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

Diffuse reflection - polygon rendering & ray tracing methods, Diffuse Refle...

Diffuse Reflection - Polygon Rendering & Ray Tracing Methods It is characteristic of light reflected from a non-shiny, dull surface. Objects illuminated solely through diff

Image - based rendering, Explore and understand light field. Checking out o...

Explore and understand light field. Checking out one of the image libraries. 1. You can modify existing source code, or develop your own to achieve light field rendering; 2.

What is shearing, What is shearing?  The shearing transformation actua...

What is shearing?  The shearing transformation actually slants the object with the X direction or the Y direction as needed.ie; this transformation slants the shape of an obje

Cases of the sutherland hodgman polygon clipping algorithm, Cases of the Su...

Cases of the Sutherland Hodgman Polygon Clipping Algorithm In order to clip polygon edges against a window edge we move from vertex V i to the subsequent vertexV i+1 and cho

Ellipse generation algorithm - 2d shape primitives, Ellipse Generation Algo...

Ellipse Generation Algorithm  You know that a circle is symmetric in all the octants, while ellipse is symmetric with respect to four quadrants.  Therefore, to draw an ellipse,

What is orthographic parallel projection, What is orthographic parallel pro...

What is orthographic parallel projection?  When the direction of the projection is normal (perpendicular) to the view plane then the projection is called as orthographic paral

Scan conversion, what are the advertising effects of scan conversion

what are the advertising effects of scan conversion

Define the term -monitoring, Define the term -Monitoring Chemical and n...

Define the term -Monitoring Chemical and nuclear plants (monitoring key parameters), hospitals (monitoring patient's vital signs), burglar alarms (monitoring for intruders) etc

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