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

Cyrus beck algorithm - line clipping algorithm, Cyrus Beck Algorithm - Line...

Cyrus Beck Algorithm - Line Clipping Algorithm Cyrus Beck Line clipping algorithm is actually, a parametric line-clipping algorithm. The term parametric means that we requi

Line segment that joining by using bresenham line algorithm, Sketch Line Se...

Sketch Line Segment That Joining By Using Bresenham Line Algorithm Example: Sketch line segment that joining (20, 10) and (25, 14) by using Bresenham line generation algorit

3d primitive and composite transformations, 3D Primitive and Composite Tran...

3D Primitive and Composite Transformations Previously you have studied and implemented 2D geometric transformations for object definitions in two dimensions. These transformati

Phong shading algorithm, Q. Describe briefly phong shading algorithm.   ...

Q. Describe briefly phong shading algorithm.   OR                Write short note on phong shading.    Phong shading   Phong shading or normal vector interpo

List five different area of application of computer graphics, Question: Lis...

Question: List five different areas of applications of computer graphics Answer: Five major areas of applications of computer graphics are:  i) Study of molecular structures.

Plane equation - curves and surfaces, Plane Equation - Curves and Surfaces ...

Plane Equation - Curves and Surfaces Plane is a polygonal surface that bisects its environment in two halves. One is termed to as forward and another as backward half of som

Unrepresentative vertex normals - modeling and rendering, Unrepresentative ...

Unrepresentative vertex normals - Modeling and Rendering Calculated vertex normals may not adequately present the surface's geometry. For illustration, if we calculate vertex

What is a blobby object, What is a Blobby object?  Some objects do not ...

What is a Blobby object?  Some objects do not handle a fixed shape, but change their surface characteristics in sure motions or when in proximity to other objects. That is call

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