8452%
61pt)}
\definecolor{temp}{hsb}{0.03332,1,1}
{\psset{fillcolor=temp}\psframe(5.690536pt,86.780899pt)(7.113174pt,99.584641pt%
)}{\psset{fillcolor=temp}\psframe(116.656296pt,2.845261pt)(130.882675pt,3.5565%
8pt)}
\definecolor{temp}{hsb}{0.04165,1,1}
{\psset{fillcolor=temp}\psframe(7.113174pt,86.780899pt)(8.535812pt,99.584641pt%
)}{\psset{fillcolor=temp}\psframe(116.656296pt,3.55658pt)(130.882675pt,4.26789%
9pt)}
\definecolor{temp}{hsb}{0.04998,1,1}
{\psset{fillcolor=temp}\psframe(8.535812pt,86.780899pt)(9.95845pt,99.584641pt)%
}{\psset{fillcolor=temp}\psframe(116.656296pt,4.267899pt)(130.882675pt,4.97921%
8pt)}
\definecolor{temp}{hsb}{0.05831,1,1}
{\psset{fillcolor=temp}\psframe(9.95845pt,86.780899pt)(11.381088pt,99.584641pt%
)}{\psset{fillcolor=temp}\psframe(116.656296pt,4.979218pt)(130.882675pt,5.6905%
36pt)}
\definecolor{temp}{hsb}{0.06664,1,1}
{\psset{fillcolor=temp}\psframe(11.381088pt,86.780899pt)(12.803726pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,5.690536pt)(130.882675pt,6.40%
1855pt)}
\definecolor{temp}{hsb}{0.07497,1,1}
{\psset{fillcolor=temp}\psframe(12.803726pt,86.780899pt)(14.226364pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,6.401855pt)(130.882675pt,7.11%
3174pt)}
\definecolor{temp}{hsb}{0.0833,1,1}
{\psset{fillcolor=temp}\psframe(14.226364pt,86.780899pt)(15.649002pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,7.113174pt)(130.882675pt,7.82%
4493pt)}
\definecolor{temp}{hsb}{0.09163,1,1}
{\psset{fillcolor=temp}\psframe(15.649002pt,86.780899pt)(17.07164pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,7.824493pt)(130.882675pt,8.53%
5812pt)}
\definecolor{temp}{hsb}{0.09996,1,1}
{\psset{fillcolor=temp}\psframe(17.07164pt,86.780899pt)(18.494278pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,8.535812pt)(130.882675pt,9.24%
7131pt)}
\definecolor{temp}{hsb}{0.10829,1,1}
{\psset{fillcolor=temp}\psframe(18.494278pt,86.780899pt)(19.916916pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,9.247131pt)(130.882675pt,9.95%
845pt)}
\definecolor{temp}{hsb}{0.11662,1,1}
{\psset{fillcolor=temp}\psframe(19.916916pt,86.780899pt)(21.339554pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,9.95845pt)(130.882675pt,10.66%
9769pt)}
\definecolor{temp}{hsb}{0.12495,1,1}
{\psset{fillcolor=temp}\psframe(21.339554pt,86.780899pt)(22.762192pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,10.669769pt)(130.882675pt,11.%
381088pt)}
\definecolor{temp}{hsb}{0.13328,1,1}
{\psset{fillcolor=temp}\psframe(22.762192pt,86.780899pt)(24.18483pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,11.381088pt)(130.882675pt,12.%
092407pt)}
\definecolor{temp}{hsb}{0.14161,1,1}
{\psset{fillcolor=temp}\psframe(24.18483pt,86.780899pt)(25.607468pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,12.092407pt)(130.882675pt,12.%
803726pt)}
\definecolor{temp}{hsb}{0.14994,1,1}
{\psset{fillcolor=temp}\psframe(25.607468pt,86.780899pt)(27.030106pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,12.803726pt)(130.882675pt,13.%
515045pt)}
\definecolor{temp}{hsb}{0.15827,1,1}
{\psset{fillcolor=temp}\psframe(27.030106pt,86.780899pt)(28.452744pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,13.515045pt)(130.882675pt,14.%
226364pt)}\ignorespaces
\definecolor{temp}{hsb}{0.16667,1,1}
{\psset{fillcolor=temp}\psframe(28.452744pt,86.780899pt)(29.875381pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,14.226364pt)(130.882675pt,15.%
649002pt)}
\definecolor{temp}{hsb}{0.18334,1,1}
{\psset{fillcolor=temp}\psframe(29.875381pt,86.780899pt)(31.298019pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,15.649002pt)(130.882675pt,17.%
07164pt)}
\definecolor{temp}{hsb}{0.20001,1,1}
{\psset{fillcolor=temp}\psframe(31.298019pt,86.780899pt)(32.720657pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,17.07164pt)(130.882675pt,18.4%
94278pt)}
\definecolor{temp}{hsb}{0.21668,1,1}
{\psset{fillcolor=temp}\psframe(32.720657pt,86.780899pt)(34.143295pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,18.494278pt)(130.882675pt,19.%
916916pt)}
