2.8 坐标平面上的误差

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  坐标平板上的误差

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  Dilations in Animation
  ::动画中的差错

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  How can you make an object look like it is moving toward or away from the camera in a 2-dimensional cartoon?
  ::你如何能让一个物体看起来像 它向着或向着镜头移动 在一个二维的卡通片中?

  

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  Notice how the cat appears to be moving towards and away from you.
  ::注意这只猫的动向

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  Rigid motions make up three of the four principles of animation; rotation , translation, and reflection . The fourth principle is dilation. The lesson discussed how dilation acts a transformation that changes the size of a figure without changing its shape.
  ::僵硬的动作构成动画的四大原则中的三条:旋转、翻译和反射。第四个原则是放大。该教训讨论了放大如何影响改变数字大小而不改变其形状的变形。

   

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  Exploring Dilations
  ::探索关系

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  Animators use dilations to make objects appear as if they are moving toward or away from the camera. A dilation that increases the size of the image makes the image appear to be getting closer to the audience. A dilation that decreases the size of the image makes the image appear to be moving away from the audience.
  ::动画师使用动画师来使对象看起来好像它们正在向着或向着相机移动。放大图像大小的放大使图像看起来越来越接近观众。放大图像大小的放大使图像看起来远离观众。

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  Use the interactive below to explore the effect of scale on the perception of distance from the object.
  ::使用下面的交互效果来探索比例对与对象距离感知的影响。

  

  INTERACTIVE

  Duck Walk

  

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  • Drag the slider to choose a dilation and press "Move" to see the duck walk.
    ::拖动滑动器以选择放大符, 按“ 移动” 以查看鸭行走 。
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  • Use the checkbox to see the coordinate plane and points.
    ::使用复选框查看坐标平面和点 。

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  Predicting Dilations
  ::预测通货膨胀

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  The rules and notation for dilations centered at the origin in the coordinate plane are as follows:
  ::以坐标平面原点为主的放大法规则和标记如下:

  Center of Dilation	Scale	Pre-image ( Point P)	Dilated Image (Point P')	Notation
  $\begin{array}{r}(0,0)\end{array}$	$\begin{array}{r}k\end{array}$	$\begin{array}{r}(x,y)\end{array}$	$\begin{array}{r}(kx,ky)\end{array}$	$\begin{array}{r}{D}_k(x,y)\to (kx,ky)\end{array}$

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  By knowing the scale, you can locate each point of the dilated image based on the location of the points in the pre-image.
  ::通过了解比例尺, 您可以根据图像前图像中点的位置, 定位放大图像的每个点 。

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  Use the interactive below to determine where the lower left-hand point of the pre-image will be after a dilation.
  ::使用下面的交互作用来确定图像预视前的左下角在放大后的位置。

  

  INTERACTIVE

  What's the Dilation?

  

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  • Enter the  @$x@$   and @$y-@$ coordinate of the new point dilated by the scale.
    ::输入由比例尺放大的新点的@ $x@ $和@ $y- @ $coorder。
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  • Once correct, click "Next" to get a new triangle.
    ::一旦正确, 请单击“ 下一步” 获得一个新的三角形 。

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  Dilation in Graphic Design
  ::图形设计中的关系

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  Dilation is used in many professions, especially in professions that rely heavily on computers. Engineers use dilations when making 3D models. Mobile application and website designers  use them to make responsive apps and websites.  Dilations are a particularly important skill  for graphic designers .
  ::许多专业,特别是严重依赖计算机的行业,都使用比照法。工程师在制作3D模型时使用比照法。移动应用程序和网站设计师利用比照法制作响应应用程序和网站。对图形设计师来说,比照法是特别重要的技能。

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  You  are likely very experienced at using dilations without even realizing it. Anytime you have used a slideshow , photo editing, or word processing program you will often see dots on the corners of a picture that you can use to dilate an image. 
  ::您很可能在使用放大图时非常有经验, 甚至没有意识到它。 每当您使用幻灯片、 照片编辑或文字处理程序时, 您通常会看到图片的角上的点, 以便放大图像 。

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  In the interactive below, you are going to use your knowledge of the four transformations to create your very own graphic design. Come up with a positive message promoting digital citizenship and create a design around it.
  ::在下文的互动中, 您将使用您对四个变换的知识来创建您自己的图形设计。 生成一个正面的信息来促进数字公民意识, 并围绕它设计一个设计 。

  

  INTERACTIVE

  Heart Stamps

  

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  Move, flip, rotate, and dilate the heart and make a design by stamping new colors. There are only 13 stamps available, so make sure to design carefully!
  ::移动、 翻转、 旋转、 放大心脏, 并加盖新颜色来设计设计 。 只有13个邮票可用, 所以一定要仔细设计 !

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   Summary
  ::摘要

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  • To dilate a point $\begin{array}{r}P(x,y)\end{array}$  by  a scale  factor of  $\begin{array}{r}k\end{array}$   using a center of dilation at the origin , multiply the $\begin{array}{r}x\text{-}\end{array}$  and $\begin{array}{r}y\text{-}\end{array}$ coordinates by  $\begin{array}{r}k.\end{array}$  The resulting point will be  $\begin{array}{r}{P}^{\prime }(kx,ky).\end{array}$
    ::将点P( x,y) 乘以 k 的缩放因子, 使用源点的放大中心, 将点P( kx,y) 乘以 x 和 y 坐标, 乘以 k。 结果的点将是 P {( kx, ky) 。
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  • The four types of transformations are translations, reflections, rotations, and dilations. Only dilations change the size of a figure.
    ::四种变换类型是翻译、反射、旋转和推算。只有推算才能改变数字大小。