{"id":2889,"date":"2024-07-21T04:25:54","date_gmt":"2024-07-21T11:25:54","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=2889"},"modified":"2024-07-21T04:25:55","modified_gmt":"2024-07-21T11:25:55","slug":"440-cycloid-on-interactive-figure-with-widgets-in-python","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/440-cycloid-on-interactive-figure-with-widgets-in-python\/","title":{"rendered":"#440 Cycloid on interactive figure with widgets in python"},"content":{"rendered":"<p><a href=\"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/440-cycloid-on-interactive-figure-with-widgets-in-python\/ex440\/\" rel=\"attachment wp-att-2890\"><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex440.png?resize=640%2C480&#038;ssl=1\" alt=\"\" width=\"640\" height=\"480\" class=\"alignnone size-full wp-image-2890\" srcset=\"https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex440.png 640w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex440-480x360.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 640px, 100vw\" \/><\/a><\/p>\n<pre class=\"lang:python decode:true \" >import numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.widgets import Slider\ntheta = np.linspace(0,2*np.pi)\ncirc_x = lambda t: t + np.cos(theta)\ncirc_y = 1 + np.sin(theta)\ncycl_x = lambda t: t - np.sin(t)\ncycl_y = lambda t: 1 - np.cos(t)\nt = 0\nfig,ax = plt.subplots()\nplt.subplots_adjust(bottom=0.2)\nplt.ylim(0, 3)\nplt.xlim(-1, 1+4*np.pi)\nplt.gca().set_aspect('equal')\nplt.grid('on')\nCirc,=plt.plot(circ_x(t), circ_y, 'k')\nCycl,=plt.plot(cycl_x(t), cycl_y(t),'r', markersize=3)\nPnt,=plt.plot(cycl_x(t), cycl_y(t),'ro', markersize=5)\naxt = plt.axes([0.18, 0.33, 0.67, 0.02])\nt_slide = Slider(axt, 't', 0, 4*np.pi,valstep=0.001, valinit=t)\ndef update(val):\n    t = t_slide.val\n    Circ.set_xdata(circ_x(t))\n    T = np.linspace(0, t, int(50*t))\n    Cycl.set_data(cycl_x(T),cycl_y(T))\n    Pnt.set_data([cycl_x(t)],[cycl_y(t)])\n    fig.canvas.draw_idle()\nt_slide.on_changed(update)\nplt.show()<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>import numpy as np import matplotlib.pyplot as plt from matplotlib.widgets import Slider theta = np.linspace(0,2*np.pi) circ_x = lambda t: t + np.cos(theta) circ_y = 1 + np.sin(theta) cycl_x = lambda t: t &#8211; np.sin(t) cycl_y = lambda t: 1 &#8211; np.cos(t) t = 0 fig,ax = plt.subplots() plt.subplots_adjust(bottom=0.2) plt.ylim(0, 3) plt.xlim(-1, 1+4*np.pi) plt.gca().set_aspect(&#8216;equal&#8217;) plt.grid(&#8216;on&#8217;) Circ,=plt.plot(circ_x(t), [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"yes","_lmt_disable":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[89,69,2],"tags":[132,133,134],"class_list":["post-2889","post","type-post","status-publish","format-standard","hentry","category-animation","category-matplotlib","category-python","tag-cycloid","tag-matplotlib-widgets","tag-slider"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-KB","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":3018,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/441-parametric-curve-lemniscate-of-bernoulli-with-slider-in-python\/","url_meta":{"origin":2889,"position":0},"title":"#441 Parametric curve Lemniscate of Bernoulli with Slider in python","author":"gantovnik","date":"2024-07-25","format":false,"excerpt":"import numpy as np import matplotlib.pyplot as plt from matplotlib.widgets import Slider def rx(t): return np.cos(t)\/(1+np.sin(t)**2) def ry(t): return np.sin(t)*np.cos(t)\/(1+np.sin(t)**2) t = 0 fig,ax1 = plt.subplots(1,1,figsize=(10,6)) plt.subplots_adjust(bottom=0.2) ax1.set_aspect('equal') ax1.set_ylim(-0.5,0.5) ax1.set_xlim(-1.2,1.2) ax1.title.set_text('Parametric curve: Lemniscate of Bernoulli') ax1.grid('on') r, = ax1.plot(rx(t), ry(t),'b', markersize=3) Pnt1, = ax1.plot(rx(t), ry(t),'ro', markersize=6) axt = plt.axes([0.25, 0.1,\u2026","rel":"","context":"In &quot;animation&quot;","block_context":{"text":"animation","link":"https:\/\/gantovnik.com\/bio-tips\/category\/animation\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex441.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex441.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex441.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex441.