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

Define addressability, What is meant by Addressability?  The Addressabi...

What is meant by Addressability?  The Addressability is the number of individual dots per inch (d.p.i) that can be formed. If the address of the current dot is (x, y) then the

Explain different linear methods for noise cleaning, Question 1 Describe t...

Question 1 Describe the process of formation of image in human eye Structure of the Human Eye Image formation in the Eye Brightness Adaptation and Discrimination

State the areas of use of data goggles, State the Areas of use of data gogg...

State the Areas of use of data goggles Entertainment   Used in television/films as special effects (for example "holodeck" in Star Trek: The Next Generation and Brazilian

Polygon meshes - modeling and rendering, Polygon Meshes - Modeling and Rend...

Polygon Meshes - Modeling and Rendering A polygonal surface to be sketched may not be easy and may have enormous curls and curves. Illustration: a crushed piece of paper or cr

2d line segment generation - 2d shape primitives, 2D Line Segment Generatio...

2D Line Segment Generation  A digitally plotted line is basically an approximation of infinite number of points on an abstract line segment by only a finite number of points on

Define advanced graphics port, Q. Define Advanced Graphics Port? AGP si...

Q. Define Advanced Graphics Port? AGP signify Advanced (or Accelerated) Graphics Port. It's a connector standard defining a high speed bus connection between the microprocessor

Shearing - 2-d and 3-d transformations, Shearing - 2-D and 3-D transformati...

Shearing - 2-D and 3-D transformations Shearing transformations are utilized for altering the shapes of 2 or 3-D objects. The consequence of a shear transformation seems like

Important points about the diffuse reflection, Important Points About the D...

Important Points About the Diffuse Reflection An extremely rough surface appears uniformly bright from each viewing direction Q the intensity of reflected light is identical i

Problem with interpolated shading - polygon rendering, Problem with Interpo...

Problem with Interpolated Shading There are several more shading models that intermediate in complication among Gouraud and Phong shading, linking the liner interpolation of t

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