Notebook

conformalMaps¶

github repository with current code https://github.com/zolabar/Conformal-Maps

github repository with original code https://github.com/im-AMS/Conformal-Maps

An interactive package for intercative use of conformal mappings¶

Function w = f(z) should be entered in standard Pythonic form, (ex:z**2 for $z^2$)
Functions entered should be availabe in SymPy lib and must be entered in same form because internally it uses sympy for symbolic conversion.
The entered function w can be a function of z or of the form x + i y

'x' and 'y' are real and imaginary variables respectively.

Typical usage

     z**2
     x**2 + I*y**2
     tan(z)

Note use 'I' for imaginary number $\rm{i}$ iota
Use transformation slider to see the transformation
Limit range limits the grid to $\pm$ slider value
Ticks increases number of gridlines

Supported Grids to transform and Advanced builtin functions for w¶

Geometry	Advanced Builtin Transformations
Rectangle	into Eccentric Annulus
Rectangle	into Elliptic Annulus
Square	-
Donut	into Eccentric Annulus
Circle	-
Single Circle	into Air Foil

In [1]:

from conformalMaps.grids import *
from conformalMaps.mappings import RectangleToEccentricAnnulus, RectangleToEllipticAnnulus, ConcentricAnnulusToEccentricAnnulus
from ipywidgets import widgets
from ipywidgets import HBox,VBox

using EccentricAnnulus as w¶

Mapping a cetrain rectangle to a specific eccentric annulus (donuts)

In [2]:

R1 = 4 # inner radius of target eccentric annulus
R2 = 7.6 # outer radius of target eccentric annulus
ep = 0.5 # relative eccentricity of target eccentric annulus

trans = RectangleToEccentricAnnulus(R1, R2, ep)


rect2 = Rectangle()

left = widgets.FloatSlider(min=-10, max=10, value=trans.left, description='left')
right = widgets.FloatSlider(min=-10, max=10, value=trans.right, description='right')

top = widgets.FloatSlider(min=-10, max=10, value=trans.top, description='top')
bottom = widgets.FloatSlider(min=-10, max=10, value=trans.bottom, description='bottom')


fine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')

Hticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')
Vticks = widgets.IntSlider(min = 2, max = 50, value=20, description='Vticks')


function = widgets.Text( value = '{0}'.format(trans.mapping(z)) , description='w : ')

frame = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')

play = widgets.Play(min= 0, max = 100, step = 5)
# widgets.jslink((frame, 'value'), (play, 'value'))
widgets.jslink((play, 'value'), (frame, 'value'))

button = widgets.Button(description="Coformal?")


analytic6 = widgets.HTML(
    value="To be checked",
    #placeholder='Some HTML',
    description='Conformality:',
)

def on_button_clicked(b): 
    if rect2.check_analytic(silent=True):
        analytic6.value = '<b>Is conformal</b>, angles are preserved :)'
    else:
        analytic6.value = '<b>Not conformal</b>, angles are not preserved ...'

        
button.on_click(on_button_clicked)  

interactive_plot = widgets.interactive(rect2.updateFunc,
                                       w = function,
                                       left = left,
                                       right = right,
                                       top= top,
                                       bottom = bottom,
                                       fine = fine,
                                      Hticks = Hticks,
                                      Vticks = Vticks,
                                      frame = frame
                                      )


w1 = VBox([ left, right])
w2 = VBox([top,bottom])
w3 = VBox([Hticks,Vticks])
w4 = HBox([w1,w2,w3])

w5 = HBox([function, fine])

anim_slider = HBox([play, frame, button, analytic6])

w = VBox([w4, w5, anim_slider, rect2.show()])

w

VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=-3.141592653589793, description='left', max=10.…

using EccentricAnnulus as w¶

Mapping a cetrain donur or concentric annulus to a specific eccentric annulus (donuts)

In [3]:

R1 = 4 # inner radius of target eccentric annulus
R2 = 7.6 # outer radius of target eccentric annulus
ep = 0.5 # relative eccentricity of target eccentric annulus

trans = ConcentricAnnulusToEccentricAnnulus(R1, R2, ep)


donut2 = Donut()




rin = widgets.FloatSlider(min=0, max=10, value=trans.rin, description='Rin')
rout = widgets.FloatSlider(min=1, max=20, value=trans.rout, description='Rout')

x0 = widgets.FloatSlider(min=-10, max=10, value=0, description='x0')
y0 = widgets.FloatSlider(min=-10, max=10, value=0, description='y0')

cticks = widgets.IntSlider(min = 2, max = 50, value=20, description='cticks')
rticks = widgets.IntSlider(min = 2, max = 50, value=20, description='rticks')

fine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')

function = widgets.Text( value = '%s' % (trans.mapping(z)) , description='w : ')

frame = widgets.FloatSlider(min=0, max=100, value=100, step = 2, description='anim')

play = widgets.Play(min= 0, max = 100, step = 5)
widgets.jslink((play, 'value'), (frame, 'value'))

button = widgets.Button(description="Coformal?")


analytic7 = widgets.HTML(
    value="To be checked",
    #placeholder='Some HTML',
    description='Conformality:',
)

def on_button_clicked(b): 
    if donut2.check_analytic(silent=True):
        analytic7.value = '<b>Is conformal</b>, angles are preserved :)'
    else:
        analytic7.value = '<b>Not conformal</b>, angles are not preserved ...'

        
button.on_click(on_button_clicked)          
        
interactive_plot = widgets.interactive(donut2.updateFunc,
                                       rin = rin,
                                       rout = rout,
                                       x0 = x0,
                                       y0 = y0,
                                       fine = fine,
                                       cticks = cticks,
                                       rticks = rticks,
                                       w = function,
                                       frame = frame)

radius = VBox([rin, rout])
offset = VBox([x0, y0])
ticks = VBox([cticks, rticks])
group = HBox([radius, offset,ticks])
animation = HBox([play, frame, analytic7])



w1 = VBox([group, HBox([fine, function, button]), animation, donut2.show()])

w1

VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=1.0, description='Rin', max=10.0), FloatSlider(…

Using EllipticAnnulus as w¶

Mapping a cetrain rectangle to a specific elliptic annulus (donut)

In [4]:

a = 5 # half axis of outer ellipse

b = 3.6 # half axis of inner ellipse

trans = RectangleToEllipticAnnulus(b, a)


rect3 = Rectangle()

left = widgets.FloatSlider(min=-10, max=10, value=trans.left, description='left')
right = widgets.FloatSlider(min=-10, max=10, value=trans.right, description='right')

top = widgets.FloatSlider(min=-10, max=10, value=trans.top, description='top')
bottom = widgets.FloatSlider(min=-10, max=10, value=trans.bottom, description='bottom')


fine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')

Hticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')
Vticks = widgets.IntSlider(min = 2, max = 50, value=20, description='Vticks')


function = widgets.Text( value = '{0}'.format(trans.mapping(z)) , description='w : ')

frame = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')

play = widgets.Play(min= 0, max = 100, step = 5)
# widgets.jslink((frame, 'value'), (play, 'value'))
widgets.jslink((play, 'value'), (frame, 'value'))

button = widgets.Button(description="Coformal?")


analytic8 = widgets.HTML(
    value="To be checked",
    #placeholder='Some HTML',
    description='Conformality:',
)

def on_button_clicked(b): 
    if rect3.check_analytic(silent=True):
        analytic8.value = '<b>Is conformal</b>, angles are preserved :)'
    else:
        analytic8.value = '<b>Not conformal</b>, angles are not preserved ...'

        
button.on_click(on_button_clicked)  

interactive_plot = widgets.interactive(rect3.updateFunc,
                                       w = function,
                                       left = left,
                                       right = right,
                                       top= top,
                                       bottom = bottom,
                                       fine = fine,
                                      Hticks = Hticks,
                                      Vticks = Vticks,
                                      frame = frame
                                      )


w1 = VBox([ left, right])
w2 = VBox([top,bottom])
w3 = VBox([Hticks,Vticks])
w4 = HBox([w1,w2,w3])

w5 = HBox([function, fine, button])

anim_slider = HBox([play, frame, analytic8])

w = VBox([w4, w5, anim_slider, rect3.show()])

w

VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=0.27302255894601435, description='left', max=10…

In [ ]: