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

Camera - polygon rendering and ray tracing methods, Camera - polygon render...

Camera - polygon rendering and ray tracing methods Camera presents "viewpoint" or "eye" of observer. In order to explain the fundamental working of camera we can consider this

BINARY, WHAT THAT S MEANS 0001

WHAT THAT S MEANS 0001

Color histogram, A color histogram is a representation of the distribution ...

A color histogram is a representation of the distribution of colors in an image. For digital images, a color histogram represents the number of pixels that have colors in each of a

Illustration of a clipping window - raster graphics, Illustration of a Clip...

Illustration of a Clipping window ABCD is placed as follows: A (100, 10), B (160, 10, C (160, 40), D (100, 40) By using Sutherland-Cohen clipping algorithm determine the vis

Three-dimensional viewing, Three-Dimensional Viewing Three dimensional ...

Three-Dimensional Viewing Three dimensional objects are created using modelling coordinate system. The modelled objects are then placed in locations specified in the scene with

Determine the advantages of raster-scan systems, Determine the advantages o...

Determine the advantages of raster-scan systems (i)  Rasterisation is now performed faster since a special purpose processor is used. (ii)  The CPU is not slowed down by the

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

Categories of line segments - 2d clipping algorithms, Categories of Line Se...

Categories of Line Segments It categorizes line segments into three categories (i) trivially rejected (ii) trivially selected (iii) may be partially visible or totally invisibl

Applications for computer animation, Applications For Computer Animation ...

Applications For Computer Animation These days, animation influences approximately every aspect of life right from entertainment to education and to security and lots of more a

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