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

Identify design patterns, Mauri Ltd has just acquired a new stock manageme...

Mauri Ltd has just acquired a new stock management system and the source codes (PhP5) also have been delivered. The coding style is fully object-oriented. The company has been u

Types of touch panels - input and output devices, Types of Touch panels ...

Types of Touch panels 1) Electrical TSS: Wire grid or the other conductive coating is utilized to specify a voltage drop at the point touched point from that the position ma

Translation and shifting in spatial domain, Translation and shifting in Spa...

Translation and shifting in Spatial Domain A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le

Representation schemes used in three dimensional object, What are the vario...

What are the various representation schemes used in three dimensional objects?  Boundary representation (B-res) - explain the 3 dimensional objects as a set of surfaces that se

What do you mean by scan conversion, What do you mean by scan conversion?  ...

What do you mean by scan conversion?  A main task of the display processor is digitizing a picture definition given in an application program into a set of pixel-intensity valu

Rotation - 2-d and 3-d transformations, Rotation - 2-d and 3-d transformati...

Rotation - 2-d and 3-d transformations Given a 2-D point P(x,y), that we want to rotate, along with respect to an arbitrary point A(h,k). Suppose P'(x'y') be the effect of ant

Define advanced graphics port, Q. Define Advanced Graphics Port? AGP si...

Q. Define Advanced Graphics Port? AGP signify Advanced (or Accelerated) Graphics Port. It's a connector standard defining a high speed bus connection between the microprocessor

Introduction of curves and surfaces, Introduction of Curves and Surfaces ...

Introduction of Curves and Surfaces This section has covered the methods of generating polygons, closed and curves surfaces. Under those methods we have discussed different ty

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