\definecolor{temp}{hsb}{0.23335,1,1}
{\psset{fillcolor=temp}\psframe(34.143295pt,86.780899pt)(35.565933pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,19.916916pt)(130.882675pt,21.%
339554pt)}
\definecolor{temp}{hsb}{0.25002,1,1}
{\psset{fillcolor=temp}\psframe(35.565933pt,86.780899pt)(36.988571pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,21.339554pt)(130.882675pt,22.%
762192pt)}
\definecolor{temp}{hsb}{0.26669,1,1}
{\psset{fillcolor=temp}\psframe(36.988571pt,86.780899pt)(38.411209pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,22.762192pt)(130.882675pt,24.%
18483pt)}
\definecolor{temp}{hsb}{0.28336,1,1}
{\psset{fillcolor=temp}\psframe(38.411209pt,86.780899pt)(39.833847pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,24.18483pt)(130.882675pt,25.6%
07468pt)}
\definecolor{temp}{hsb}{0.30003,1,1}
{\psset{fillcolor=temp}\psframe(39.833847pt,86.780899pt)(41.256485pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,25.607468pt)(130.882675pt,27.%
030106pt)}
\definecolor{temp}{hsb}{0.3167,1,1}
{\psset{fillcolor=temp}\psframe(41.256485pt,86.780899pt)(42.679123pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,27.030106pt)(130.882675pt,28.%
452744pt)}
\definecolor{temp}{hsb}{0.33337,1,1}
{\psset{fillcolor=temp}\psframe(42.679123pt,86.780899pt)(44.101761pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,28.452744pt)(130.882675pt,29.%
875381pt)}
\definecolor{temp}{hsb}{0.35004,1,1}
{\psset{fillcolor=temp}\psframe(44.101761pt,86.780899pt)(45.524399pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,29.875381pt)(130.882675pt,31.%
298019pt)}
\definecolor{temp}{hsb}{0.36671,1,1}
{\psset{fillcolor=temp}\psframe(45.524399pt,86.780899pt)(46.947037pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,31.298019pt)(130.882675pt,32.%
720657pt)}
\definecolor{temp}{hsb}{0.38338,1,1}
{\psset{fillcolor=temp}\psframe(46.947037pt,86.780899pt)(48.369675pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,32.720657pt)(130.882675pt,34.%
143295pt)}
\definecolor{temp}{hsb}{0.40005,1,1}
{\psset{fillcolor=temp}\psframe(48.369675pt,86.780899pt)(49.792313pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,34.143295pt)(130.882675pt,35.%
565933pt)}
\definecolor{temp}{hsb}{0.41672,1,1}
{\psset{fillcolor=temp}\psframe(49.792313pt,86.780899pt)(51.214951pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,35.565933pt)(130.882675pt,36.%
988571pt)}
\definecolor{temp}{hsb}{0.43339,1,1}
{\psset{fillcolor=temp}\psframe(51.214951pt,86.780899pt)(52.637589pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,36.988571pt)(130.882675pt,38.%
411209pt)}
\definecolor{temp}{hsb}{0.45006,1,1}
{\psset{fillcolor=temp}\psframe(52.637589pt,86.780899pt)(54.060226pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,38.411209pt)(130.882675pt,39.%
833847pt)}
\definecolor{temp}{hsb}{0.46673,1,1}
{\psset{fillcolor=temp}\psframe(54.060226pt,86.780899pt)(55.482864pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,39.833847pt)(130.882675pt,41.%
256485pt)}
\definecolor{temp}{hsb}{0.4834,1,1}
{\psset{fillcolor=temp}\psframe(55.482864pt,86.780899pt)(56.905502pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,41.256485pt)(130.882675pt,42.%
679123pt)}\ignorespaces
\definecolor{temp}{hsb}{0.5,1,1}
{\psset{fillcolor=temp}\psframe(56.905502pt,86.780899pt)(58.32814pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,42.679123pt)(130.882675pt,43.%
390442pt)}
\definecolor{temp}{hsb}{0.50833,1,1}
{\psset{fillcolor=temp}\psframe(58.32814pt,86.780899pt)(59.750778pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,43.390442pt)(130.882675pt,44.%
101761pt)}
\definecolor{temp}{hsb}{0.51666,1,1}
{\psset{fillcolor=temp}\psframe(59.750778pt,86.780899pt)(61.173416pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,44.101761pt)(130.882675pt,44.%
81308pt)}
\definecolor{temp}{hsb}{0.52499,1,1}
{\psset{fillcolor=temp}\psframe(61.173416pt,86.780899pt)(62.596054pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,44.81308pt)(130.882675pt,45.5%
24399pt)}
