Write short notes on composite transformation, viewing transformation
Answers
If a transformation of the plane T1 is followed by a second plane transformation T2, then the result itself may be represented by a single transformation T which is the composition of T1 and T2 taken in that order.
This is written as T = T1∙T2.
Composite transformation can be achieved by concatenation of transformation matrices to obtain a combined transformation matrix.
A combined matrix :-
[T][X]=[X][T1][T2][T3][T4]….[Tn]
Where [Ti] is any combination of
Translation
Scaling
Shearing
Rotation
Reflection
The change in the order of transformation would lead to different results, as in general matrix multiplication is not cumulative, that is [A]. [B] ≠ [B]. [A] and the order of multiplication.
The basic purpose of composing transformations is to gain efficiency by applying a single composed transformation to a point, rather than applying a series of transformation, one after another.
For example, to rotate an object about an arbitrary point (Xp, Yp), we have to carry out three steps:- • Translate point (Xp, Yp) to the origin. • Rotate it about the origin. • Finally, translate the center of rotation back where it belonged.
A composite transformation is when two or more transformations are performed on a figure (called the preimage) to produce a new figure (called the image). Example A. Describe the transformations in the diagram below. The transformations involve a reflection and a rotation.
The viewing transformation is the operation that maps a perspective view of an object in world coordinates into a physical device's display space. ... Screen space refers to a coordinate system attached to a display device with the xy plane coincident with the display surface.