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    forma de las caras de los objetos que se encuentran fuera de los ejes isométricos.

    Santiago

    Chicos, ¿alguien sabe la respuesta?

    obtenga forma de las caras de los objetos que se encuentran fuera de los ejes isométricos. de este sitio.

    Proyección isométrica

    Proyección isométrica

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    Figuras en proyección isométrica

    Una proyección isométrica es un método de representación gráfica, más específicamente una axonométrica1​ cilíndrica2​ortogonal.3​ Constituye en una representación visual de un objeto tridimensional que se reduce en dos dimensiones, en la que los tres ejes ortogonales principales, al proyectarse, forman ángulos de 120°, y las dimensiones paralelas a dichos ejes se miden en una misma escala.

    El término isométrico proviene del idioma griego: "igual al tiempo", y al castellano "igual medida" ya que la escala de medición es la misma en los tres ejes principales (x, y, z).

    La isometría es una de las formas de proyección utilizadas en dibujo técnico que tiene la ventaja de permitir la representación a escala, y la desventaja de no reflejar la disminución aparente de tamaño -proporcional a la distancia- que percibe el ojo humano.

    Índice

    1 Historia 2 Visualización 3 Dibujo isométrico 4 Aplicaciones

    4.1 En el diseño y el dibujo técnico

    4.2 En Arquitectura 4.3 En videojuegos

    5 Aspectos matemáticos

    5.1 Factor de reducción sobre los ejes

    5.2 Transformación de coordenadas

    5.2.1 Transformación de un círculo del plano conteniendo dos ejes

    6 Notas 7 Véase también 8 Bibliografía 9 Enlaces externos

    Historia[editar]

    Artículo principal:

    Proyección isométrica.

    Modelo de motor de molienda (1822), dibujado en una isométrica a 30°.4​

    Ejemplo de arte chino en una edición ilustrada del Romance de los Tres Reinos, China, ca. siglo XV.

    Formalizado en primer lugar en 1822 por el profesor William Farish (1759-1837), el concepto de isometría había existido en una forma empírica más o menos aproximada desde siglos antes.5​6​ Desde mediados del siglo XIX, la isometría se convirtió en una «herramienta inestimable para los ingenieros, y poco después la axonometría y la isometría fueron incorporadas en el plan de estudios de los cursos de formación de arquitectura en Europa y los EE.UU.»7​ Según Jan Krikke (2000),8​ sin embargo," «la axonometría se originó en China. Su función en el arte chino fue similar al de la perspectiva lineal en el arte europeo. La axonometría, y la gramática pictórica que va con ella, ha adquirido una nueva significación con el advenimiento de la computación visual».8​

    Un ejemplo de las limitaciones de la proyección isométria: la diferencia de altura entre las bolas azul y roja no se puede determinar.

    La escalera de Penrose representa una escalera que parece subir (sentido antihorario) o descender (en sentido horario) ya que forma un bucle continuo.

    Como todos los tipos de proyección paralela, los objetos dibujados con proyección isométrica no aparecen mayores o menores a medida que se alejen o acerquen al espectador. Mientras es ventajosa para los dibujos arquitectónicos, en los que las mediciones deben ser tomadas directamente, el resultado es una distorsión de la percepción, ya que a diferencia de la proyección de perspectiva, no es cómo funciona normalmente la visión humana o la fotografía. También puede dar lugar fácilmente a situaciones en las que la profundidad y la altura son difíciles de medir, como se muestra en la imagen de la derecha. Esto puede parecer paradójico o crear formas imposibles, como las escalera de Penrose.

    Visualización[editar]

    La isometría determina una dirección de visualización en la que la proyección de los ejes coordenados , , conforman el mismo ángulo, es decir, 120° entre sí. Los objetos se muestran con una rotación del punto de vista de 30º en las tres direcciones principales (x, y, z).

    Esta perspectiva puede visualizarse considerando el punto de vista situado en el vértice superior de una habitación cúbica, mirando hacia el vértice opuesto. los ejes x e y son las rectas de encuentro de las paredes con el suelo, y el eje z, el vertical, el encuentro de las paredes. En el dibujo, los ejes (y sus líneas paralelas), mantienen 120° entre ellos.

    Dentro del conjunto de proyecciones axonométricas o cilíndricas, existen otros tipos de perspectiva, que difieren por la posición de los ejes principales, y el uso de diferentes coeficientes de reducción para compensar las distorsiones visuales.

    Dibujo isométrico[editar]

    Las figuras de la izquierda son las vistas en sistema diédrico, mientras que a la derecha se ve una proyección isométrica con una sección parcial.