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":58,"url":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/fourier-expansion-of-a-rectangular-wave\/","url_meta":{"origin":2889,"position":1},"title":"#7: Fourier expansion of a rectangular wave","author":"gantovnik","date":"2018-12-24","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np os.chdir('\/home\/vg\/Downloads\/projects\/ex7') os.getcwd() plt.figure(figsize=(10,8)) N = 2**8 t = np.linspace(0,1,N) y = np.zeros(N) for n in range(1,32,2): y = y + 4\/(np.pi*n)*np.sin(2*np.pi*n*t*2) plt.plot(t,y) plt.axis([0,1,-1.4,1.4]) plt.grid() plt.xlabel('Time, sec') plt.ylabel('Value') plt.title('Fourier expansion of a rectangular wave') plt.savefig(\"example7.png\", dpi=100) plt.show() plt.close()","rel":"","context":"In &quot;math&quot;","block_context":{"text":"math","link":"https:\/\/gantovnik.com\/bio-tips\/category\/math\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/ex7.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/ex7.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/ex7.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/ex7.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":1880,"url":"https:\/\/gantovnik.com\/bio-tips\/2023\/07\/356-animation-of-plot-legend-using-python\/","url_meta":{"origin":2889,"position":2},"title":"#356 Animation of plot legend using python","author":"gantovnik","date":"2023-07-01","format":false,"excerpt":"","rel":"","context":"In &quot;animation&quot;","block_context":{"text":"animation","link":"https:\/\/gantovnik.com\/bio-tips\/category\/animation\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex356.gif?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex356.gif?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex356.gif?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":1199,"url":"https:\/\/gantovnik.com\/bio-tips\/2021\/11\/210-parametric-curve-in-3d\/","url_meta":{"origin":2889,"position":3},"title":"#210 Parametric curve in 3D","author":"gantovnik","date":"2021-11-27","format":false,"excerpt":"","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2021\/11\/ex210.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":4043,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/09\/446-mechanical-vibrations-of-a-material-point\/","url_meta":{"origin":2889,"position":4},"title":"#446 Mechanical vibrations of a material point","author":"gantovnik","date":"2024-09-01","format":false,"excerpt":"import numpy as np import matplotlib.pyplot as plt from scipy.integrate import odeint import math def y(t): y=np.exp(-4*t) * (1 - np.cos(t) + (np.cos(1.0)-1)\/np.sin(1.0)*np.sin(t)) return y plt.rcParams[\"figure.figsize\"] = [5.50, 5.50] plt.rcParams[\"figure.autolayout\"] = True t = np.linspace(0, 1, 100) plt.plot(t, y(t)) plt.grid() plt.xlabel('t') plt.ylabel('y(t)') plt.savefig(\"ex446.png\", dpi=100) plt.show()","rel":"","context":"In &quot;differential equations&quot;","block_context":{"text":"differential equations","link":"https:\/\/gantovnik.com\/bio-tips\/category\/differential-equations\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/09\/ex446.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/09\/ex446.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/09\/ex446.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":2053,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/01\/406-nonlinear-least-squares-fitting-using-leastsq-from-scipy-optimize-in-python\/","url_meta":{"origin":2889,"position":5},"title":"#406 Nonlinear least squares fitting using leastsq from scipy.optimize in python","author":"gantovnik","date":"2024-01-14","format":false,"excerpt":"","rel":"","context":"In &quot;matplotlib&quot;","block_context":{"text":"matplotlib","link":"https:\/\/gantovnik.com\/bio-tips\/category\/matplotlib\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex406.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex406.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex406.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2889","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/comments?post=2889"}],"version-history":[{"count":2,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2889\/revisions"}],"predecessor-version":[{"id":2892,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2889\/revisions\/2892"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=2889"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=2889"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=2889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}