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 bitmap data, File Formats that are used for ...

File Formats that are used for Bitmap Data Bitmap data can be saved in a wide variety of file formats are: • BMP: restricted file format that is not appropriate for use in

Viewing transformation, Viewing Transformation In previous section, we...

Viewing Transformation In previous section, we have discussed about the geometric transformations as Translation, Shearing, Reflection, Scaling and Rotation. Rotation, Reflect

Distinguish between mono and stereo sound, Problem: (a) Distinguish be...

Problem: (a) Distinguish between mono and stereo sound? (b) Calculate the size of a 5 minutes mono sound file of CD quality and with a 16 -bit rate. (c) With reference

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

Do we have need of to generate full circumference of circle, 1.   Do we hav...

1.   Do we have need of to generate the full circumference of the circle utilizing the algorithm or  can we can produces it in a quadrant or octant only and after that utilization

Digital audio comprises audio signals, Digital audio comprises audio signal...

Digital audio comprises audio signals stored in a digital format. Particularly, the term encompasses the subsequent: 1)   Audio conversion: 1.   Analogue to digital conversi

Optical character recognition software, Optical Character Recognition Softw...

Optical Character Recognition Software (OCR) Frequently, you will have printed matter and the other text to incorporate in your project although no electronic text file. Along

Construction of a solid with a translational sweep, Construction of a Solid...

Construction of a Solid with a Translational Sweep Figure demonstrates construction of a solid along with a translational sweep. Translating the control points of the periodic

Transformation for 3-d shearing, 2-dimensional xy-shearing transformation, ...

2-dimensional xy-shearing transformation, as explained in equation (19), can also be simply extended to 3-dimensional case. All coordinates are translated as a function of displace

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