Section outline

  • How Are Cartoons Related to Geometry?
    ::卡通与几何关系如何?

    Until the early 2000s, cartoons were created by rapidly displaying sequences of hand-drawn images. Animators used this "traditional animation" technique to create cartoon animations dating as far back as the invention of the Phenakistoscope  in 1833. Animators  had to painstakingly draw each image, and a 20-minute cartoon made this way required around 30,000 hand-drawn images!
    ::直到20世纪初,漫画都是通过快速展示手绘图像序列而制作的。 动画家利用这种“传统动画”技术创造了动画动画,这些动画可追溯到1833年的Phenakistoscope发明。 动画家们不得不费尽心机地绘制每幅图像,而一个20分钟的动画制作过程需要大约30,000张手绘图像!

    Phenakistoscope animation of man pumping water
    Sample phenakistoscope animation.

    In the early 2000s, the introduction of computer software completely changed the way cartoons were created by allowing animators to use rigid motion. Computers allowed animators to draw a character or object once, then specify where and how it should move rather than drawing each movement frame by frame.
    ::在2000年代初期,计算机软件的引入彻底改变了漫画的创建方式,允许动画家使用僵硬运动。 计算机允许动画家一次性绘制字符或对象,然后具体说明它应该移动到哪里和如何移动,而不是按框架绘制每个移动框架。

    In this lesson, you will  learn about the basic types of rigid motions. You will learn more about each type in other lessons. For now, just focus on the differences between the types and how to identify each.
    ::在此教训中, 您将了解僵硬动议的基本类型。 您将在其他教训中学习更多关于每种类型的内容 。 目前, 您只关注类型之间的差异以及如何识别每种类型 。

    Rigid motion changes the location of a figure, or the direction it is facing, but does not change its size or shape.  The three  basic  rigid  motions  are translation, reflection , and rotation .
    ::硬动作会改变数字的位置或方向,但不会改变其大小或形状。 三种基本硬动作是翻译、反射和旋转。

    Rigid Motion types include translations (also called slides), rotations, and reflections
    Basic Rigid Motions

    A pre-image describes a point or shape  before it is moved. Apostrophes are used to  identify a point or shape which has been translated, reflected, or rotated. If an original point is called A, the corresponding point  that has undergone the rigid motion will be called A' (read as "A prime" - in math, an apostrophe commonly indicates the word "prime").
    ::预映像描述移动前的点或形状。 代号缩略图用于识别翻译、 反射或旋转的点或形状。 如果原点被称为 A, 则经历僵硬动作的相应点将被称为 A ”( 读为“ 质数 ” - 在数学中, 代号通常表示“ 质数 ” ) 。

    Two lightning bolt images, one called the image and the other called the pre-image.
    Shape ABC is translated and the new image is "A-Prime, B-Prime, C-Prime."

     

    Transportation Translation
    ::运输翻译

    Translations move an image a certain distance in a specific direction without changing the size or shape of the image. Every point of the image is moved the same distance and in the same direction. Use the interactive below to explore how shapes are translated using direction and distance.
    ::翻译将图像移到特定方向,而不改变图像的大小或形状。图像的每个点都移动同一距离和方向。使用下面的交互作用来探索如何使用方向和距离翻译形状。

     

    INTERACTIVE
    Car Translation
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    • Move the red point to change the direction of translation .
      ::移动红点以改变翻译方向。
    • Change the distance of the translation with the white point, then click ‘Move’!
      ::用白点更改翻译的距离, 然后单击“ 移动 ” !
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    Translations are commonly used in video game design. Some popular video games, such as Flappy Bird, use only translations. How could this interactive be turned into a video game without changing how the car moves?
    ::视频游戏设计通常使用翻译。 一些流行的视频游戏,如Flappy Bird,只使用翻译。 如何将这种互动转化为电子游戏而不改变汽车移动方式?

    Discussion  Question
    ::讨论问题

    Create or describe a scene from a movie or video game that would involve an animation using only a translation.
    ::创建或描述电影或视频游戏中仅使用翻译而涉及动画的场景 。

     

    Plane Ordinary Reflections
    ::平时思考

    Reflections flip an image over a mirror line . Every point of the flipped image is the same distance from the mirror line as the original shape.   A reflection is a rigid motion where the object will reflect in a certain direction over a mirror line . Use the interactive below to explore how shapes are reflected across a mirror line. 
    ::反射镜像将图像翻转到反射线上。 翻转图像的每个点与反射线的距离与原始形状的距离相同。 反射是一个僵硬的动作, 对象会从反射线的某个方向反射到反射线上。 使用下面的交互动作来探索反射镜线上的形状如何反射 。

     

    INTERACTIVE
    Plane Flip
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    • Move the points to change the line.
      ::移动点以更改线条 。
    • Then press flip to reflect the plane across the line!
      ::然后按翻转来反射横跨线的飞机!
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    Discussion  Question
    ::讨论问题

    Earlier, you created a scene involving an animation that used a translation. Add an animation to your scene the uses a reflection.
    ::早些时候, 您创建了一个包含动画的场景, 动画使用了翻译。 在您的场景中添加动画, 并使用反射 。

     

    Rocket  Rotation
    ::火箭旋转

    Rotations turn an image around a center of rotation . As the image turns, every point of the image remains the same distance from the center of rotation as when it started. De scribing a rotation type of rigid motion  requires the location of the center of rotation and the number of degrees to rotate the image.
    ::旋转将图像围绕旋转中心旋转。 当图像旋转时, 图像的每一个点都与旋转中心保持与开始时相同的距离。 描述旋转类型的硬动作需要旋转中心的位置和旋转图像的度数。

    Use the interactive below to explore how shapes are rotated around a center of rotation. Then answer the questions.
    ::使用下面的互动来探索形状如何围绕旋转中心旋转。 然后回答问题 。

     

    INTERACTIVE
    Spaceship Rotations
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    • Use the direction buttons to choose to move clockwise or counterclockwise.
      ::使用方向按钮选择顺时针或逆时针移动 。
    • Choose an angle and then press rotate!
      ::选择一个角度, 然后按旋转 !
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    Discussion  Question
    ::讨论问题

    Add an animation involving a rotation to the scene you created in activity 1 and activity 2.
    ::在您在活动1和活动2中创建的场景中添加包含旋转的动画。

     

    Rigid Motions United
    ::硬体动议联合

    The first cartoon  that was created using only modern 2D animation was ¡Mucha Lucha! in 2002. Today, nearly all cartoons are created using computer programs that use rigid motions to control the movements of characters and objects. Below is an example of a simple animation.
    ::第一个仅使用现代 2D 动画制作的漫画是2002 年的 Mucha Lucha! 今天,几乎所有的漫画都是使用计算机程序制作的,这些程序使用僵硬的动作来控制字符和物体的移动。 下面是简单动画的一个例子。

    Watch  the  animation and try to identify any translations, rotations, and reflections that take place. 
    ::观看动画, 并尝试识别任何翻译、 旋转和反射 。

     

    INTERACTIVE
    Rigid Motion Animation
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    • Press animate to see the animation.
      ::按动画来查看动画 。
    • Press stop to stop the animation.
      ::按住停止停止动画 。
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        Summary
    ::摘要

    • Rigid Motions change the position or orientation of a n image or point, but do not change the size or the shape of it.
      ::硬动作改变图像或点的位置或方向,但不改变图像或点的大小或形状。
    • Rotations, transformations, and reflections are all rigid motions.
      ::变换、变换和反省都是僵硬的动议