Page 139 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Unit 8: Implementing of Scaling in 2D Transformation

150 Notes
150
Enter your choice: 2
Enter the fixed point
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150
Enter your choice: 3
Enter the fixed point
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150
******2DTransformations******* 1.Translation
2. Rotation
3. Scaling
4. Reflection
5. Shearing
6. Exit
Enter your choice: 5
*******Shearing*********
1. x-direction shear
2. y-direction shear
Enter your choice: 1
Enter the value of shear: 2
Enter your choice: 2
Enter the value of shear: 2
RESULT: Thus the c program to implement 2D transformations was coded and executed
successfully.

2×SaI, short for 2× Scale and Interpolation engine, was inspired by Eagle.

8.2.6 Homogeneous Coordinates
In general, when you want to execute a complex transformation, you usually compose it by
combining a number of essential transformations. The above equation for q, however, is awkward
to read because scaling is done by matrix multiplication and translation is done by vector addition.
In order to represent all transformations in the same form, computer scientists have devised what
are called homogeneous coordinates. Do not try to apply any exotic interpretation to them. They
are merely a mathematical hoax to create the representation be more steady and easier to apply.
S È 0 0˘
Í x ˙
[x y 1] = [x y 1] 0 S y 0 ˙
Í
Í 0 0 1 ˙
Homogeneous Form of Scale: Î ˚
Recall the (x, y) form of Scale:
s È 0 ˘
S(s x , s y ) = Í x ˙
Î 0 s y ˚

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