\definecolor{temp}{hsb}{0.53332,1,1}
{\psset{fillcolor=temp}\psframe(62.596054pt,86.780899pt)(64.018692pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,45.524399pt)(130.882675pt,46.%
235718pt)}
\definecolor{temp}{hsb}{0.54165,1,1}
{\psset{fillcolor=temp}\psframe(64.018692pt,86.780899pt)(65.44133pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,46.235718pt)(130.882675pt,46.%
947037pt)}
\definecolor{temp}{hsb}{0.54998,1,1}
{\psset{fillcolor=temp}\psframe(65.44133pt,86.780899pt)(66.863968pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,46.947037pt)(130.882675pt,47.%
658356pt)}
\definecolor{temp}{hsb}{0.55831,1,1}
{\psset{fillcolor=temp}\psframe(66.863968pt,86.780899pt)(68.286606pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,47.658356pt)(130.882675pt,48.%
369675pt)}
\definecolor{temp}{hsb}{0.56664,1,1}
{\psset{fillcolor=temp}\psframe(68.286606pt,86.780899pt)(69.709244pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,48.369675pt)(130.882675pt,49.%
080994pt)}
\definecolor{temp}{hsb}{0.57497,1,1}
{\psset{fillcolor=temp}\psframe(69.709244pt,86.780899pt)(71.131882pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,49.080994pt)(130.882675pt,49.%
792313pt)}
\definecolor{temp}{hsb}{0.5833,1,1}
{\psset{fillcolor=temp}\psframe(71.131882pt,86.780899pt)(72.55452pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,49.792313pt)(130.882675pt,50.%
503632pt)}
\definecolor{temp}{hsb}{0.59163,1,1}
{\psset{fillcolor=temp}\psframe(72.55452pt,86.780899pt)(73.977158pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,50.503632pt)(130.882675pt,51.%
214951pt)}
\definecolor{temp}{hsb}{0.59996,1,1}
{\psset{fillcolor=temp}\psframe(73.977158pt,86.780899pt)(75.399796pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,51.214951pt)(130.882675pt,51.%
92627pt)}
\definecolor{temp}{hsb}{0.60829,1,1}
{\psset{fillcolor=temp}\psframe(75.399796pt,86.780899pt)(76.822433pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,51.92627pt)(130.882675pt,52.6%
37589pt)}
\definecolor{temp}{hsb}{0.61662,1,1}
{\psset{fillcolor=temp}\psframe(76.822433pt,86.780899pt)(78.245071pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,52.637589pt)(130.882675pt,53.%
348907pt)}
\definecolor{temp}{hsb}{0.62495,1,1}
{\psset{fillcolor=temp}\psframe(78.245071pt,86.780899pt)(79.667709pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,53.348907pt)(130.882675pt,54.%
060226pt)}
\definecolor{temp}{hsb}{0.63328,1,1}
{\psset{fillcolor=temp}\psframe(79.667709pt,86.780899pt)(81.090347pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,54.060226pt)(130.882675pt,54.%
771545pt)}
\definecolor{temp}{hsb}{0.64161,1,1}
{\psset{fillcolor=temp}\psframe(81.090347pt,86.780899pt)(82.512985pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,54.771545pt)(130.882675pt,55.%
482864pt)}
\definecolor{temp}{hsb}{0.64994,1,1}
{\psset{fillcolor=temp}\psframe(82.512985pt,86.780899pt)(83.935623pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,55.482864pt)(130.882675pt,56.%
194183pt)}
\definecolor{temp}{hsb}{0.65827,1,1}
{\psset{fillcolor=temp}\psframe(83.935623pt,86.780899pt)(85.358261pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,56.194183pt)(130.882675pt,56.%
905502pt)}\ignorespaces
\definecolor{temp}{hsb}{0.66667,1,1}
{\psset{fillcolor=temp}\psframe(85.358261pt,86.780899pt)(86.780899pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,56.905502pt)(130.882675pt,58.%
32814pt)}
\definecolor{temp}{hsb}{0.68334,1,1}
{\psset{fillcolor=temp}\psframe(86.780899pt,86.780899pt)(88.203537pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,58.32814pt)(130.882675pt,59.7%
50778pt)}
\definecolor{temp}{hsb}{0.70001,1,1}
{\psset{fillcolor=temp}\psframe(88.203537pt,86.780899pt)(89.626175pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,59.750778pt)(130.882675pt,61.%
173416pt)}
\definecolor{temp}{hsb}{0.71668,1,1}
{\psset{fillcolor=temp}\psframe(89.626175pt,86.780899pt)(91.048813pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,61.173416pt)(130.882675pt,62.%
596054pt)}
\definecolor{temp}{hsb}{0.73335,1,1}
