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File:Magnetic field of an idealized sextupole.svg

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Summary

Description
English: Magnetic field of an idealized sextupole
Date
Source python/matplotlib
Author Andre.holzner
SVG development
InfoField
 
The source code of this SVG is invalid due to an error.
 
This W3C-invalid plot was created with Matplotlib.
Source code
InfoField
Matplotlib source code
from pylab import *

xpoints = arange(-6,6,0.05)
ypoints = arange(-6,6,0.05)
X,Y = meshgrid(xpoints, ypoints)

circularMask = False

areaRadius = 4

# order of the magnet
n = 3

def func(x,y):
    # the function to draw
    return ((x + 1j * y)**(n)).real

func = vectorize(func)

V = func(X,Y)


# mask points which we don't want to draw
if circularMask:
    # circular mask
    distance = sqrt(X**2 + Y**2)
    V = ma.masked_where(distance > areaRadius, V)
else:
    # polygonal mask

    # principal directions are at  (i + 0.5) / (2n) * 2pi
    # 
    for i in range(2*n):
        angle = (i + 0.5) / float(2*n) * 2*pi
    
        # define a straight angle perpendicular to angle
        # mask all points on one side of this line
        anchor_x = areaRadius * cos(angle)
        anchor_y = areaRadius * sin(angle)

        normal_x = cos(angle)
        normal_y = sin(angle)
        
        def acceptFunc(x,y):
            value = (x - anchor_x) * normal_x + (y - anchor_y) * normal_y
            return value > 0
        
        acceptFunc = vectorize(acceptFunc)
        
        V = ma.masked_where(acceptFunc(X,Y), V)        

    
    
if True:
    # levels equidistant in function value

    V /= V.max()

    levels = arange(-2,2,0.05)

else:
    # levels equidistant on x and y axis

    # determine the levels to draw from values on one of the axes

    levels = [ float(func(x,0)) for x in arange(min(xpoints), max(xpoints),0.50) ] + \
        [ float(func(0,y)) for y in arange(min(ypoints), max(ypoints),0.50) ]
    levels = sorted(list(set(levels)))

    
figure(figsize=(6,6)); 
Q = contour(X,Y, V, colors=  'black', linestyles = 'solid', 
    levels = levels
)
axis([-5,5,-5,5])
xlabel("x coordinate")
ylabel("y coordinate")

# mask points which we don't want to draw
if not circularMask:
    # polygonal mask

    # principal directions are at  (i + 0.5) / (2n) * 2pi
    # 
    for i in range(2*n):
        angle = (i + 0.5) / float(2*n) * 2*pi
        
        if i % 2:
            label = "N"
            color = 'red'
        else:
            label = "S"
            color = 'green'
        
        anchor_x = 1.1 * areaRadius * cos(angle)
        anchor_y = 1.1 * areaRadius * sin(angle)

        text(anchor_x, anchor_y, label, size = 20, color = color,
             horizontalalignment='center',
             verticalalignment='center')

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.

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15 December 2012

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Date/TimeThumbnailDimensionsUserComment
current23:34, 15 December 2012Thumbnail for version as of 23:34, 15 December 2012540 × 540 (180 KB)Andre.holzner{{subst:Upload marker added by en.wp UW}} {{Information |Description = {{en|Magnetic field of an idealized sextupole}} |Source = python/matplotlib |Date = 2012-12-15 |Author = Andre.holzner }} ;Other information: {{en|from pylab...

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