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

3d studio max -softwares for computer animation, 3DStudio Max -Softwares fo...

3DStudio Max -Softwares for computer animation The successor to 3-DStudio 3.0, 3-DStudio Max runs in WindowsNT. This is completely object-oriented, featuring new enhancements a

Sequence of steps to generate a full animation, Sequence of Steps to Genera...

Sequence of Steps to Generate a Full Animation The sequence of steps to generate a full animation would be as given below: 1)  Improve a script or story for the animation.

Bezier cubic curves, Q.   What are Bezier cubic curves? Derive their proper...

Q.   What are Bezier cubic curves? Derive their properties. OR  What are Bezier cubic curves? Derive these properties. Also show that the sum of the blending functions is identical

Remote sensing packages-Image processing, Remote Sensing Packages: general...

Remote Sensing Packages: generally utilized software illustration is-" ERDAS" Characteristics: I.Best suitable for satellite imagery system. II. ERDAS uses geo-spatial in

Rotation about the origin - 2-d and 3-d transformations, Rotation about the...

Rotation about the origin - 2-d and 3-d transformations Specified a 2-D point P(x,y), which we need to rotate, along with respect to the origin O. The vector OP has a length '

Random scan display device - types of refresh monitors, Random Scan Display...

Random Scan Display Device The original cathode ray tube, developed in the late fifties and early sixties, produced charts and pictures, line through line on the tube surface

Raster and random scan displays - hardware primitive, Raster and random sca...

Raster and random scan displays In Raster scan displays, whole screen is refreshed a number of times in a second to keep the picture visible on the screen. This is called refre

Basic transformations - 2-d and 3-d transformations, Basic Transformations ...

Basic Transformations - 2-d and 3-d Transformations Consider the xy-coordinate system upon a plane. An object or Obj in a plane can be identified as a set of points. All objec

Define the term multimedia, Question (a) Define the term Multimedia. ...

Question (a) Define the term Multimedia. (b) Describe any four important tools you know about for a virtual campus. (c) Following our discussion in our lecture list an

Lossless audio formats, Lossless Audio Formats: Lossless audio formats as ...

Lossless Audio Formats: Lossless audio formats as TTA and FLAC give a compression ratio of around 2:1, sometimes extra. During exchange, for their lower compression ratio, such co

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