Page 147 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Unit 8: Implementing of Scaling in 2D Transformation

• all transformations expressed as matrices Notes
2. Used by the window system:
• for conversion from model to window

• for conversion from window to model
3. Used by the application:

• for modelling transformations
Self Assessment Questions
6. There is simply a ………… trick to make the representation be more consistent and easier
to use.
7. Homogeneous coordinates (HC) add an extra ………. dimension.
8. To scale or rotate about a particular point we must first ……. the objects so that the fixed
point is at the origin.
9. Scaling does not preserve …….. in objects.
10. If scaling is not at origin, translates ……… relative to origin often not desired.
11. 2D transformations are used by the window system for conversion from model to ……..

12. We scale an object by scaling the …………… of each vertex in the object.
13. Scaling is use to changing the ………. of an object.
14. 2D transformations are simple in using ………….
15. A linear transformation is a function between two vector spaces that preserves the
operations of vector addition and scalar multiplication.
(a) True (b) False

8.3 Summary

• Transformations are used to position objects, to shape objects, to change viewing positions,
and even to change how something is viewed.
• Scale is changing the size of an object.
• A linear transformation is a function between two vector spaces that preserves the
operations of vector addition and scalar multiplication.
• 2D transformations are used by the window system for conversion from window to model.

• 2D transformations are simple in using homogeneous coordinates.
• If scaling is not at origin, translates house relative to origin often not desired.
• There is simply a mathematical trick to make the representation be more consistent and
easier to use.
• 2D transformations are used by the application for modelling transformations.
• In 2D transformations, all transformations expressed as matrices.

8.4 Keywords

Homogeneous Coordinates: It usually used to perform a complex transformation.
Linear Transformation: It is a function between two vector spaces that preserves the operations
of vector addition and scalar multiplication.

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