{"id":1980,"date":"2023-12-18T15:19:14","date_gmt":"2023-12-18T23:19:14","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=1980"},"modified":"2024-01-14T15:07:46","modified_gmt":"2024-01-14T23:07:46","slug":"397-spiral-that-goes-around-circular-paraboloid-by-python","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2023\/12\/397-spiral-that-goes-around-circular-paraboloid-by-python\/","title":{"rendered":"#397 Spiral that goes around circular paraboloid by python"},"content":{"rendered":"<p><a href=\"https:\/\/gantovnik.com\/bio-tips\/2023\/12\/397-spiral-that-goes-around-circular-paraboloid-by-python\/ex397\/\" rel=\"attachment wp-att-1981\"><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex397.png?resize=640%2C480&#038;ssl=1\" alt=\"\" width=\"640\" height=\"480\" class=\"alignnone size-full wp-image-1981\" srcset=\"https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex397.png 640w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex397-480x360.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 640px, 100vw\" \/><\/a><\/p>\n<a href='https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex398.pdf' class='small-button smallblue'>Link text<\/a>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nimport numpy as np\r\nimport matplotlib.pyplot as plt\r\nfig = plt.figure()\r\nax = plt.axes(projection='3d')\r\n# Surface ------------------\r\n# Create the mesh in polar coordinates and compute corresponding Z\r\nr0 = 5\r\nr = np.linspace(0, r0, 50)\r\np = np.linspace(0, 2*np.pi, 50)\r\nR, P = np.meshgrid(r, p)\r\nZ = -R**2 + r0**2\r\n# Express the mesh in the cartesian system\r\nX, Y = R*np.cos(P), R*np.sin(P)\r\n# Plot the surface\r\nax.plot_surface(X, Y, Z, linewidth=0, antialiased=False, alpha=0.2)\r\n# Spiral -------------------\r\nu = np.arange(0, 29, 0.1)\r\nx = 0.17*u*np.cos(u)\r\ny = 0.17*u*np.sin(u)\r\nz = -(x**2 + y**2) + r0**2\r\n# Plot spiral\r\nax.plot3D(x, y, z, 'r')\r\nplt.savefig(&quot;ex397.png&quot;, dpi=100)\r\nplt.show()\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>import numpy as np import matplotlib.pyplot as plt fig = plt.figure() ax = plt.axes(projection=&#8217;3d&#8217;) # Surface &#8212;&#8212;&#8212;&#8212;&#8212;&#8212; # Create the mesh in polar coordinates and compute corresponding Z r0 = 5 r = np.linspace(0, r0, 50) p = np.linspace(0, 2*np.pi, 50) R, P = np.meshgrid(r, p) Z = -R**2 + r0**2 # Express the mesh [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1981,"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":[69,2],"tags":[94],"class_list":["post-1980","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matplotlib","category-python","tag-spiral"],"modified_by":"gantovnik","jetpack_featured_media_url":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex397.png?fit=640%2C480&ssl=1","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-vW","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":1199,"url":"https:\/\/gantovnik.com\/bio-tips\/2021\/11\/210-parametric-curve-in-3d\/","url_meta":{"origin":1980,"position":0},"title":"#210 Parametric curve in 3D","author":"gantovnik","date":"2021-11-27","format":false,"excerpt":"[code language=\"python\"] import numpy as np import matplotlib.pyplot as plt ax = plt.figure().add_subplot(projection='3d') # Prepare arrays x, y, z theta = np.linspace(-4 * np.pi, 4 * np.pi, 100) z = np.linspace(-2, 2, 100) r = z**2 + 1 x = r * np.sin(theta) y = r * np.cos(theta) ax.plot(x, y,\u2026","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":2059,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/01\/407-multiple-axes-animation-using-python\/","url_meta":{"origin":1980,"position":1},"title":"#407 Multiple axes animation using python","author":"gantovnik","date":"2024-01-14","format":false,"excerpt":"y=sin(x) [code language=\"python\"] import matplotlib.pyplot as plt import numpy as np import matplotlib.animation as animation from matplotlib.patches import ConnectionPatch fig, (axl, axr) = plt.subplots( ncols=2, sharey=True, figsize=(6, 2), gridspec_kw=dict(width_ratios=[1, 3], wspace=0), ) axl.set_aspect(1) axr.set_box_aspect(1 \/ 3) axr.yaxis.set_visible(False) axr.xaxis.set_ticks([0, np.pi, 2 * np.pi], [\"0\", r\"$\\pi$\", r\"$2\\pi$\"]) # draw circle with initial\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\/01\/ex407.gif?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex407.gif?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex407.gif?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":1984,"url":"https:\/\/gantovnik.com\/bio-tips\/2023\/12\/398-find-points-of-intersection-of-two-circles\/","url_meta":{"origin":1980,"position":2},"title":"#398 Find points of intersection of two circles","author":"gantovnik","date":"2023-12-26","format":false,"excerpt":"- how to find an equation of the common chord of two intersected circles. [code language=\"python\"] import numpy as np import matplotlib.pyplot as plt import math def get_intersections(x0, y0, r0, x1, y1, r1): # circle 1: (x0, y0), radius r0 # circle 2: (x1, y1), radius r1 d=math.sqrt((x1-x0)**2 + (y1-y0)**2)\u2026","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\/2023\/12\/ex398.png?fit=640%2C480&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex398.png?fit=640%2C480&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/12\/ex398.png?fit=640%2C480&ssl=1&resize=525%2C300 1.5x"},"classes":[]},{"id":1877,"url":"https:\/\/gantovnik.com\/bio-tips\/2023\/07\/355-animation-of-domain-coloring-using-python\/","url_meta":{"origin":1980,"position":3},"title":"#355 Animation of domain coloring using python","author":"gantovnik","date":"2023-07-01","format":false,"excerpt":"[code language=\"python\"] # pip install celluloid #%matplotlib qt import numpy as np from matplotlib import pyplot as plt from matplotlib.colors import hsv_to_rgb from celluloid import Camera fig = plt.figure() camera = Camera(fig) for a in np.linspace(0, 2 * np.pi, 30, endpoint=False): x = np.linspace(-3, 3, 800) X, Y = np.meshgrid(x,\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\/2023\/07\/ex355.gif?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex355.gif?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex355.gif?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":3018,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/441-parametric-curve-lemniscate-of-bernoulli-with-slider-in-python\/","url_meta":{"origin":1980,"position":4},"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":2889,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/440-cycloid-on-interactive-figure-with-widgets-in-python\/","url_meta":{"origin":1980,"position":5},"title":"#440 Cycloid on interactive figure with widgets in python","author":"gantovnik","date":"2024-07-21","format":false,"excerpt":"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 - np.sin(t) cycl_y = lambda t: 1 - np.cos(t) t = 0 fig,ax = plt.subplots() plt.subplots_adjust(bottom=0.2) plt.ylim(0, 3)\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\/ex440.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex440.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex440.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/1980","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=1980"}],"version-history":[{"count":1,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/1980\/revisions"}],"predecessor-version":[{"id":2070,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/1980\/revisions\/2070"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media\/1981"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=1980"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=1980"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=1980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}