Page 94 - DCAP504_Computer Graphics

Unit 6: 2-D Transformation

(e) Which among the following is the inverse transformation matrix of clockwise rotation
transformation?

cos θ sin θ  0
 
 sin θ cos θ  0
 0 0 1 
(i)  
cos θ − sin θ  0
 
 sin θ cos θ  0
 0 0 1 
(ii)  

 cos θ sin θ  0
 
 − sin θ cos θ  0
 0 0 1 
(iii)  
cos θ sin θ  0
 
 sin θ − cos θ  0
 0 0 1 
(iv)  
6.8 Review Questions
1. “2-D transformation is nothing but mapping or transformation a 2-D point.” Explain.
2. “Translation transformation moves object from one position to another in 2-D space.” Discuss.

3. How do you scale a 2-D object using transformation matrix?
4. “Reflection and scaling transformation are related.” Explain.
5. “Reflection about Y axis is different from reflection about X axis.” Do you agree? Justify.
6. “Rotation transformation rotates the point coordinates by an angle clockwise or
counterclockwise.” Explain with an example.

7. Do you think X-shear and Y-shear are different? Discuss.
8. “Homogeneous coordinate system represents 2-D object as 3-D objects.” Explain.
9. Can you combine scaling and shear transformations? Discuss.
10. “The coordinates of rectangle object can be obtained after it undergoes X-shear transformation.“
Explain.

11. “Scaling is affine transformation.” Do you agree? Justify.
12. “The affine transformation of Rn is of the form Rn.” Explain.
Answers: Self Assessment
1. (a) True (b) False (c) True
(d) False (e) True (f) True

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