{\psset{fillcolor=temp}\psframe(91.048813pt,86.780899pt)(92.471451pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,62.596054pt)(130.882675pt,64.%
018692pt)}
\definecolor{temp}{hsb}{0.75002,1,1}
{\psset{fillcolor=temp}\psframe(92.471451pt,86.780899pt)(93.894089pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,64.018692pt)(130.882675pt,65.%
44133pt)}
\definecolor{temp}{hsb}{0.76669,1,1}
{\psset{fillcolor=temp}\psframe(93.894089pt,86.780899pt)(95.316727pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,65.44133pt)(130.882675pt,66.8%
63968pt)}
\definecolor{temp}{hsb}{0.78336,1,1}
{\psset{fillcolor=temp}\psframe(95.316727pt,86.780899pt)(96.739365pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,66.863968pt)(130.882675pt,68.%
286606pt)}
\definecolor{temp}{hsb}{0.80003,1,1}
{\psset{fillcolor=temp}\psframe(96.739365pt,86.780899pt)(98.162003pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,68.286606pt)(130.882675pt,69.%
709244pt)}
\definecolor{temp}{hsb}{0.8167,1,1}
{\psset{fillcolor=temp}\psframe(98.162003pt,86.780899pt)(99.584641pt,99.584641%
pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,69.709244pt)(130.882675pt,71.%
131882pt)}
\definecolor{temp}{hsb}{0.83337,1,1}
{\psset{fillcolor=temp}\psframe(99.584641pt,86.780899pt)(101.007278pt,99.58464%
1pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,71.131882pt)(130.882675pt,72%
.55452pt)}
\definecolor{temp}{hsb}{0.85004,1,1}
{\psset{fillcolor=temp}\psframe(101.007278pt,86.780899pt)(102.429916pt,99.5846%
41pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,72.55452pt)(130.882675pt,73%
.977158pt)}
\definecolor{temp}{hsb}{0.86671,1,1}
{\psset{fillcolor=temp}\psframe(102.429916pt,86.780899pt)(103.852554pt,99.5846%
41pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,73.977158pt)(130.882675pt,7%
5.399796pt)}
\definecolor{temp}{hsb}{0.88338,1,1}
{\psset{fillcolor=temp}\psframe(103.852554pt,86.780899pt)(105.275192pt,99.5846%
41pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,75.399796pt)(130.882675pt,7%
6.822433pt)}
\definecolor{temp}{hsb}{0.90005,1,1}
{\psset{fillcolor=temp}\psframe(105.275192pt,86.780899pt)(106.69783pt,99.58464%
1pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,76.822433pt)(130.882675pt,78%
.245071pt)}
\definecolor{temp}{hsb}{0.91672,1,1}
{\psset{fillcolor=temp}\psframe(106.69783pt,86.780899pt)(108.120468pt,99.58464%
1pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,78.245071pt)(130.882675pt,79%
.667709pt)}
\definecolor{temp}{hsb}{0.93339,1,1}
{\psset{fillcolor=temp}\psframe(108.120468pt,86.780899pt)(109.543106pt,99.5846%
41pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,79.667709pt)(130.882675pt,8%
1.090347pt)}
\definecolor{temp}{hsb}{0.95006,1,1}
{\psset{fillcolor=temp}\psframe(109.543106pt,86.780899pt)(110.965744pt,99.5846%
41pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,81.090347pt)(130.882675pt,8%
2.512985pt)}
\definecolor{temp}{hsb}{0.96673,1,1}
{\psset{fillcolor=temp}\psframe(110.965744pt,86.780899pt)(112.388382pt,99.5846%
41pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,82.512985pt)(130.882675pt,8%
3.935623pt)}
\definecolor{temp}{hsb}{0.9834,1,1}
{\psset{fillcolor=temp}\psframe(112.388382pt,86.780899pt)(113.81102pt,99.58464%
1pt)}{\psset{fillcolor=temp}\psframe(116.656296pt,83.935623pt)(130.882675pt,85%
.358261pt)}\ignorespaces}
\end{pspicture} \begin{pspicture}(-42.679123pt,-42.679123pt)(42.679123pt,42.679123pt){
{\psline{<->}(-42.679123pt,0.0pt)(42.679123pt,0.0pt)}\rput[t](36.988571pt,0.0%
pt){$+1$}
\rput[t](-36.988571pt,0.0pt){$-1$}
{\psline{<->}(0.0pt,-42.679123pt)(0.0pt,42.679123pt)}\rput[l](0.0pt,36.988571%
pt){$+\iunit$}
\rput[l](0.0pt,-36.988571pt){$-\iunit$}
}
{\psset{linestyle=none, linewidth=0.0pt, fillstyle=solid}
\definecolor{temp}{hsb}{0.0,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{0.0}{4.5}}
\definecolor{temp}{hsb}{0.00833,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{4.5}{9.0}}
\definecolor{temp}{hsb}{0.01666,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{9.0}{13.5}}
