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

File formats that are used for vector data, File Formats that are used for ...

File Formats that are used for Vector Data This data can be saved in a wide variety of file formats are as: •EPS: the most well-accepted file format to exchange vector dra

Define refresh rate and refresh buffer, Refresh Rate: refreshing on raster...

Refresh Rate: refreshing on raster - scan displays is carried out at the rate of 60 to 80 frames per second, although some system are designed for higher refresh rates. Sometimes,

What is fixed point scaling, What is fixed point scaling?  The location...

What is fixed point scaling?  The location of a scaled object can be controlled by a position known as the fixed point that is to remain unchanged after the scaling transformat

C++ programming, self test exercise 17 asked you to overload the operator >...

self test exercise 17 asked you to overload the operator >> and the operator Overload biinary operator + to add pairs according to the rule (a, b) + (c, d) = (a + c, b, + d) overl

Reflection and shear - output primitives, Reflection and Shear There ar...

Reflection and Shear There are a few important transformations which are not primitive in the sense that they can be expressed as compositions of translation, rotation and scal

Crt, crt is an analog or digital device

crt is an analog or digital device

Briefly explain the 12 stages in image processing, QUESTION (a) In Autom...

QUESTION (a) In Automatic Contrast Adjustment briefly explain how to stretch an image to its full intensity (b) Write down a mathematical function of a Modified Automatic Con

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