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

Languge, what languge do computers speak

what languge do computers speak

Construction of a solid with a translational sweep, Construction of a Solid...

Construction of a Solid with a Translational Sweep Figure demonstrates construction of a solid along with a translational sweep. Translating the control points of the periodic

Cohen sutherland, explain cohen sutherland line clipping algorithm

explain cohen sutherland line clipping algorithm

Identify what the use of homogenous co-ordinates, 1. Why are homogeneous co...

1. Why are homogeneous co-ordinates utilized in computer vision? I want to identify what the use of homogenous co-ordinates makes possible in terms of camera models. 2. Consider

Differences of forward kinematics and inverse kinematics, Question 1: (...

Question 1: (a) Provide a clear explanation of what is ‘rigging' and its use? (b) What are the basic differences of Forward Kinematics (FK) and Inverse Kinematics (IK)? Wh

Gif file compression, GIF File Compression The Graphic Interchange Form...

GIF File Compression The Graphic Interchange Format file format utilizes a relatively basic form of file compression which squeezes out inefficiencies within the data storage w

Three dimensional display methods - 2d clipping algorithms, Three dimension...

Three dimensional display methods: Among the simplest three dimensional surface representations are the polygonal surfaces.  A polygonal surface is described by vertices

Flash - software to generate computer animations, Flash - software to gener...

Flash - software to generate computer animations Flash: Learning Macro-Media's Flash can quite complicated, although you can do almost anything along with it. You can devel

Offset lithography printing, QUESTION A trainee designer, Susan, joins ...

QUESTION A trainee designer, Susan, joins your place of work. During a workshop, you are asked to present on printing procedures and agencies in Mauritius. Susan asks you what

Vecgen algorithm, Working of vecgen algorithm with diagram

Working of vecgen algorithm with diagram

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