Mumbai university > Comp > SEM 4 > Computer Graphics

Marks: 5M

Year: May 2015

1. 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.

2. This is written as T = T1∙T2.

3. Composite transformation can be achieved by concatenation of transformation matrices to obtain a combined transformation matrix.

4. A combined matrix :-

$$[T][X] = [X] [T1] [T2] [T3] [T4] …. [Tn]$$

1. Where $[T_i]$ is any combination of

   • Translation
   • Scaling
   • Shearing
   • Rotation
   • Reflection

2. 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.

3. 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.

4. 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.