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

Texturing - texture coordinate, Background Texturing is like wallpaperin...

Background Texturing is like wallpapering; you are pasting an image onto the OpenGL Quad primitive.  Recall that GL_QUAD is specified by four vertices.  An image, or a texture,

Distinguish between uniform scaling and differential scaling, Distinguish b...

Distinguish between uniform scaling and differential scaling?  When the scaling factors sx and sy are assigned to the similar value, a uniform scaling is produced that maintain

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.

Filling algorithm, Analise floodfill algirithm & boundryfillalgorithim

Analise floodfill algirithm & boundryfillalgorithim

Explain what the term blocking means in animation, Question 1: (a) Exp...

Question 1: (a) Explain what are Final Gathering and Global Illumination and state why you would use those features when you render in MAYA. (b) List clearly the steps in

Presentation graphics-introduction to computer graphics, Presentation Graph...

Presentation Graphics The instant you are going to represent yourself or your product or company or research paper and so on. Only standing and speaking is fairly ineffective.

Light sources - polygon rendering and ray tracing methods, Light Sources - ...

Light Sources - polygon rendering and ray tracing methods Light Sources are key parts in any ray traced scene, since without them; there would be no rays to trace. Light sour

Functioning of input devices - 2d shape primitives, Functioning of Input De...

Functioning of Input Devices Functioning of input devices-Keyboard, mouse, trackball and space ball, Joystick, data glove, digitizer, scanner, touch panel, light pen, voice sys

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