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

Computational algorithm for simulating physical system, computational algor...

computational algorithm for simulating the behavior of different physical and mathematical systems Monte Carlo methods are an extensively utilized class of computational algor

Create an animated application, The purpose of this assignment is for you t...

The purpose of this assignment is for you to create an animation like you would see on an electronic greeting card. Have fun and be creative.  Here are the requirements: you

Determine the steps uses in cohen sutherland line clipping, Steps uses in t...

Steps uses in the Cohen Sutherland Line Clipping Algorithm are: Figure: Steps for Cohen Sutherland Line Clipping STEP 1: Input:  x L , x R , y T , y B

Physics - based modeling, Draw the five regular polyhedras using physics-ba...

Draw the five regular polyhedras using physics-based modeling method. Implement a fractal algorithm with possible personal extensions. Also, specify the extensions.

What do you understand by the term contone, Question : (a) What do you...

Question : (a) What do you understand by the term ‘contone'? (b) What are spot colours? (c) You have been asked to prepare an artwork (a magazine) to send to a printer.

Horizontal retrace - display devices, Horizontal retrace - Display Devices ...

Horizontal retrace - Display Devices In a refresh CRT monitor, the time it takes for an electron beam to return to the left most point on the next horizontal line after refresh

Psychrometric properties - design project, Read the next page and work thro...

Read the next page and work through the steps: a.  Select a location (anywhere in the world) and research the typical weather (temperature, barometric pressure, and humidity).

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

Simulation-applications for computer animation, Simulation: There are seve...

Simulation: There are several things, places and events people cannot witness in first person. There are a lot of causes for this. Several may happen too rapidly, several may be t

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