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

Scan conversion - 2d shape primitives, Scan conversion: For display of...

Scan conversion: For display of a continuously defined object, a method to map a continuous abstract object or shape into a discrete plane of computer display is needed.  This

What do you understand by the term contone, Question : (a) What do you...

Question : (a) What do you understand by the term ‘contone'? (b) What are spot colours? (c) You have been asked to prepare an artwork (a magazine) to send to a printer.

Define emissive and non-emissive displays, What do you mean by emissive and...

What do you mean by emissive and non-emissive displays?  The emissive display changes electrical energy into light energy. The plasma panels, thin film electro-luminescent disp

Determine the transformation matrix for cavalier projection, Determine the ...

Determine the transformation matrix for: a) Cavalier projection with θ=45 0 , and b) Cabinet projection with θ=30 0    c) Draw the projection of unit cube for all transfor

Important points about the frame buffers - graphics hardware, Important Poi...

Important Points about the Frame Buffers 1) Within a frame buffer, information storage starts from top left corner and goes until the bottom right corner. 2) By using this

Transformation for 3-d translation, Suppose P be the point object along wit...

Suppose P be the point object along with the coordinate (x,y,z). We want to translate such object point to the new position as, P'(x',y',z') through the translation Vector as V=t x

State the advantages and disadvantages of CAD, State the Advantages AND Dis...

State the Advantages AND Disadvantages of CAD       Advantages of CAD                                                               Disadvantages of CAD - Easier to modif

Objectives-visible-surface detection, After going through this section, you...

After going through this section, you should be capable to: know the meaning of Visible-surface detection; distinguish among image-space and object-space approach for vi

Removing polygons hidden through a surrounding polygon, Removing Polygons H...

Removing Polygons Hidden through a Surrounding Polygon: The key to capable visibility calculation lies actually a polygon is not visible whether it is in back of a surrounding

Limitations of cohen sutherland line clipping algorithm, Limitations of Coh...

Limitations of Cohen Sutherland line clipping Algorithm The algorithm is merely applicable to rectangular windows and not to the other convex shaped window. Consequently, a

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