Shape Transformations

Introduction to shape transformations:

  • Shape transformations is a change of position of an object on a plane.
  • Shape transformations are a function that is mapping to a set x into another set or mapping itself. Basically the Geometry transformation can be classified into two types. They are rigid and non- rigid transformation.
  • Here we are going to learn about different shape transformations.

 

Types of shape transformations:

 

Three main types of shape transformations are

  1. Translation
  2. Rotation
  3. Reflection

 

Special type of transformations are

  • Dilation
  • Glide reflection

 

Translations:

  • The mainly basic transformation is the translation.  The formal definition of a translation is "each point of the pre-image is moved the equal distance in the same direction to form the image.
  • Further advanced transformation geometry is finished on the coordinate plane.  The transformation is would be T(x, y) = (x+5, y+3).(x+5,y+3)

 

Rotation:

  • The distance between the center and any point of the object is same. Around the center each point makes a circle. Around the center point we can rotate the objects by an angle. It can be done with the counterclockwise.
  • That is with the fixed point we can spin the object.

 

Reflections:

 

The reflection is a "flip" of an aim over a line. 

The two very common reflections is given by

  •  A horizontal reflection
  •  A vertical reflection.

The colored vertices used for each of the triangle.  The line of reflection is halfway from both red points, blue points, and green points. The line of reflection is directly in the center of both points.

Dilation:

  •  Dilation is used to change the image size. The scale factor is used to measure the how much the image is smaller or greater.

Glide reflection:

  • Glide reflection is the combination of line of reflection and beside the translation line.

  • A glide reflection  it always combines a reflection with a translation along the direction of the mirror line

  • It is the only transformation it contains more than one step

  • Here first the reflection take place after that the translation will takes