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

Transformation, Define transformation. Explain all basic transformation

Define transformation. Explain all basic transformation

Polygon representation methods - modeling and rendering, Polygon Representa...

Polygon Representation Methods - Modeling and Rendering Any scene to be created by computer graphics may include a variety of objects, a few of them natural and manmade. Hence

Soft image and strata studio - computer animation, Soft Image and Strata ...

Soft Image and Strata Studio - Computer Animation SoftImage It is the one of most well known computer animation software packages. It is used in several top production

What are the disadvantages with the boundary representation, Disadvantages ...

Disadvantages with the Boundary Representation (i) It requires more storage than the corresponding half-space method. (ii) There is no guarantee that the object created is v

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

Simple graphical user interface, The RIA should consist of: i) A simple ...

The RIA should consist of: i) A simple Graphical User Interface (GUI) constructed from a simple navigation system (comprising of around 5 key frames) making use of the Flash tim

Entertainment - applications for computer animation, Entertainment - Applic...

Entertainment - Applications For Computer Animation Advertising, Games, Film, Video, Television, Multimedia are various of the entertainment fields wherein computer animation h

Categories of parallel projection - viewing transformation, Categories of P...

Categories of Parallel Projection Parallel projection can be categorized as per to the angle which the direction of projection makes along with the projection plane. For illu

Categories of reflection - ray tracing methods , Categories of Reflection -...

Categories of Reflection - Ray Tracing Methods In order to achieve realism, such phenomenon of reflection, which occurs because of interaction of light and surface, is require

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