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

Arguments made in favour of analog sound, Arguments made in favour of Analo...

Arguments made in favour of Analog Sound Shape of the waveforms: from digital signals sound reconstructed which is claimed to be harsher and unnatural compared to analog si

Interactive picture construction techniques, Explain the interactive pictur...

Explain the interactive picture construction techniques.    interactive picture- construction methods are commonly used in variety of applications, including design and painting pa

Visible-surface detection, Visible-Surface Detection For the generation...

Visible-Surface Detection For the generation of realistic graphics display you know that hidden surfaces and hidden lines should be identified for removing. For this reason we

Raster & Vector display, what is refresh buffer/ identify the content and o...

what is refresh buffer/ identify the content and organisation of the refresh buffer for the case of raster display and vector display.

Disadvantage of the raster scan display device, Disadvantage of the Raster ...

Disadvantage of the Raster Scan Display Device The major disadvantage of the raster scan is the jagged nature of the lines, happening from the information that the pixels are

Data set, In this project, the image data set consists of 320 training imag...

In this project, the image data set consists of 320 training images and 285 test images. Table 1 shows the image data set in details. In addition to the original images, th

Combination of positive and negative accelerations, Combination of Positive...

Combination of Positive and Negative Accelerations Actually, it is not that a body once decelerated or accelerated will remain so, although the motion may include both speed-up

Write short notes on active and passive transformations, Write short notes ...

Write short notes on active and passive transformations?  In the active transformation the points x and x represent different coordinates of the similar coordinate system. Here

Proof of subsequent properties of bezier curves, Proof of subsequent proper...

Proof of subsequent properties of Bezier curves Note: Proof of subsequent properties of Bezier curves is left as a work out for the students P' (0) = n (p 1 - p 0 ) P

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