example_voila.ipynb

{"metadata":{"orig_nbformat":4,"kernelspec":{"name":"python3","display_name":"Python 3 (ipykernel)","language":"python"},"language_info":{"name":"python","version":"3.8.12","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"}},"nbformat_minor":5,"nbformat":4,"cells":[{"cell_type":"code","source":"from IPython.display import HTML","metadata":{"trusted":true},"execution_count":15,"outputs":[],"id":"f18c6fe9-565a-491f-bfbe-97764728a538"},{"cell_type":"code","source":"title='ConformalMaps'\nHTML('<h1 style=\"font-size:40px;\"><center>%s</center></h1>'%title)","metadata":{"trusted":true},"execution_count":16,"outputs":[{"execution_count":16,"output_type":"execute_result","data":{"text/plain":"<IPython.core.display.HTML object>","text/html":"<h1 style=\"font-size:40px;\"><center>ConformalMaps</center></h1>"},"metadata":{}}],"id":"1ae7c449-00fc-44e2-848d-998f21eec94d"},{"cell_type":"code","source":"HTML('<center><b>Github Code </b><a href=\"https://github.com/zolabar/Conformal-Maps\">(current, </a><a href=\"https://github.com/im-AMS/Conformal-Maps\"> original)</a></center>')","metadata":{"trusted":true},"execution_count":17,"outputs":[{"execution_count":17,"output_type":"execute_result","data":{"text/plain":"<IPython.core.display.HTML object>","text/html":"<center><b>Github Code </b><a href=\"https://github.com/zolabar/Conformal-Maps\">(current, </a><a href=\"https://github.com/im-AMS/Conformal-Maps\"> original)</a></center>"},"metadata":{}}],"id":"97b00c23-5ffa-4b8f-9a76-07e6274ee7d2"},{"cell_type":"code","source":"HTML('<center><h>Z. Lauer-Baré, & Aditya. (2021). Conformal-Maps: Code for interactive conformal mapping with python and jupyter notebook (v1.0.1). Zenodo</h><a href=\"https://doi.org/10.5281/zenodo.5717868\"> DOI 10.5281/zenodo.5717868</a></center>')","metadata":{"trusted":true},"execution_count":18,"outputs":[{"execution_count":18,"output_type":"execute_result","data":{"text/plain":"<IPython.core.display.HTML object>","text/html":"<center><h>Z. Lauer-Baré, & Aditya. (2021). Conformal-Maps: Code for interactive conformal mapping with python and jupyter notebook (v1.0.1). Zenodo</h><a href=\"https://doi.org/10.5281/zenodo.5717868\"> DOI 10.5281/zenodo.5717868</a></center>"},"metadata":{}}],"id":"9d7dc491-734e-40c1-9979-77168300ad01"},{"cell_type":"markdown","source":"### An interactive package for intercative use of conformal mappings\n\n* Function **w = f(z) should be entered in standard Pythonic form**, (ex:z**2 for $z^2$)\n\n* Functions entered should be availabe in SymPy lib and must be entered in same form because internally it uses sympy for symbolic conversion.\n\n* The entered function w can be a function of z or of the form x + i y\n'x' and 'y' are real and imaginary variables respectively.\n\n* Typical usage\n```\n     z**2\n     x**2 + I*y**2\n     tan(z)\n```\n* **Note use 'I' for imaginary number $\\rm{i}$ iota**\n\n* Use transformation slider to see the transformation\n* Limit range limits the grid to $\\pm$ slider value\n* Ticks increases number of gridlines","metadata":{},"id":"2086dae8-548c-4355-99a1-b6ff5804658a"},{"cell_type":"markdown","source":"# Supported Grids to transform and Advanced builtin functions for w\n\n","metadata":{},"id":"e02ba02b"},{"cell_type":"markdown","source":"<table>\n  <tr>\n    <th><p style=\"font-size:20px;\">Geometry</p></th>\n    <th><p style=\"font-size:20px;\">Advanced Builtin Transformations</p></th>\n  </tr>\n  <tr>\n    <td><p style=\"font-size:20px;color:blue;\">Rectangle</p></td>\n    <td><p style=\"font-size:20px;color:red;\">into Eccentric Annulus</p></td>\n  </tr>\n  <tr>\n    <td><p style=\"font-size:20px;color:blue;\">Rectangle</p></td>\n    <td><p style=\"font-size:20px;color:red;\">into Elliptic Annulus</p></td>\n  </tr>\n  <tr>\n    <td><p style=\"font-size:20px;color:blue;\">Square</p></td>\n    <td><p style=\"font-size:20px;color:blue;\">-</p></td>\n  </tr>\n  <tr>\n    <td><p style=\"font-size:20px;color:blue;\">Donut</p></td>\n    <td><p style=\"font-size:20px;color:red;\">into Eccentric Annulus</p></td>\n  </tr>\n  <tr>\n    <td><p style=\"font-size:20px;color:blue;\">Circle</p></td>\n    <td><p style=\"font-size:20px;color:blue;\">-</p></td>\n  </tr>    \n  <tr>\n    <td><p style=\"font-size:20px;color:blue;\">Single Circle</p></td>\n    <td><p style=\"font-size:20px;color:red;\">into Air Foil</p></td>\n  </tr>         \n</table>","metadata":{},"id":"f6b75e83"},{"cell_type":"code","source":"from conformalMaps.grids import *\nfrom conformalMaps.mappings import RectangleToEccentricAnnulus, RectangleToEllipticAnnulus, ConcentricAnnulusToEccentricAnnulus\nfrom ipywidgets import widgets\nfrom ipywidgets import HBox,VBox","metadata":{"trusted":true},"execution_count":19,"outputs":[],"id":"d3de9f20"},{"cell_type":"markdown","source":"# Using Rectangle grid","metadata":{},"id":"b63d302e"},{"cell_type":"code","source":"rect = Rectangle()\n\nleft = widgets.FloatSlider(min=-10, max=10, value=-1, description='left')\nbottom = widgets.FloatSlider(min=-10, max=10, value=-1, description='bottom')\n\ntop = widgets.FloatSlider(min=-10, max=10, value=1, description='top')\nright = widgets.FloatSlider(min=-10, max=10, value=1, description='right')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nHticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')\nVticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Vticks')\n\n\nfunction = widgets.Text( value = 'z**2' , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic0 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if rect.check_analytic(silent=True):\n        analytic0.