    Una variedad muy utilizada de la perspectiva isométrica es el dibujo isométrico. En la isométrica el coeficiente de reducción de las dimensiones . Al ser la reducción idéntica en los tres ejes el dibujo isométrico se realiza sin reducción, con las dimensiones paralelas a los ejes a escala 1:1 o escala natural, sin que cambie la apariencia del dibujo salvo en su tamaño. Esto permite tanto dibujar directamente estas dimensiones en el papel lo que facilita el dibujo por coordenadas cartesianas como medir directamente en el dibujo las de un objeto. La apariencia del dibujo es idéntica aunque más grande, y las dimensiones que en la perspectiva correcta serían iguales a las reales (las paralelas al plano de proyección) son mayores.

    fuente : es.wikipedia.org

    La Perspectiva Isométrica

    Perspectiva Isométrica: Concepto Es una forma de proyección gráfica o, más específicamente, una axonométrica (proyección medida mediante ...

    La Perspectiva Isométrica

    - julio 08, 2018

    Perspectiva Isométrica: Concepto

    Es una forma de proyección gráfica o, más específicamente, una axonométrica (proyección medida mediante ejes X, Y y Z) cilíndrica ortogonal. Es una representación de un objeto tridimensional en dos dimensiones en la que los tres ejes de referencia tienen ángulos de 120º, y las dimensiones guardan la misma escala sobre cada uno de ellos. Por ende los 3 ejes X, Y y Z tiene la misma magnitud y escala.

    La isometría es una de las formas de proyección más utilizadas en dibujo técnico ya que tiene la ventaja de permitir la representación a escala en sus tres dimensiones, pero que tiene la desventaja de no reflejar la percepción «real» del ojo humano.

    VENTAJAS DEL DIBUJO ISOMÉTRICO

    Una de las grandes ventajas del dibujo isométrico es que se puede realizar el dibujo de cualquier modelo sin utilizar ninguna escala  especial, ya que las líneas paralelas a los ejes se toman en su verdadera magnitud. Así por ejemplo, el cubo cuando lo dibujamos en forma isométrica queda con todas sus aristas de igual medida.

    EJES UTILIZADOS EN EL DIBUJO ISOMÉTRICO

    La base del dibujo isométrico es un sistema  de tres ejes que se llaman  “ejes isométricos” que representan a las tres aristas de un cubo, que forman entre sí ángulos de 120°.

    a) LÍNEAS ISOMÉTRICAS:

    Son aquellas líneas que son paralelas a cualquiera de los tres ejes isométricos.

    b) LÍNEAS NO ISOMÉTRICAS:

    Son aquellas líneas inclinadas sobre las cuales no se pueden medir distancias verdaderas; estas líneas cuando se encuentran presente en un dibujo isométrico no se hallan ni a lo largo de los ejes ni son paralelas a los mismos. Además las líneas no isométricas se dibujan tomando como puntos de referencia otros puntos pertenecientes a líneas isométricas.

    Aplicaciones

    En el diseño y el dibujo técnico

    En diseño industrial se representa una pieza desde diferentes puntos de vista, perpendicular a los ejes coordenados naturales. Una pieza con movimiento mecánico presenta en general formas con ejes de simetría o caras planas. Tales ejes, o las aristas de las caras, permiten definir una proyección ortogonal.

    Se puede fácilmente dibujar una perspectiva isométrica de la pieza a partir de tales vistas, lo que permite mejorar la comprensión de la forma del objeto.

    En arquitectura

    El castillo del Louvre, dibujo isométrico de Viollet-Le-Duc, (814-1879)

    La perspectiva de este dibujo del castillo no es isométrica, si así lo fuera, las torres del castillo estarían dibujadas con la misma altura y diámetro, además las líneas de cumbreras de los tejados serían paralelas entre si, formando un rombo o romboide dependiendo de la planta del castillo. Eugène Viollet-le-Duc utilizó este sistema en muchos dibujos de sus edificios, evitando acentuar la importancia de unos volúmenes sobre otros e independizándose del punto de vista del observador.

    En videojuegos

    Cierto número de videojuegos pone en acción a sus personajes utilizando un punto de vista en perspectiva isométrica, o mejor dicho, en la jerga usual, en "perspectiva 3/4". Desde un ángulo práctico, ello permite desplazar los elementos gráficos sin modificar el tamaño, limitación inevitable para ordenadores con baja capacidad gráfica.

    A fin de evitar el pixelado, en algunos casos se llevó la proyección a un sistema 2:1, vale decir a una inclinación de 26,6º (arctan 0,5) en lugar de 30º, que no corresponde a una proyección isométrica propiamente dicha, sino .

    El progresivo incremento en las capacidades gráficas de los ordenadores ha posibilitado el uso cada vez más generalizado de sistemas de proyección más realistas, basados en la perspectiva naturalmente percibida por el ojo humano: la perspectiva cónica.

    Videojuego Isométrico

    Isométrico perspectiva Tipos de perspectivas

    fuente : perspectivasdt.blogspot.com

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    fuente : brainly.lat

    ¿Quieres ver la respuesta o más?
    Santiago 16 day ago
    4

    Chicos, ¿alguien sabe la respuesta?

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