\definecolor{temp}{hsb}{0.02499,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{13.5}{18.0}}
\definecolor{temp}{hsb}{0.03332,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{18.0}{22.5}}
\definecolor{temp}{hsb}{0.04165,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{22.5}{27.0}}
\definecolor{temp}{hsb}{0.04998,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{27.0}{31.5}}
\definecolor{temp}{hsb}{0.05831,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{31.5}{36.0}}
\definecolor{temp}{hsb}{0.06664,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{36.0}{40.5}}
\definecolor{temp}{hsb}{0.07497,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{40.5}{45.0}}
\definecolor{temp}{hsb}{0.0833,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{45.0}{49.5}}
\definecolor{temp}{hsb}{0.09163,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{49.5}{54.0}}
\definecolor{temp}{hsb}{0.09996,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{54.0}{58.5}}
\definecolor{temp}{hsb}{0.10829,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{58.5}{63.0}}
\definecolor{temp}{hsb}{0.11662,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{63.0}{67.5}}
\definecolor{temp}{hsb}{0.12495,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{67.5}{72.0}}
\definecolor{temp}{hsb}{0.13328,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{72.0}{76.5}}
\definecolor{temp}{hsb}{0.14161,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{76.5}{81.0}}
\definecolor{temp}{hsb}{0.14994,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{81.0}{85.5}}
\definecolor{temp}{hsb}{0.15827,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{85.5}{90.0}}
\ignorespaces
\definecolor{temp}{hsb}{0.16667,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{90.0}{94.5}}
\definecolor{temp}{hsb}{0.18334,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{94.5}{99.0}}
\definecolor{temp}{hsb}{0.20001,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{99.0}{103.5}}
\definecolor{temp}{hsb}{0.21668,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{103.5}{108.0}}
\definecolor{temp}{hsb}{0.23335,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{108.0}{112.5}}
\definecolor{temp}{hsb}{0.25002,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{112.5}{117.0}}
\definecolor{temp}{hsb}{0.26669,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{117.0}{121.5}}
\definecolor{temp}{hsb}{0.28336,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{121.5}{126.0}}
\definecolor{temp}{hsb}{0.30003,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{126.0}{130.5}}
\definecolor{temp}{hsb}{0.3167,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{130.5}{135.0}}
\definecolor{temp}{hsb}{0.33337,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{135.0}{139.5}}
\definecolor{temp}{hsb}{0.35004,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{139.5}{144.0}}
\definecolor{temp}{hsb}{0.36671,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{144.0}{148.5}}
\definecolor{temp}{hsb}{0.38338,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{148.5}{153.0}}
\definecolor{temp}{hsb}{0.40005,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{153.0}{157.5}}
\definecolor{temp}{hsb}{0.41672,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{157.5}{162.0}}
\definecolor{temp}{hsb}{0.43339,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{162.0}{166.5}}
\definecolor{temp}{hsb}{0.45006,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{166.5}{171.0}}
\definecolor{temp}{hsb}{0.46673,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{171.0}{175.5}}
\definecolor{temp}{hsb}{0.4834,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{175.5}{180.0}}
\ignorespaces
\definecolor{temp}{hsb}{0.5,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{180.0}{184.5}}
\definecolor{temp}{hsb}{0.50833,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{184.5}{189.0}}
\definecolor{temp}{hsb}{0.51666,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{189.0}{193.5}}
\definecolor{temp}{hsb}{0.52499,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{193.5}{198.0}}
\definecolor{temp}{hsb}{0.53332,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{198.0}{202.5}}
\definecolor{temp}{hsb}{0.54165,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{202.5}{207.0}}
\definecolor{temp}{hsb}{0.54998,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{207.0}{211.5}}
\definecolor{temp}{hsb}{0.55831,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{211.5}{216.0}}
\definecolor{temp}{hsb}{0.56664,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{216.0}{220.5}}
\definecolor{temp}{hsb}{0.57497,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{220.5}{225.0}}
\definecolor{temp}{hsb}{0.5833,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{225.0}{229.5}}
\definecolor{temp}{hsb}{0.59163,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{229.5}{234.0}}
\definecolor{temp}{hsb}{0.59996,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{234.0}{238.5}}
\definecolor{temp}{hsb}{0.60829,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{238.5}{243.0}}
\definecolor{temp}{hsb}{0.61662,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{243.0}{247.5}}
\definecolor{temp}{hsb}{0.62495,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{247.5}{252.0}}
\definecolor{temp}{hsb}{0.63328,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{252.0}{256.5}}
\definecolor{temp}{hsb}{0.64161,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{256.5}{261.0}}
\definecolor{temp}{hsb}{0.64994,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{261.0}{265.5}}
\definecolor{temp}{hsb}{0.65827,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{265.5}{270.0}}
\ignorespaces
\definecolor{temp}{hsb}{0.66667,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{270.0}{274.5}}
\definecolor{temp}{hsb}{0.68334,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{274.5}{279.0}}
\definecolor{temp}{hsb}{0.70001,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{279.0}{283.5}}
\definecolor{temp}{hsb}{0.71668,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{283.5}{288.0}}
\definecolor{temp}{hsb}{0.73335,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{288.0}{292.5}}
\definecolor{temp}{hsb}{0.75002,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{292.5}{297.0}}
\definecolor{temp}{hsb}{0.76669,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{297.0}{301.5}}
\definecolor{temp}{hsb}{0.78336,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{301.5}{306.0}}
\definecolor{temp}{hsb}{0.80003,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{306.0}{310.5}}
\definecolor{temp}{hsb}{0.8167,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{310.5}{315.0}}
\definecolor{temp}{hsb}{0.83337,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{315.0}{319.5}}
\definecolor{temp}{hsb}{0.85004,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{319.5}{324.0}}
\definecolor{temp}{hsb}{0.86671,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{324.0}{328.5}}
\definecolor{temp}{hsb}{0.88338,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{328.5}{333.0}}
\definecolor{temp}{hsb}{0.90005,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{333.0}{337.5}}
\definecolor{temp}{hsb}{0.91672,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{337.5}{342.0}}
\definecolor{temp}{hsb}{0.93339,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{342.0}{346.5}}
\definecolor{temp}{hsb}{0.95006,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{346.5}{351.0}}
\definecolor{temp}{hsb}{0.96673,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{351.0}{355.5}}
\definecolor{temp}{hsb}{0.9834,1,1}
{\psset{fillcolor=temp}\pswedge(0.0pt,0.0pt){28.452744pt}{355.5}{360.0}}
\ignorespaces}
\end{pspicture}
Figure 3: Continuous phase mapping

Specifically, by scaling the phase angle in [0,2π) to q in the interval [0,4), the hue (in degrees) is computed as

hue=60{qif 0q<12q-1if 1q<2q+1if 2q<32(q-1)if 3q<4