Transformation for 3-d scaling, Computer Graphics

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

Posted Date: 4/3/2013 6:11:20 AM | Location : United States







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
Related Questions
What happens while two polygons have similar z value and the z-buffer algorithm is utilized? Solution : z-buffer algorithms, varies colors at a pixel if z(x,y)

What is meant by scan code? When a key is pressed on the keyboard, the keyboard controller places a code bear to the key pressed into a part of the memory known as the keyboard

Features for good 3-Dimentional modeling software are as: Multiple windows which permit you to view your model in each dimension. Capability to drag and drop primitive

Understanding the Concept of hypertext and hypermedia: For know the principle of Hypertext and Hypermedia we will look at how the human memory works.

Various cases of Cohen Sutherland Line Clippings Currently, we study how this clipping algorithm works. For the sake of simplicity we will tackle all the cases with the assist

Determine the transformation matrix for: a) Cavalier projection with θ=45 0 , and b) Cabinet projection with θ=30 0    c) Draw the projection of unit cube for all transfor

What is Resolution, how to adjust it.  Resolution: The maximum number of points that can be displayed without overlap on a CRT is referred to as the resolution . A more prec

Transformation for Isometric projection - Transformation Suppose that P(x,y,z) be any point in a space.  Assume as a given point P(x,y,z) is projected to the P'(x'y',z') on t

X-shear Regarding the Origin - 2-d and 3-d transformations Suppose an object point P(x,y) be moved to P'(x',y') in the x-direction, via the given scale parameter 'a',that is,

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