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.
Based on type:
Based on whether the transformation alters the form of an object:
- Non Deformative: Translations, Rotations and Reflections are non deformative transformations
- Deformative: Scalings and Shearings are deformative transformations
Based on steps involved in transforming the object:
- 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:
Each of these transformation can be accomplished by multiplying the position vector of point by a single matrix.
- All Translations
- Rotations in 2D with respect to origin. Rotations in 3D with respect to origin along coordinate axes.
- Reflections in 2D across coordinate axes and in 3D along coordinate planes
- Non anchord Scalings and Shearings (i.e when the object is not anchord to a particular point/passes through that point)
- Composite Transformations: These are transformations that are a combination of 2 or more simple transformations. Following are composite transformations:
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.
- Rotations in 2D or 3D with respect to any arbitrary point. Rotations in 3D along any arbitrary axis
- Reflection in 2D across and arbitrary line and in 3D accross an arbitrary plane
- Anchord Scalings and Shearings (i.e when the object is anchord to a particular point/passes through that point)