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

File formats that are used for bitmap data, File Formats that are used for ...

File Formats that are used for Bitmap Data Bitmap data can be saved in a wide variety of file formats are: • BMP: restricted file format that is not appropriate for use in

Bezier surfaces - modeling and rendering, Bezier Surfaces - Modeling and Re...

Bezier Surfaces - Modeling and Rendering Two sets of Bezier curve can be utilized to design an object surface by identifying by an input mesh of control points. The Bézier su

Positive accelerations - computer animation, Positive Accelerations - Compu...

Positive Accelerations - Computer Animation So as to incorporate increasing speed in an animation the time spacing among the frames should increase, hence greater change in th

Properties of bezier curves - modeling and rendering, Properties of Bezier ...

Properties of Bezier Curves - modeling and rendering A very helpful property of a Bezier curve is that it always passes via the first and last control points. Such the bounda

Crt, explain the working procedure of crt digram

explain the working procedure of crt digram

Convex shaped window and concave or non convex shaped window, Well you migh...

Well you might surprise to what a convex window? In common, on the basis of the shapes the windows are categorized into two classes: i) A Convex shaped windows: Windows of a s

Mapping of a fraction -windowing transformations, Mapping of a Fraction -Wi...

Mapping of a Fraction -Windowing Transformations The mapping of a fraction of a world coordinate scene to device coordinates is considered to as Viewing Transformation. In com

What are the advantages of rendering by patch splitting, What are the advan...

What are the advantages of rendering by patch splitting?  i. It is fast-especially on workstations with a hardware polygon-rendering pipeline.  ii. Its speed can be varied b

Describe the wiggler function in animation help, Question 1: (a) Descri...

Question 1: (a) Describe the term Mask Path and give brief steps how you could change a rectangle into a triangle with respect to time in AE CS3. (b) Expressions are ve

Detecting skin in colour images, In this lab you will learn how to use chro...

In this lab you will learn how to use chrominance1 to segment coloured images. Here you be detecting skin, however, you could use this method to detect other coloured regions in im

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