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic0.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(rect.updateFunc,\n                                       w = function,\n                                       left = left,\n                                       right = right,\n                                       top= top,\n                                       bottom = bottom,\n                                       fine = fine,\n                                      Hticks = Hticks,\n                                      Vticks = Vticks,\n                                      frame = frame\n                                      )\n\n\nw1 = VBox([ left, right])\nw2 = VBox([top,bottom])\nw3 = VBox([Hticks,Vticks])\nw4 = HBox([w1,w2,w3])\n\nw5 = HBox([function, fine, button])\n\nanim_slider = HBox([play, frame, analytic0])\n\nw = VBox([w4, w5, anim_slider, rect.show()])\n\nw","metadata":{"trusted":true},"execution_count":20,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=-1.0, description='left', max=10.0, min=-10.0),…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"6b69fc7e6c2d4a1390becb61225acea9"}},"metadata":{}}],"id":"153baaac"},{"cell_type":"markdown","source":"# Using Square Grid","metadata":{},"id":"12e20ecb"},{"cell_type":"code","source":"sq = Square()\n\nside = widgets.FloatSlider(min=0.01, max=10, value=1, description='side')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nHticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')\nVticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Vticks')\n\n\nfunction = widgets.Text( value = 'z**2' , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic1 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if sq.check_analytic(silent=True):\n        analytic1.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic1.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(sq.updateFunc,\n                                       w = function,\n                                       side = side,\n                                       fine = fine,\n                                      Hticks = Hticks,\n                                      Vticks = Vticks,\n                                      frame = frame\n                                      )\n\n# w1 = VBox([ left, right])\n# w2 = VBox([top,bottom])\nbox1 = HBox([side, Hticks,Vticks])\n\nbox2 = HBox([function, fine, button])\n\nanim_slider = HBox([play, frame, analytic1])\n\nw = VBox([box1, box2, anim_slider, sq.show()])\n\nw","metadata":{"trusted":true},"execution_count":21,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(FloatSlider(value=1.0, description='side', max=10.0, min=0.01), IntSlider(value=…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"5163d02ea56249ab813054419008d231"}},"metadata":{}}],"id":"7c4bc2f1"},{"cell_type":"code","source":"r = sym.sqrt(x**2+y**2)\n\nf = x*(sym.sqrt(x**2+y**2-x**2*y**2))/r + sym.I*y*(sym.sqrt(x**2+y**2-x**2*y**2))/r # transforms unit square\n\nsq2 = Square()\n\nside = widgets.FloatSlider(min=0.01, max=10, value=1, description='side')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nHticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')\nVticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Vticks')\n\n\nfunction = widgets.Text(  value = '%s' %(f) , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic2 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if sq2.check_analytic(silent=True):\n        analytic2.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic2.