File:Atan2.PNG
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Atan2.PNG (640 × 480 pixels, file size: 7 KB, MIME type: image/png)
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[edit]DescriptionAtan2.PNG |
English: Atan2 function. On horizontal axis 0X there is complex argument of point of unit circle. It is measured ( principal value ) from 0 to 2pi ( modulo 2 pi).
On vertical axis 0Y ther is output of function atan2 :
where is a point of unit circle :
such
so
Atan2 function gives argument of complex number with principal value in range -pi to pi, , that is -π < atan2(y, x) ≤ π. Such definition makes function single-valued, [1] but creates discontinuity at angle pi. Maxima source code It uses gnuplot through Maxima L(t):=exp(%i*t*2*%pi); /* unit circle parametrised with angle in turns */ plot2d( [atan2(imagpart(L(x)),realpart(L(x)))], [x,0,1], [y,-2*%pi,2*%pi], [plot_format, gnuplot], [gnuplot_term,"png"], [gnuplot_out_file, "atan2.png"], [legend, "atan2"], [xlabel,"angle in radians"], [ylabel,"angle in radians"], [gnuplot_preamble," set key left top; set xtics ('pi/2' 0.25, 'pi' 0.5, '3pi/2' 0.75,'2pi' 1.0); set ytics ('-2pi' -6.283, '-pi' -3.1415, '-pi/2' -1.5708, '0' 0, 'pi/2' 1.5708, 'pi' 3.1415, '2pi' 6.283); set grid xtics ytics "] );After plotting in Maxima vertical line was manually removed ( using image editor) and red circles was added. |
Date | |
Source | Own work |
Author | Adam majewski |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 16:56, 5 February 2009 | 640 × 480 (7 KB) | Soul windsurfer (talk | contribs) | {{Information |Description={{en|1=Atan2 function}} |Source=Own work by uploader |Author=Adam majewski |Date=2009.02.05 |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> |
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