Introduction of 2-D and 3-D Transformations
In this, the subsequent things have been discussed in detail as given below:
- Different geometric transformations as translation, scaling, reflection, shearing and rotation.
- Translation, Reflection and Rotation transformations are utilized to manipulate the specified object, where Shearing and Scaling both transformation changes their sizes.
- Translation is the process of altering the position but not the shape/size, of an object with respect to the origin of the coordinate axes.
- In 2-D rotation, an object is rotated via an angle θ. There are two cases of 2-Dimentional rotation: case1- rotation regarding to the origin and case2- rotation regarding to an arbitrary point. Consequently, in 2-D, a rotation is prescribed by an angle of rotation θ and a centre of rotation, as P. Conversely, in 3-D rotations, we require to mention the angle of rotation and the axis of rotation.
- Scaling process is mostly utilized to change the shape or size of an object. The scale factors find out whether the scaling is a magnification, s>1 or a reduction as s<1.
- Shearing transformation is a particular case of translation. The consequence of this transformation looks like "pushing" a geometric object in a direction which is parallel to a coordinate plane as 3D or a coordinate axis as 2D. How far a direction is pushed is found by its shearing factor.
- Reflection is a transformation that generates the mirror image of an object. For reflection we require to know the reference axis or reference plane depending upon where the object is 2-D or 3-D.
- Composite transformation engages more than one transformation concatenated in a particular matrix. Such process is also termed as concatenation of matrices. Any transformation made about an arbitrary point makes use of composite transformation as Rotation regarding to an arbitrary point, reflection regarding to an arbitrary line, and so on.
- The utilization of homogeneous coordinate system to shows the translation transformation into matrix form, enlarges our N-coordinate system along with (N+1) coordinate system.