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n    \nbutton.on_click(on_button_clicked)       \n    \ninteractive_plot = widgets.interactive(sq2.updateFunc,\n                                       w = function,\n                                       side = side,\n                                       fine = fine,\n                                      Hticks = Hticks,\n                                      Vticks = Vticks,\n                                      frame = frame\n                                      )\n\n\n\n\n# w1 = VBox([ left, right])\n# w2 = VBox([top,bottom])\nbox1 = HBox([side, Hticks,Vticks])\n\nbox2 = HBox([function, fine, button])\n\nanim_slider = HBox([play, frame, analytic2])\n\n\n\n\n\nw = VBox([box1, box2, anim_slider, sq2.show()])\n\nw\n","metadata":{"trusted":true},"execution_count":22,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(FloatSlider(value=1.0, description='side', max=10.0, min=0.01), IntSlider(value=…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"93979582bc4f47609de5f143cba610cf"}},"metadata":{}}],"id":"cf16bc35"},{"cell_type":"markdown","source":"# Using Donut Grid","metadata":{},"id":"07951056"},{"cell_type":"code","source":"donut = Donut()\n\nrin = widgets.FloatSlider(min=0, max=10, value=1, description='Rin')\nrout = widgets.FloatSlider(min=1, max=20, value=3, description='Rout')\n\nx0 = widgets.FloatSlider(min=-10, max=10, value=0, description='x0')\ny0 = widgets.FloatSlider(min=-10, max=10, value=0, description='y0')\n\ncticks = widgets.IntSlider(min = 2, max = 50, value=4, description='cticks')\nrticks = widgets.IntSlider(min = 2, max = 50, value=4, description='rticks')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nfunction = widgets.Text( value = 'z**2' , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 2, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic3 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if donut.check_analytic(silent=True):\n        analytic3.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic3.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(donut.updateFunc,\n                                       rin = rin,\n                                       rout = rout,\n                                       x0 = x0,\n                                       y0 = y0,\n                                       fine = fine,\n                                       cticks = cticks,\n                                       rticks = rticks,\n                                       w = function,\n                                       frame = frame)\n\nradius = VBox([rin, rout])\noffset = VBox([x0, y0])\nticks = VBox([cticks, rticks])\ngroup = HBox([radius, offset,ticks])\nanimation = HBox([play, frame, analytic3])\n\nw1 = VBox([group, HBox([fine, function, button]), animation, donut.show()])\n\nw1","metadata":{"trusted":true},"execution_count":23,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=1.0, description='Rin', max=10.0), FloatSlider(…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"d06ec96d35e041a6bd68b3a43f0e1087"}},"metadata":{}}],"id":"c26ddb21"},{"cell_type":"markdown","source":"# Using Circle Grid","metadata":{},"id":"74f79d1c"},{"cell_type":"code","source":"circle = Circle()\n\nr = widgets.FloatSlider(min=0.1, max=10, value=1, description='R')\n\n\nx0 = widgets.FloatSlider(min=-10, max=10, value=0, description='x0')\ny0 = widgets.FloatSlider(min=-10, max=10, value=0, description='y0')\n\ncticks = widgets.IntSlider(min = 2, max = 50, value=4, description='cticks')\nrticks = widgets.IntSlider(min = 0, max = 50, value=4, description='rticks')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nfunction = widgets.Text( value = 'z**2' , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 2, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 2)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic4 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if circle.check_analytic(silent=True):\n        analytic4.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic4.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(circle.updateFunc,\n                                       r = r,\n                                       x0 = x0,\n                                       y0 = y0,\n                                       fine = fine,\n                                       cticks = cticks,\n                                       rticks = rticks,\n                                       w = function,\n                                       frame = frame)\n\nradius = VBox([r, fine])\noffset = VBox([x0, y0])\nticks = VBox([cticks, rticks])\ngroup = HBox([radius, offset,ticks])\nanimation = HBox([play, frame, button, analytic4])\n\nw1 = VBox([group, function, animation, circle.show()])\n\nw1\n# display(interactive_plot,circle.show())","metadata":{"trusted":true},"execution_count":24,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=1.0, description='R', max=10.0, min=0.1), IntSl…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"45841b7ac4654f1a9d3561b966024863"}},"metadata":{}}],"id":"b86e31d2"},{"cell_type":"markdown","source":"# Using Single_circle","metadata":{},"id":"6ba2084c"},{"cell_type":"code","source":"single = Single_circle(rticks=0)\n\nr = widgets.FloatSlider(min=0.1, max=10, value=1.08, description='R')\n\n\nx0 = widgets.FloatSlider(min=-10, max=10, value=-0.08, description='x0')\ny0 = widgets.FloatSlider(min=-10, max=10, value=0.08, description='y0')\n\nrticks = widgets.IntSlider(min = 0, max = 50, value=0, description='rticks')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nfunction = widgets.Text( value = 'z+1/z' , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 2, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 2)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic5 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if single.check_analytic(silent=True):\n        analytic5.