{"id":23284,"date":"2026-03-06T10:55:21","date_gmt":"2026-03-06T15:55:21","guid":{"rendered":"https:\/\/blog.espol.edu.ec\/algoritmos101\/?p=23284"},"modified":"2026-04-30T22:39:48","modified_gmt":"2026-05-01T03:39:48","slug":"superficie-revolucion","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/cv-unidades\/superficie-revolucion\/","title":{"rendered":"1.5 Superficie de Revoluci\u00f3n y cil\u00edndrica - Gr\u00e1fica con Python"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flex wp-block-group-is-layout-flex\">\n<p><a href=\"#arcocircunferencia\">arco de circunferencia<\/a><\/p>\n\n\n\n<p><a href=\"#algoritmo\">algoritmo<\/a><\/p>\n\n\n\n<p><a href=\"#grafica\">gr\u00e1fica<\/a><\/p>\n\n\n\n<p><a href=\"#cilindrica\">cil\u00edndrica<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"arcocircunferencia\">1. Ejemplo - arco de circunferencia<\/h2>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"480\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2026\/04\/SuperficiesRevolucion01_arcocircunferencia3D.png\" alt=\"Superficies Revoluci\u00f3n 01 arco circunferencia gr\u00e1fica 3D\" class=\"wp-image-23294\" \/><\/figure>\n\n\n\n<p><strong>Referencia<\/strong>: Stewart 8.2 Ejemplo 1 p554<\/p>\n\n\n\n<p>La curva es un arco de la circunferencia con radio=2. Realice la gr\u00e1fica de la curva y de superficie de revoluci\u00f3n.<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\">y = \\sqrt{4-x^2} <\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\">-1 \\leq x \\leq 1 <\/span>\n\n\n\n<figure class=\"wp-block-image alignleft size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2026\/04\/SuperficiesRevolucion01_arcocircunferencia2D.png\" alt=\"Superficies Revoluci\u00f3n 01 arco circunferencia 2D\" class=\"wp-image-23287\" style=\"width:350px\" \/><\/figure>\n\n\n\n<p>Primero se realiza la gr\u00e1fica de la curva en 2D para generar un corte de la superficie cuando z=0.<\/p>\n\n\n\n<p>Luego se hace rotar en el eje de las x la curva para generar la superficie en 3D.<\/p>\n\n\n\n<p>El proceso para las combinaciones entre las coordenadas x,w es semejante al usado para la gr\u00e1fica de funciones de dos variables usando np.meshgrid(xi, wj)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"algoritmo\">1.1 Algoritmo en Python<\/h3>\n\n\n<div class=\"wp-block-syntaxhighlighter-code alignwide\"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# Stewart 8.2 Ejemplo 1 p554\n# Superficies de Revoluci\u00f3n\nimport numpy as np\n\n# INGRESO\nf = lambda x: np.sqrt(4-x**2)\nax = -1 # eje x intervalo&#x5B;ax,bx]\nbx = 1\nmuestrasx = 31\naw = 0   # angulo w de rotaci\u00f3n &#x5B;aw,bw]\nbw = 2*np.pi\nmuestrasw = 31\ntitulo = 'Superficie de revoluci\u00f3n'\n\n# PROCEDIMIENTO\n# grafica 2D para la curva eje x,y\nxi = np.linspace(ax, bx, muestrasx)\nfi = f(xi)\nf0 = np.zeros(muestrasx,dtype=float)\n\n# grafica 3D muestras en x y angulo w\nwj = np.linspace(aw, bw, muestrasw)\nX, W = np.meshgrid(xi, wj)\n# proyeccion en ejes Y, Z\nYf = f(xi)*np.cos(W)\nZf = f(xi)*np.sin(W)\n\n# SALIDA\nprint(titulo)\nprint('xi:',xi)\nprint('wj:',wj)\n<\/pre><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"grafica\">1.2 Gr\u00e1fica con Python<\/h3>\n\n\n<div class=\"wp-block-syntaxhighlighter-code alignwide\"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# GRAFICA\nimport matplotlib.pyplot as plt\n\n# grafica 2D ------------------\nfig2D = plt.figure()\ngraf2D = fig2D.add_subplot(111)\ngraf2D.plot(xi,fi,color='blue',label='f(x)')\ngraf2D.plot(0,0,'o',color='red') # origen\n# entorno de gr\u00e1fica 2D\ngraf2D.axhline(0,color='gray')\ngraf2D.axvline(0,color='gray')\ngraf2D.set_xlabel('x')\ngraf2D.set_ylabel('f(x)')\ngraf2D.set_title('Curva - '+titulo)\ngraf2D.grid()\nplt.tight_layout()\n#plt.show()\n\n# grafica 3D -------------\nfig3D = plt.figure()\ngraf3D = fig3D.add_subplot(111, projection='3d')\n\ngraf3D.plot_surface(X, Yf, Zf,\n                    color='blue', label='f(x)')\ngraf3D.plot(0,0,0,'o',color='red')\n# entorno de la gr\u00e1fica 3D\ngraf3D.set_xlabel('x')\ngraf3D.set_ylabel('y')\ngraf3D.set_zlabel('z')\ngraf3D.set_title(titulo)\n# grafica.legend()\neleva = 23 # elevaci\u00f3n\nazim = -17 # azimuth\ndeltaw = 5 # rotaci\u00f3n de ejes\ngraf3D.view_init(eleva, azim)\n\n# rotacion de ejes\nfor azim_k in range(azim, 360+azim, deltaw ):\n    graf3D.view_init(eleva, azim_k)\n    plt.draw()\n    plt.pause(.001)\nplt.tight_layout()\nplt.show()\n<\/pre><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flex wp-block-group-is-layout-flex\">\n<p><a href=\"#arcocircunferencia\">arco de circunferencia<\/a><\/p>\n\n\n\n<p><a href=\"#algoritmo\">algoritmo<\/a><\/p>\n\n\n\n<p><a href=\"#grafica\">gr\u00e1fica<\/a><\/p>\n\n\n\n<p><a href=\"#cilindrica\">cil\u00edndrica<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"cilindrica\">2. Ejemplo - Cil\u00edndrica<\/h2>\n\n\n\n<p><strong>Referencia<\/strong>: Stewart 12.6 Ejemplo 1 p835<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> y = \\sqrt{1-x^2} <\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> -1 \\leq x \\leq 1 <\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> -2 \\leq z \\leq 2 <\/span>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2026\/04\/SuperficiesCilindricas01_cilindro3D.png\" alt=\"Superficies Cilindricas 01 cilindro gr\u00e1fica 3D\" class=\"wp-image-23297\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 Algoritmo en Python<\/h3>\n\n\n<div class=\"wp-block-syntaxhighlighter-code alignwide\"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# cilindro en Python\nimport numpy as np\n\n# INGRESO\nfx = lambda x: np.sqrt(1-x**2)\nax = -1 # eje x intervalo&#x5B;ax,bx]\nbx = 1\nmuestrasx = 200\naz = -2   # eje z intervalo&#x5B;az,bz]\nbz = 2\nmuestrasz = 200\ntitulo = 'Superficie - cilindro'\n\n# PROCEDIMIENTO\n# grid del cilindro\nxi = np.linspace(ax,bx, muestrasx)\nzj = np.linspace(az,bz, muestrasz)\nX,Z =np.meshgrid(xi, zj)\nYf = fx(X)\n\n# SALIDA\nprint(titulo)\n# print('xi:',xi)\n# print('zj:',zj)\n<\/pre><\/div>\n\n\n<h3 class=\"wp-block-heading\">2.2 Gr\u00e1fica en Python para superficie cil\u00edndrica<\/h3>\n\n\n<div class=\"wp-block-syntaxhighlighter-code alignwide\"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# GRAFICA 3D ------------------\nimport matplotlib.pyplot as plt\nfig3D = plt.figure()\ngraf3D = fig3D.add_subplot(111, projection='3d')\n\n# Plot del cilindro en dos partes\ngraf3D.plot_surface(X, Yf, Z) # Mitad delantera\ngraf3D.plot_surface(X, -Yf, Z) # Mitad trasera\n\n#entorno de la gr\u00e1fica 3D\ngraf3D.set_xlabel('x')\ngraf3D.set_ylabel('y')\ngraf3D.set_zlabel('z')\ngraf3D.set_title(titulo)\nplt.tight_layout()\nplt.show()\n<\/pre><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flex wp-block-group-is-layout-flex\">\n<p><a href=\"#arcocircunferencia\">arco de circunferencia<\/a><\/p>\n\n\n\n<p><a href=\"#algoritmo\">algoritmo<\/a><\/p>\n\n\n\n<p><a href=\"#grafica\">gr\u00e1fica<\/a><\/p>\n\n\n\n<p><a href=\"#cilindrica\">cil\u00edndrica<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n","protected":false},"excerpt":{"rendered":"<p>arco de circunferencia algoritmo gr\u00e1fica cil\u00edndrica 1. Ejemplo - arco de circunferencia Referencia: Stewart 8.2 Ejemplo 1 p554 La curva es un arco de la circunferencia con radio=2. Realice la gr\u00e1fica de la curva y de superficie de revoluci\u00f3n. Primero se realiza la gr\u00e1fica de la curva en 2D para generar un corte de la [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"wp-custom-template-entrada-fp-unidades","format":"standard","meta":{"footnotes":""},"categories":[238],"tags":[],"class_list":["post-23284","post","type-post","status-publish","format-standard","hentry","category-cv-unidades"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/23284","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=23284"}],"version-history":[{"count":12,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/23284\/revisions"}],"predecessor-version":[{"id":24460,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/23284\/revisions\/24460"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=23284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=23284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=23284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}