{"id":24770,"date":"2026-06-30T15:40:00","date_gmt":"2026-06-30T20:40:00","guid":{"rendered":"https:\/\/blog.espol.edu.ec\/algoritmos101\/?p=24770"},"modified":"2026-07-01T11:21:50","modified_gmt":"2026-07-01T16:21:50","slug":"s1eva2026paoi_t3-drone-zona-desastre","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-s1eva30\/s1eva2026paoi_t3-drone-zona-desastre\/","title":{"rendered":"s1Eva2026PAOI_T3 Drone en zona de desastre"},"content":{"rendered":"\n<p>Ejercicio: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-1eva30\/1eva2026paoi_t3-drone-zona-desastre\/\" data-type=\"post\" data-id=\"24732\">1Eva2026PAOI_T3 Drone en zona de desastre<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"557\" height=\"421\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2026\/06\/dobleteSismico01.png\" alt=\"puntos de observaci\u00f3n para selecci\u00f3n de trayectoria.\" class=\"wp-image-24733\" \/><\/figure>\n\n\n\n<p>las coordenadas posibles para el ejercicio son:<\/p>\n\n\n\n<pre class=\"wp-block-code alignwide\"><code>xi = &#091;4.04, 4.17, 4.39, 4.77, 5.14, 5.32, 6.87, 6.87, 7.58, 8.03, 8.25, 8.60, 8.96, 9.86]\nyi = &#091;5.85, 9.94, 3.90, 2.43, 7.70, 9.52, 7.65, 3.55, 2.94, 7.56, 3.81, 6.31, 4.99, 9.32]<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">literal a. Planteamiento<\/h2>\n\n\n\n<p>Si selecciona los puntos: primero y \u00faltimo con dos puntos intermedios se obtendr\u00e1n 4 puntos para un polinomio de grado 3.<\/p>\n\n\n\n<p>p(x) = a + b x + cx<sup>2<\/sup>+d<\/p>\n\n\n\n<p>Siguiendo el modelo de Vandermonde, se escribe el t\u00e9rmino de mayor grado primero.<\/p>\n\n\n\n<p>p(x) = a x<sup>3<\/sup> + b x<sup>2<\/sup> + cx+d<\/p>\n\n\n\n<p>Por ejemplo, para los pares ordenados:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>xi = &#091;4.04, 5.32, 6.87, 9.86]\nfi = &#091;5.85, 9.52, 7.65, 9.32]<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">literal b. M\u00e9todo de Lagrange<\/h2>\n\n\n\n<p>Siguiendo el m\u00e9todo de Lagrange, se obtendr\u00eda el polinomio:<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> p(x) = 5.85\\frac{(x-5.32)(x-6.87)(x-9.86)}{(4.04-5.32)(4.04-6.87)(4.04-9.86)}+<\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> +9.52\\frac{(x-4.04)(x-6.87)(x-9.86)}{(5.32-4.04)(5.32-6.87)(5.32-9.86)}+<\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> +7.65\\frac{(x-4.04)(x-5.32)(x-9.86)}{(6.87-4.04)(6.87-5.32)(6.87-9.86)}+<\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> +9.32\\frac{(x-4.04)(x-5.32)(x-6.87)}{(9.86-4.04)(9.86-5.32)(9.86-6.87)}+<\/span>\n\n\n\n<h2 class=\"wp-block-heading\">literal c. Polinomio simplificado<\/h2>\n\n\n\n<p>Simplificando las expresiones con el algoritmo:<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> p(x) = 0.31412 x^3 - 6.5377x^2 + 43.2911x - 83.0535 <\/span>\n\n\n\n<p>La gr\u00e1fica del polinomio se muestra a continuaci\u00f3n.<\/p>\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\/06\/DroneTrayectoria01.png\" alt=\"Drone en trayectoria de prueba 01\" class=\"wp-image-24772\" \/><\/figure>\n\n\n\n<p>Usando el algoritmo se obtiene:<\/p>\n\n\n\n<pre class=\"wp-block-code alignwide\"><code>&#091;4.04 5.32 6.87 9.86]\n&#091;5.85 9.52 7.65 9.32]\n    valores de fi:  &#091;5.85 9.52 7.65 9.32]\ndivisores en L&#091;i]:  &#091;-21.082368   9.00736  -13.115635  79.004172]\n\nInterpolaci\u00f3n Lagrange\n1.05691345743925*(x - 9.86)*(x - 6.87)*(x - 4.04) +\n0.117968453615336*(x - 6.87)*(x - 5.32)*(x - 4.04) +\n-0.277483060726385*(x - 9.86)*(x - 6.87)*(x - 5.32) +\n-0.583273322260036*(x - 9.86)*(x - 5.32)*(x - 4.04)\n\nPolinomio de Lagrange: \n0.314125528068165*x**3 - 6.53770577033544*x**2 + 43.2911387961625*x - 83.0535883598156\np(x):\n                   3                     2                                    \n0.314125528068165\u22c5x  - 6.53770577033544\u22c5x  + 43.2911387961625\u22c5x - 83.0535883598156<\/code><\/pre>\n\n\n\n<p>Literal d. otra trayectoria con algoritmo<\/p>\n\n\n\n<p>Se deja como tarea junto a las preguntas literal e  del ejercicio.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ejercicio: 1Eva2026PAOI_T3 Drone en zona de desastre las coordenadas posibles para el ejercicio son: literal a. Planteamiento Si selecciona los puntos: primero y \u00faltimo con dos puntos intermedios se obtendr\u00e1n 4 puntos para un polinomio de grado 3. p(x) = a + b x + cx2+d Siguiendo el modelo de Vandermonde, se escribe el t\u00e9rmino [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"wp-custom-template-entrada-mn-ejemplo","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[58,54],"class_list":["post-24770","post","type-post","status-publish","format-standard","hentry","category-mn-s1eva30","tag-ejemplos-python","tag-mnumericos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/24770","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=24770"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/24770\/revisions"}],"predecessor-version":[{"id":24782,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/24770\/revisions\/24782"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=24770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=24770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=24770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}