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic5.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(single.updateFunc,\n                                       r = r,\n                                       x0 = x0,\n                                       y0 = y0,\n                                       fine = fine,\n                                       rticks = rticks,\n                                       w = function,\n                                       frame = frame)\n\nradius = VBox([r, fine])\noffset = VBox([x0, y0])\n# ticks = VBox([cticks, rticks])\ngroup = HBox([radius, offset,rticks])\nanimation = HBox([play, frame, button, analytic5])\n\nw1 = VBox([group, function, animation, single.show()])\n\nw1","metadata":{"trusted":true},"execution_count":25,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=1.08, description='R', max=10.0, min=0.1), IntS…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"c81b4bbe07344482bd690635ddd14ed6"}},"metadata":{}}],"id":"f7e107b4"},{"cell_type":"markdown","source":"# Using Builtin complicated functions for w\n\nIn engineering one may be interested in solving the Laplace or Poisson equation in \"complicated\" domains as eccentric annuli or elliptic annuli. With the help of builtin functions from ```conformalMaps``` one can see how those domains are conformally related to simple domains as concentric annuli or rectangles.","metadata":{},"id":"83d3c250"},{"cell_type":"markdown","source":"### using EccentricAnnulus as w\nMapping a cetrain rectangle to a specific eccentric annulus (donuts)","metadata":{},"id":"896a0be9"},{"cell_type":"code","source":"R1 = 4 # inner radius of target eccentric annulus\nR2 = 7.6 # outer radius of target eccentric annulus\nep = 0.5 # relative eccentricity of target eccentric annulus\n\ntrans = RectangleToEccentricAnnulus(R1, R2, ep)\n\n\nrect2 = Rectangle()\n\nleft = widgets.FloatSlider(min=-10, max=10, value=trans.left, description='left')\nright = widgets.FloatSlider(min=-10, max=10, value=trans.right, description='right')\n\ntop = widgets.FloatSlider(min=-10, max=10, value=trans.top, description='top')\nbottom = widgets.FloatSlider(min=-10, max=10, value=trans.bottom, description='bottom')\n\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nHticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')\nVticks = widgets.IntSlider(min = 2, max = 50, value=20, description='Vticks')\n\n\nfunction = widgets.Text( value = '{0}'.format(trans.mapping(z)) , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\n# widgets.jslink((frame, 'value'), (play, 'value'))\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic6 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if rect2.check_analytic(silent=True):\n        analytic6.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic6.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(rect2.updateFunc,\n                                       w = function,\n                                       left = left,\n                                       right = right,\n                                       top= top,\n                                       bottom = bottom,\n                                       fine = fine,\n                                      Hticks = Hticks,\n                                      Vticks = Vticks,\n                                      frame = frame\n                                      )\n\n\nw1 = VBox([ left, right])\nw2 = VBox([top,bottom])\nw3 = VBox([Hticks,Vticks])\nw4 = HBox([w1,w2,w3])\n\nw5 = HBox([function, fine])\n\nanim_slider = HBox([play, frame, button, analytic6])\n\nw = VBox([w4, w5, anim_slider, rect2.show()])\n\nw\n\n","metadata":{"trusted":true},"execution_count":26,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=-3.141592653589793, description='left', max=10.…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"611ec2059c674977b82d2707ee1e36bd"}},"metadata":{}}],"id":"d250315c"},{"cell_type":"markdown","source":"### using EccentricAnnulus as w\nMapping a cetrain donur or concentric annulus to a specific eccentric annulus (donuts)","metadata":{},"id":"66f37f4f"},{"cell_type":"code","source":"R1 = 4 # inner radius of target eccentric annulus\nR2 = 7.6 # outer radius of target eccentric annulus\nep = 0.5 # relative eccentricity of target eccentric annulus\n\ntrans = ConcentricAnnulusToEccentricAnnulus(R1, R2, ep)\n\n\ndonut2 = Donut()\n\n\n\n\nrin = widgets.FloatSlider(min=0, max=10, value=trans.rin, description='Rin')\nrout = widgets.FloatSlider(min=1, max=20, value=trans.rout, description='Rout')\n\nx0 = widgets.FloatSlider(min=-10, max=10, value=0, description='x0')\ny0 = widgets.FloatSlider(min=-10, max=10, value=0, description='y0')\n\ncticks = widgets.IntSlider(min = 2, max = 50, value=20, description='cticks')\nrticks = widgets.IntSlider(min = 2, max = 50, value=20, description='rticks')\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nfunction = widgets.Text( value = '%s' % (trans.mapping(z)) , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 2, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic7 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if donut2.check_analytic(silent=True):\n        analytic7.