1.10 坐标板上的旋转-interactive

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  坐标板上的旋转

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  Rotations in Video Games
  ::视频游戏中的变换

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  Rotations are commonly used in video games anytime something turns. In 2-dimensional video games, rotations could be used for a character turning when the camera is fixed overhead or when any object in the environment turns. In 3-dimensional video games, rotations are being used nearly every second whether the camera is turning, a character is turning or an object in the environment is turning. Video game developers need to be able to program rotations to ensure that the game looks and behaves exactly how they want.
  ::视频游戏通常在视频游戏中任意旋转。在二维视频游戏中,当相机固定在上方或当环境中的任何对象旋转时,可使用旋转来转换字符。在三维视频游戏中,旋转几乎每秒就使用一次,无论相机正在旋转、字符正在旋转或环境中的对象正在旋转。视频游戏开发者需要能够编程旋转以确保游戏的外观和行为符合他们的要求。

   

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  Understanding Rotations
  ::理解 轮换

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  Here you will be looking at rotations on the Cartesian coordinate plane . A rotation occurs when an image turns around a center of rotation with every point of the rotated image remaining the same distance from the center of rotation. For now, you will specifically be looking at 90°, 180°, and 270° rotations around the origin .
  ::这里您将查看笛卡尔坐标平面上的旋转。 当图像围绕旋转中心旋转时会发生旋转, 旋转图像的每一点与旋转中心保持相同的距离。 目前, 您将具体查看90°、 180°和270°左右的旋转 。

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  Unless otherwise specified, a positive rotation is counterclockwise , and a negative rotation is clockwise .
  ::除非另有说明,正旋转是逆时针,负旋转是顺时针。

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  Use the interactive below to explore how 90°, 180°, and 270° rotations are related to the $\begin{align*}x\end{align*}$  coordinates and $\begin{align*}y\end{align*}$  coordinates of a point.
  ::使用下面的交互作用来探讨90°、180°和270°旋转与点的x坐标和y坐标的关系。

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. Allow students time to explore the interactive. Ask them to make a table to catalog 90°, 180°, or 270° both clockwise and counterclockwise. They should list the starting coordinate, the rotated coordinate, and what they believe the rule is.
     ::允许学生有时间探索互动关系。 让他们制作一个表格, 以列出90°, 180°, 或270°的目录, 包括时钟和逆时针。 他们应该列出起始坐标、 旋转坐标, 以及他们认为规则是什么 。
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  2. Why do you notice about a 90° clockwise rotation and a 270° counterclockwise rotation?
     ::为何你注意到90°时钟旋转 270°时钟逆时钟旋转?

   

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  Predicting Rotations
  ::预测轮调

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  The rules for rotations are listed in the table below:
  ::下表列出了轮换规则:

  Center of Rotation	Angle of Rotation	Pre-image (Point P )	Rotated Image (Point P ′ )	Notation (Point P ′ )
  (0, 0)	播放段落 90°  Clockwise ::90° 顺时针 播放段落 270° Counterclockwise ::270° 逆时针	$\begin{align*}(x,y)\end{align*}$	$\begin{align*}(y,\text{-}x)\end{align*}$	播放段落 $\begin{align*}R_{90} (x,y)→(y,\text{-}x)\end{align*}$ ::R90(x,y)(y,-x)
  (0, 0)	播放段落 180 °  Clockwise ::180° 顺时针 播放段落 180 °  Counterclockwise ::180° 逆时针	$\begin{align*}(x,y)\end{align*}$	$\begin{align*}(\text{-}x,\text{-}y)\end{align*}$	$\begin{align*}R_{180} (x,y)→(\text{-}x,\text{-}y)\end{align*}$
  (0, 0)	播放段落 270° Clockwise ::270° 顺时针 播放段落 90° Counterclockwise ::90° 逆时针	$\begin{align*}(x,y)\end{align*}$	$\begin{align*}(\text{-}y,x)\end{align*}$	$\begin{align*}R_{270} (x,y)→(\text{-}y,x)\end{align*}$

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  Example:
  ::示例:

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  Rotate the point (5, 8) about the origin 270° clockwise.
  ::顺时针旋转原点( 5, 8) 270 ° 。

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  The rule for rotating an object 270° clockwise about the origin is to take the opposite value of the $\begin{align*}x\end{align*}$  coordinate and then switch it with the $\begin{align*}y\end{align*}$  coordinate. The opposite of 5 is -5 and, switching the coordinates, we obtain our answer: (8, -5).
  ::对象 270 ° 时钟旋转原值的规则是取X 坐标的相反值,然后用 Y 坐标切换。 5 的相反值是 - 5, 交换坐标, 我们得到答案是: (8, 5) 。

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  Now, with the interactive below,practice using these rules to predict where a point that has been rotated about the origin will land.
  ::现在,在下面的交互作用下, 使用这些规则来预测 有关原产地的转动点 将到达何处。

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  Discussion Question
  ::讨论问题

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  How do rotations on the coordinate plane differ from the rotations you have practiced before? How is it the same? Think about your answers in terms of the .
  ::坐标平面上的旋转与您以前练习过的旋转有何不同? 相同吗? 考虑一下您的答案 。

   

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  Rotating Shapes
  ::旋转形状

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  When translating or reflecting shapes, each point in the shape is determined individually. As you might expect, you take the same approach to rotate shapes.
  ::当翻译或反映形状时, 形状中的每个点都是单独决定的。 正如您可能期望的那样, 您会采取相同的方法来旋转形状 。

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  For example, to rotate a shape 90° clockwise about a given location, rotate each individual point 90° clockwise around the location.
  ::例如,要对特定位置旋转形状90°时钟,每个单个点90°时钟围绕位置旋转。

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  Use the interactive below apply this approach to predict the new location of $\begin{align*}ABC\end{align*}$  for each given rotation.
  ::使用以下交互式互动方法来预测每个特定旋转的ABC新位置。

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    Summary
  ::摘要

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  • Unless otherwise specified, a positive rotation is counterclockwise, and a negative rotation is clockwise.
    ::除非另有说明,正旋转是逆时针,负旋转是顺时针。
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  • The notation used for rotations on the coordinate plane is:  $\begin{align*}R_{\text{number of degrees}} (x,y)→(x', y').\end{align*}$  
    ::坐标平面旋转所用的标记是:度数(x,y)%(x_,y_)%(x_,y_)。
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  • To rotate a shape, you should usually rotate each vertex of the image individually.
    ::要旋转形状, 您通常应该单独旋转图像的每个顶部 。