3-D Transformation is the process of manipulating the view of a three-D object with respect to its original position by modifying its physical attributes through various methods of transformation like Translation, Scaling, Rotation, Shear, etc
Properties of 3-D Transformation :
- Lines are preserved,
- Parallelism is preserved,
- Proportional distances are preserved.
Types of Transformations :
It is the process of changing the relative location of a 3-D object with respect to the original position by changing its coordinates. Translation transformation matrix in the 3-D image is shown as –
Where Dx, Dy, Dz are the Translation distances, let a point in 3D space is P(x, y, z) over which we want to apply Translation Transformation operation and we are given with translation distance [Dx, Dy, Dz] So, new position of the point after applying translation operation would be –
Problem : Perform translation transformation on the following figure where the given translation distances are Dx = 2, Dy = 4, Dz = 6.
Solution : On applying Translation Transformation we get corresponding points –
After performing translation transformation over the Fig.1, it will look like as below –
The steps involved in projection transformation?
A projection transformation also prepares for these follow-on tasks: Clipping - the removal of elements that are not in the camera’s line of sight. Viewport mapping - convert a camera’s viewing window into the pixels of an image. Hidden surface removal - determining which objects are in front of other objects.
3D Transformations take place in a three dimensional plane. 3D Transformations are important and a bit more complex than 2D Transformations. Transformations are helpful in changing the position, size, orientation, shape etc of the object.