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

Open Gl, Write a program in C/C++ using OpenGL to create (without using bui...

Write a program in C/C++ using OpenGL to create (without using built in function) a square by implementing shear algorithm along 1. X-axis, 2.Y-axis.

Phong model or phong specular reflection model, Phong Model or Phong Specul...

Phong Model or Phong Specular Reflection Model It is an empirical model that is not based on physics, although physical observation. Phong observed here for extremely shiny su

Forensics-applications for computer animation, Forensics: Accidents occur ...

Forensics: Accidents occur every minute. Very frequently, there are no witnesses except for the individuals concerned in the accident or worse yet, there are no surviving witnesse

Scan conversion - 2d shape primitives, Scan conversion: For display of...

Scan conversion: For display of a continuously defined object, a method to map a continuous abstract object or shape into a discrete plane of computer display is needed.  This

Scientific visualization, Scientific Visualization This is complex for...

Scientific Visualization This is complex for the human brain to create sense out of the large volume of numbers produced through a scientific computation. Statistical and nume

Line clipping algorithm - cohen sutherland algorithm, Line Clipping Algorit...

Line Clipping Algorithm - Cohen Sutherland Algorithm Line is a series of endless number of points; here no two points contain space in among them. Hence, the above said inequa

Determine the perspective transformation matrix, Determine the perspective ...

Determine the perspective transformation matrix upon to z = 5 plane, when the center of projection is at origin. Solution. As z = 5 is parallel to z = 0 plane, the normal is s

Methods for drawing thick lines, Describe any two methods for drawing thick...

Describe any two methods for drawing thick lines. Two method for drawing thick lines are: (1) Using the line- width command: "setline width scale factor (iw)" Line width param

Pen tablet and plotter - graphics hardware, Pen Tablet and Plotter ...

Pen Tablet and Plotter Pen Tablet: It is a digitizer tablet which is specialized for handwriting and hand marking. LCD-based tablets imitate the flow of ink as the tip tou

Interactive computer animation, Interactive Computer Animation Interac...

Interactive Computer Animation Interactive Computer Animation that is interactively utilized by users for example: games. Sprite animation is interactive and utilized broadly

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