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

Whether cavalier projection is a parallel projection, State whether the fol...

State whether the following statements are true or false. Give reasons/examples to justify your answer.  a)  Cavalier projection is a parallel projection. b)  Angles are not

Merits -phong shading or normal vector interpolation shading, Merits -Phong...

Merits -Phong shading or Normal Vector Interpolation Shading Hence by finding intensities at various points across the edge we determine the intensity that is varying across t

Multimedia, Multimedia- It is a new aspect of literacy which is being recog...

Multimedia- It is a new aspect of literacy which is being recognized as technology expands the manner people communicate. The principle of literacy increasingly, is a measure of th

Boundary fill algorithm - output primitives, Boundary Fill Algorithm Bo...

Boundary Fill Algorithm Boundary fill algorithm is suitable when the boundary has single color while flood fill algorithm is more suitable for filling regions which are defined

Painting and drawing, Painting and Drawing While we talk about graphic...

Painting and Drawing While we talk about graphics, we mean pictures can be either photographs or illustrations. If you want to acquire graphics into a Web page or multimedia r

Concept for eliminating hidden lines, Concept for Eliminating Hidden Lines,...

Concept for Eliminating Hidden Lines, Surfaces or Edges To exemplify the concept for eliminating hidden-lines, surfaces or edges, see a classic wire frame model of a cube as i

Multimedia entertainment, Multimedia Entertainment: The field of ente...

Multimedia Entertainment: The field of entertainment uses multimedia extensively. One of the earliest and the most popular applications of multimedia are for games. Multimedi

Relationships between scaling and wavelet function spaces, QUESTION (a)...

QUESTION (a) Median filters do not cater for a dynamic range of pixels in a given area, S. Thus to ensure that no loss of image details occur in S, adaptive median filters coul

What is aspect ratio, What is Aspect ratio?  The ratio of vertical poin...

What is Aspect ratio?  The ratio of vertical points to the horizontal points essential to produce length of lines in both directions of the screen is known as the Aspect ratio.

Trivial acceptance case of cohen sutherland line clippings, Trivial accepta...

Trivial acceptance case of cohen sutherland line clippings Case 1: it is Trivial acceptance case whether the UDLR bit codes of the end points P, Q of a provided line is 0000

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