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.s_x,y.s_y,z.s_z), here s_x, s_y, and s_z are the scaling factors in the x,y, and z-directions correspondingly.

 Hence, scaling w.r.t. origin is given by:

Ss_x,s_y,s_z =    x'= x.s_x

y'= y.s_y                                                  

z'= z.s_z---------(43)

In matrix form:

------------------------(44)

In terms of Homogeneous coordinate system, above equation (44) is written as:

As, P'=P. Ss_x,s_y,s_z      -----------------------------(45)

Posted Date: 3/22/2013 7:22:27 AM | Location : United States

Ask an Expert

Related Discussions:- Transformation for 3-d scaling, Assignment Help, Ask Question on Transformation for 3-d scaling, Get Answer, Expert's Help, Transformation for 3-d scaling Discussions

Write discussion on Transformation for 3-d scaling
Your posts are moderated

Write your message here..

Related Questions

What do you understand by complementary colors, Problem : a. (i) Giv... Problem : a. (i) Give another name for adjacent color. (ii) Describe briefly what do you understand by an adjacent color? b. (i) Describe briefly what do you unders

Anti- aliasing, Anti- aliasing: Most aliasing artifacts, when appear in a ... Anti- aliasing: Most aliasing artifacts, when appear in a static image at a moderate resolution, are often tolerable, and in many cases, negligible. However, they can have a signi

Process of objects in raster display and random display, Explain process of... Explain process of displaying objects in raster display and random display. Draw block diagrams of the architecture of both the display systems.

Image classification, The image classification is the process to categorize... The image classification is the process to categorize images into one of several classes or categories. In this project, there are seven categories (Piano, Kangaroo, Strawberry, Su

List out the merits and demerits of dvst, List out the merits and demerits ... List out the merits and demerits of DVST?  The merits and demerits of direct view storage tubes [DVST] are as follows  It has a flat screen Refreshing of screen is

Assumptions for polygon or area clipping algorithm, Assumptions for Polygon... Assumptions for Polygon or Area Clipping Algorithm Assumption: The viewport and window are rectangular. So only, by identifying the maximum and the minimum coordinates t

Reflection, What is the advantages and disadvantages of reflection ? What is the advantages and disadvantages of reflection ?

What do you mean by parabolic splines, What do you mean by parabolic spline... What do you mean by parabolic splines?  For parabolic splines a parabola is fitted by the first three points p1, p2,p3 of the data array of kot points. Then a second parabolic

Given two triangles p along with vertices as p1(100, Given two triangles P ... Given two triangles P along with vertices as P1(100,100,50), P2(50,50,50), P3(150,50,50) and q along with vertices as Q1(40,80,60), q2(70,70,50), Q3( 10,75,70), determine that tria

Pcs or personal computers really - hardware for animation, PCs or Personal ... PCs or Personal Computers Really - Hardware for Animation  these are really versatile machines that have been around for years. PCs are the favorite of many computer users, due