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

Define octrees, Define Octrees?  Hierarchical tree structures called oc...

Define Octrees?  Hierarchical tree structures called octrees, are used to show solid objects in some graphics systems. Medical imaging and other applications that needs display

Cases for subdivisions of polygon-visible surface detection, Cases for Subd...

Cases for Subdivisions of Polygon No additional subdivisions of a particular area are desired, if one of the subsequent conditions is true as: Case 1: All the polygons ar

Please give me ans, Differences between digital differential analyzer and ...

Differences between digital differential analyzer and VECGEN line algorithm?

Graphic primitives, Graphic Primitives In previous section, we have di...

Graphic Primitives In previous section, we have discussed refreshing display devices and its categories which are Raster and Random Scan display devices. We have also discusse

Area subdivision method - visible surface detection, Area subdivision Metho...

Area subdivision Method - Visible Surface Detection What are the circumstances to be fulfilled, in Area-subdivision method, thus a surface not to be divided in addition? S

Disadvantages of analogue signal over digital signal, Problem: (a) Lis...

Problem: (a) List four components of ‘Multimedia'. (b) Write short notes on the following: (i) itunes (ii) ipods (c) Some Multimedia development teams can have an

Pitfalls in computer simulation - computer aided design, Pitfalls in comput...

Pitfalls in computer simulation Though generally avoided in computer simulations, in strict logic the rules governing floating point arithmetic even apply. For illustration, t

What is the feature of inkjet printers, What is the feature of Inkjet print...

What is the feature of Inkjet printers? Features of inkjet printers: They can print 2 to 4 pages/minutes. Resolution is about 360d.p.i. Thus better print quality is achie

Difference of gaussians, Difference of Gaussians In this project we wi...

Difference of Gaussians In this project we will implement the difference of Gaussians (DoG) edge detector and learn its characteristics. Part A: Design and implement a proc

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