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  • 关系属性

    Dilations in Animation
    ::动画中的差错

    The lesson     discussed  how animators use rigid motions.  Rigid motions change the location or orientation of an image but not the size or shape. The three basic rigid motions are translations, reflections , and rotations . In addition to being rigid motions, these are also considered transformations. Transformations change the location or orientation of an image but not the shape. Rigid motions are transformations that move an image, but do not change the size.  The only transformation that is not a rigid motion is dilation. A dilation is a transformation that changes the size of a figure.
    ::模拟器如何使用僵硬动作。 僵硬动作会改变图像的位置或方向, 但不改变大小或形状。 三种基本僵硬动作是翻译、 反射和旋转。 除了僵硬动作外, 这些也被视为变换。 变换会改变图像的位置或方向, 而不是形状。 僵硬动作是移动图像的变换, 但不会改变大小。 唯一不是僵硬动作的变换就是变形。 变形会改变数字的大小。

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    Understanding Dilations
    ::理解 理解 关系

    To  perform a dilation, you need to specify a scale factor and a center of dilation. The scale factor is the number which is used to multiply the size of the image. The center of dilation is the point  from which the image is being dilated. 
    ::要进行放大, 您需要指定一个比例因子和一个计算中心。 缩放因子是用来乘以图像大小的数字。 放大中心是放大图像的点 。

    Use the  interactive below to experiment with scale.
    ::使用下方的交互性来实验比例尺。

     

    INTERACTIVE
    Walking Man
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    • Change the dilation factor using the slider.
      ::使用滑动滑动器更改膨胀系数 。
    • Press the "Move" button to move the person or "Reset" button to bring him back to his original position.
      ::按“ 移动” 按钮将人移动或“ 重置” 按钮将他带回原来的位置 。
    • Notice how the man is also being reflected to make him look like he is walking.
      ::注意这名男子如何被反映 使他看起来像在走路。
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    Discussion  Question
    ::讨论问题

    The animator of this interactive used another rigid motion-based trick to enhance the illusion of the man moving closer or further away. Can you identify it?
    ::这个互动的动画师又用另一个僵硬的动作把戏 来强化男人的幻觉 接近或更远。你能认出它吗?

     

    Measure Sides and Angles
    ::测量边和角度

    E ngineer s use dilation any time they design something by making a blueprint. A blueprint is a  scale drawing of a structure with proportional dimensions and the same angles . By measuring the sides and angles on the blueprint, construction workers can find the dimensions and angles  of  the real structure.
    ::工程师们在设计某件作品时都会通过制定蓝图来使用放大法。 蓝图是一个比例尺结构的绘制图,其尺寸和角度是成比例的。 通过测量蓝图的侧面和角度,建筑工人可以找到真实结构的尺寸和角度。

    lesson content
    A construction blueprint

    Use the interactive below to determine how the side lengths and angles are affected by a dilation.
    ::使用下面的交互作用来确定侧边长度和角度如何受到放大的影响。

     

    INTERACTIVE
    Measuring Dilation
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    • Move the red points to dilate the green shape or to measure the side lengths and angles of the two shapes.
      ::移动红点以扩大绿色形状或测量两个形状的侧边长度和角度。
    • Use the dropdown menu to switch between the ruler or protractor.
      ::使用下拉菜单在标尺或减速器之间切换。
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    Determining the Scale Factor
    ::确定比额表因素

    If an image has been dilated, it is important to be able to determine the scale factor which produced the image so that other images can be dilated by the same amount. For example, in animation, if an object is moving toward the screen, every part of the object should be dilating accordingly. To do this ,  remember the following formula:
    ::如果图像被放大,必须能够确定生成图像的缩放因子,以便其他图像能够以同样数量被放大。例如,在动画中,如果一个对象正在向屏幕移动,该对象的每个部分都应相应扩大。要做到这一点,请记住以下公式:

    (pre-image side length) × (scale factor) = image side length

    :sad预图像副边长)xx(比例因数)=图像副边长

    Example
    ::示例示例示例示例

    I f  A B = 5  and  A ′ B ′ = 8 ,  what scale factor  was used?
    ::如果AB=5和AB=8,使用何种比例系数?

    ( 5 ) ( x ) = 8 x = 1.6

    :sad5)(x)=8x=1.6

    Use the interactive below to determine the dilation which produced the image.
    ::使用下方的交互性来确定生成图像的放大度。

     

    INTERACTIVE
    What's the Dilation?
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    Enter the dilation factor that produces the pink triangle image from the blue triangle.
    ::输入从蓝色三角形生成粉红色三角形图像的放大系数。

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     Summary
    ::摘要

    • Dilation is a type of transformation that changes the size of a figure based on a scale factor and center of dilation.
      ::膨胀是一种变异类型,根据比例系数和膨胀中心改变一个数字的大小。
    • The scale factor is the  value  by which each dimension of the image is multiplied .
      ::缩放系数是图像每个维度乘以的值。
    • The center of dilation is the point from which the image is dilated.
      ::放大中心是放大图像的点。