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic7.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)          \n        \ninteractive_plot = widgets.interactive(donut2.updateFunc,\n                                       rin = rin,\n                                       rout = rout,\n                                       x0 = x0,\n                                       y0 = y0,\n                                       fine = fine,\n                                       cticks = cticks,\n                                       rticks = rticks,\n                                       w = function,\n                                       frame = frame)\n\nradius = VBox([rin, rout])\noffset = VBox([x0, y0])\nticks = VBox([cticks, rticks])\ngroup = HBox([radius, offset,ticks])\nanimation = HBox([play, frame, analytic7])\n\n\n\nw1 = VBox([group, HBox([fine, function, button]), animation, donut2.show()])\n\nw1\n","metadata":{"trusted":true},"execution_count":27,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=1.0, description='Rin', max=10.0), FloatSlider(…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"c790add33deb4b10909637a8c5136f64"}},"metadata":{}}],"id":"58bd9b5b"},{"cell_type":"markdown","source":"### Using EllipticAnnulus as w\nMapping a cetrain rectangle to a specific elliptic annulus (donut)","metadata":{},"id":"e2ec43dc"},{"cell_type":"code","source":"a = 5 # half axis of outer ellipse\n\nb = 3.6 # half axis of inner ellipse\n\ntrans = RectangleToEllipticAnnulus(b, a)\n\n\nrect3 = Rectangle()\n\nleft = widgets.FloatSlider(min=-10, max=10, value=trans.left, description='left')\nright = widgets.FloatSlider(min=-10, max=10, value=trans.right, description='right')\n\ntop = widgets.FloatSlider(min=-10, max=10, value=trans.top, description='top')\nbottom = widgets.FloatSlider(min=-10, max=10, value=trans.bottom, description='bottom')\n\n\nfine = widgets.IntSlider(min = 20, max = 100, value=50, description='Fine')\n\nHticks = widgets.IntSlider(min = 2, max = 50, value=10, description='Hticks')\nVticks = widgets.IntSlider(min = 2, max = 50, value=20, description='Vticks')\n\n\nfunction = widgets.Text( value = '{0}'.format(trans.mapping(z)) , description='w : ')\n\nframe = widgets.FloatSlider(min=0, max=100, value=100, step = 5, description='anim')\n\nplay = widgets.Play(min= 0, max = 100, step = 5)\n# widgets.jslink((frame, 'value'), (play, 'value'))\nwidgets.jslink((play, 'value'), (frame, 'value'))\n\nbutton = widgets.Button(description=\"Coformal?\")\n\n\nanalytic8 = widgets.HTML(\n    value=\"To be checked\",\n    #placeholder='Some HTML',\n    description='Conformality:',\n)\n\ndef on_button_clicked(b): \n    if rect3.check_analytic(silent=True):\n        analytic8.value = '<b style=\"color:green;\">Is conformal</b>, angles are preserved :)'\n    else:\n        analytic8.value = '<b style=\"color:red;\">Not conformal</b>, angles are not preserved ...'\n\n        \nbutton.on_click(on_button_clicked)  \n\ninteractive_plot = widgets.interactive(rect3.updateFunc,\n                                       w = function,\n                                       left = left,\n                                       right = right,\n                                       top= top,\n                                       bottom = bottom,\n                                       fine = fine,\n                                      Hticks = Hticks,\n                                      Vticks = Vticks,\n                                      frame = frame\n                                      )\n\n\nw1 = VBox([ left, right])\nw2 = VBox([top,bottom])\nw3 = VBox([Hticks,Vticks])\nw4 = HBox([w1,w2,w3])\n\nw5 = HBox([function, fine, button])\n\nanim_slider = HBox([play, frame, analytic8])\n\nw = VBox([w4, w5, anim_slider, rect3.show()])\n\nw\n\n","metadata":{"trusted":true},"execution_count":28,"outputs":[{"output_type":"display_data","data":{"text/plain":"VBox(children=(HBox(children=(VBox(children=(FloatSlider(value=0.27302255894601435, description='left', max=10…","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"ee7c54fea6eb4fe39e53eb4d1535a482"}},"metadata":{}}],"id":"1cf788da"},{"cell_type":"code","source":"","metadata":{"trusted":true},"execution_count":null,"outputs":[],"id":"858287ac"},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[],"id":"4d2bf03d-6861-4ba6-9505-9e33dfee3ad7"}]}