Derive the single combined transformation matrix, Computer Graphics

Assignment Help:

A 2D geometric shape is rotated about a point with coordinates (1,2)  by 90°  in a clockwise direction.  Then, the shape is scaled about the same point in the x-coordinate by 2 times and in the y-coordinate by 3 times. Finally, the shape is reflected about the origin.  Derive the single combined transformation matrix for these operations.

Answer: The sequence of transformations is as follows. 

887_Derive the single combined transformation matrix.png

From right to left the sequence is as follows- (i) Translate so that (1,2) moves to origin (ii) Rotate about the origin by -90°  (iii) Scale by (2,3) (iv) Translate back so that (1,2)  is at its previous position (v) Flip about the origin. Single combined transformation can be obtained by multiplying all these matrices.


Related Discussions:- Derive the single combined transformation matrix

Translate a square - 2-d and 3-d transformations, Example1: Translate a sq...

Example1: Translate a square ABCD along with the coordinates as: A(0,0),B(5,0),C(5,5),D(0,5) via 2 units in x-direction and 3 units in y-direction. Solution: We can show the

Scenes - polygon rendering and ray tracing methods, Scenes - polygon render...

Scenes - polygon rendering and ray tracing methods In the context of ray tracing, a scene is a set of objects and light sources which will be viewed through a camera. All of

Explain the working of animators, Explain the working of Animators Anim...

Explain the working of Animators Animators want to create a human image that moves and interacts with its background in such a way that viewers can't tell if a specific scene i

Interactive 3d computer graphics, Describe interactive model of computer gr...

Describe interactive model of computer graphics and application areas of interactive computer graphics.

Computer aided design and computer aided manufacturing, The development of ...

The development of CAD had little consequence on CNC initially because of the various abilities and file formats used through drawing and machining programs. Conversely, as Compute

Flat panel displays - hardware primitives, Flat Panel Displays - Hardware P...

Flat Panel Displays - Hardware Primitives 1.  Flat panel displays have now become more common. These include liquid crystal displays (LCD) and thin film electroluminescent disp

What are the disadvantages of CAD, Disadvantages of CAD - Risk of deski...

Disadvantages of CAD - Risk of deskilling - High training costs to use packages - Can move work overseas     One CAD operator can do work of 5 manual draftsmen

Subdivision of polygon - visible surface detection , Subdivision of polyg...

Subdivision of polygon Test to find out the visibility of a single surface are made through comparing surfaces that as polygons P along regarding a specified screen area A.

Classification of print finishing processes, Problem: a. Provide exampl...

Problem: a. Provide examples of classification of print finishing processes. b. In advertising, what do you meant by creative strategies? c. Creative strategies are div

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd