Transformation for 3-d scaling, Computer Graphics

Assignment Help:

Transformation for 3-D Scaling

As we already seen that the scaling process is mainly utilized to change the size of an object. The scale factors find out whether the scaling is a magnification as s>1 or a reduction, s<1. 2-dimensional scaling, is in equation (8), can be simply extended to scaling in 3-dimensional case by consisting the z-dimension.

For any point (x,y,z), we move in (x.sx,y.sy,z.sz), here sx, sy, and sz are the scaling factors in the x,y, and z-directions correspondingly.

Hence, scaling w.r.t. origin is given by:

Ssx,sy,sz =    x'= x.sx

         y'= y.sy                                                  

z'= z.sz

In matrix form:

1186_Transformation for 3-D Scaling 1.png

In terms of Homogeneous coordinate system, above equation is written as:

1834_Transformation for 3-D Scaling 2.png

As, P'=P. Ssx,sy,sz


Related Discussions:- Transformation for 3-d scaling

Audio file formats, Audio File Formats: It is a container format for ...

Audio File Formats: It is a container format for storing audio data in a computer system. Many file formats are there for storing audio files. The common approach towards

Role of computer graphics in education and training, Question: Explain how ...

Question: Explain how computer graphics would play a useful role in education and training. Answer: Computer graphics has occupied an important role in education and training.

Distinguish between uniform scaling and differential scaling, Distinguish b...

Distinguish between uniform scaling and differential scaling?  When the scaling factors sx and sy are assigned to the similar value, a uniform scaling is produced that maintain

Line clipping algorithm - cohen sutherland algorithm, Line Clipping Algorit...

Line Clipping Algorithm - Cohen Sutherland Algorithm Line is a series of endless number of points; here no two points contain space in among them. Hence, the above said inequa

Scientific visualization, Scientific Visualization This is complex for...

Scientific Visualization This is complex for the human brain to create sense out of the large volume of numbers produced through a scientific computation. Statistical and nume

Different advertising hooks, Question: (a) Name two visual effects you...

Question: (a) Name two visual effects you would use to communicate: i. Good old days ii. Rebellion iii. Fear (b) Explain each of your answers given in section (a).

Curves and surfaces - modeling and rendering, Curves and Surfaces - Model...

Curves and Surfaces - Modeling   and Rendering We have studied the method of drawing curves in diverse coordinate systems. Also we got the concept that it is the revolution of

Magnify a triangle with vertices, Magnify a triangle with vertices A = (1,1...

Magnify a triangle with vertices A = (1,1), B = (3,1) and C = (2,2) to twice its size in such a way that A remains in its original position.  Answer: You need to apply scaling b

Objectives-multimedia, Objectives-Multimedia After going through this s...

Objectives-Multimedia After going through this section, you should be capable to: explain hypertext and hypermedia ideas, illustrate how multimedia applications are

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