Transformation

Mathematically or physically, Transformation refers to bringing abount a change in position, orientation and/or form of an object. Transformations can be classified in following ways.

  1. Based on type:
    1. Translation
    2. Rotation
    3. Reflection
    4. Scaling
    5. Shearing
  2. Based on whether the transformation alters the form of an object:
    1. Non Deformative: Translations, Rotations and Reflections are non deformative transformations
    2. Deformative: Scalings and Shearings are deformative transformations
  3. Based on steps involved in transforming the object:
    1. Simple Transformations: These are transformations that can be accomplished in a single step and cannot be broken down into further simpler steps. Following are simple transformations:
      1. All Translations
      2. Rotations in 2D with respect to origin. Rotations in 3D with respect to origin along coordinate axes.
      3. Reflections in 2D across coordinate axes and in 3D along coordinate planes
      4. Non anchord Scalings and Shearings (i.e when the object is not anchord to a particular point/passes through that point)
      Each of these transformation can be accomplished by multiplying the position vector of point by a single matrix.
    2. Composite Transformations: These are transformations that are a combination of 2 or more simple transformations. Following are composite transformations:
      1. Rotations in 2D or 3D with respect to any arbitrary point. Rotations in 3D along any arbitrary axis
      2. Reflection in 2D across and arbitrary line and in 3D accross an arbitrary plane
      3. Anchord Scalings and Shearings (i.e when the object is anchord to a particular point/passes through that point)
      Each step in each of these transformation is accomplished by multiplying the position vector of point by a single matrix. For e.g if any transformation can be accomlished in 5 steps, then it shall involve multiplication of 5 matrices.