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

Types of authoring tools in multimedia, Types of Authoring Tools Autho...

Types of Authoring Tools Authoring tools are grouped depends on metaphor used for sequencing or organizing multimedia components and events as: Page or Card Based Tools

Define the term -monitoring, Define the term -Monitoring Chemical and n...

Define the term -Monitoring Chemical and nuclear plants (monitoring key parameters), hospitals (monitoring patient's vital signs), burglar alarms (monitoring for intruders) etc

Discuss in detail about rendering, Discuss in detail about rendering Co...

Discuss in detail about rendering Computer animation uses a technique termed as avars (animation variable) where starting point is generally a series of stick figures; for exam

Give three ways to display a panel, QUESTION (a) Give some ways you can...

QUESTION (a) Give some ways you can change the magnification of a document? (b) Give three ways to display a panel? (c) Identify the differences between Selection tool an

Z-buffer algorithm, How to implement z-buffer algorithm using C programming...

How to implement z-buffer algorithm using C programming

Bezier curves - 2d shape primitives, Bezier curves: Theses are special...

Bezier curves: Theses are special polynomial curves expressed using Bernstein polynomials. Spline curves are simple extensions of Bézier curves composed of two or more polynom

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

Principle vanishing point - perspective projections, Principle Vanishing po...

Principle Vanishing point - Perspective Projections Assume that line 1 and l2 be two straight lines parallel to each other that are also parallel to x-axis. If the projection

Taxonomy of projection - viewing transformation, Taxonomy of Projection - v...

Taxonomy of Projection - viewing transformation There are different types of projections as per to the view that is essential. The subsequent figure 3 demonstrates taxonomy o

What does refreshing of the screen mean, What does refreshing of the screen...

What does refreshing of the screen mean? Some method is required for maintaining the picture on the screen. Refreshing of screen is completed by keeping the phosphorus glowing

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