Find the normalization transformation, Computer Graphics

Illustration: Find the normalization transformation N that uses the rectangle W (1, 1), X (5, 3), Y (4, 5) and Z (0, 3) as a window and also the normalized device screen like the viewport.

2190_Find the normalization transformation 1.png

Figure: Example Transformations

Currently, we observe that the window edges are not parallel to the coordinate axes. Consequently we will first rotate the window regarding W hence it is aligned along with the axes.

Now, tan α= (3 -1)/(5-1) = 1/2

⇒ Sin α =    1 /√5;   Cos α = 2/√5

Now, we are rotating the rectangle in clockwise direction. Consequently α is negative which is, - α.

The rotation matrix about W (1, 1):

550_Find the normalization transformation 2.png

[TR.θ]W =

945_Find the normalization transformation 3.png

The x extent of the rotated window is the length of WX:

√(42 + 22) = 2√5

As same, the y extent is length of WZ that is,

√ (12 + 22) =   √5

For scaling the rotated window to the normalized viewport we calculate sx and sy as,

 sx = (viewport x extent)/(window x extent)= 1/2√5

sy = (viewport y  extent)/(window y extent) =   1/√5

925_Find the normalization transformation 4.png

As in expression (1), the common form of transformation matrix showing mapping of a window to a viewport:

[T] =

Within this problem [T] may be termed as N as this is a case of normalization transformation with,

xwmin = 1                        xvmin = 0

ywmin = 1                        yvmin = 0

 sx = 1/2√5      

 sy =  1/√5

Via substituting the above values in [T] which is N:

N =

1677_Find the normalization transformation 5.png

Here, we compose the rotation and transformation N to determine the needed viewing transformation NR.

 NR = N [TR.θ]W =

2096_Find the normalization transformation 6.png

Posted Date: 4/3/2013 4:05:30 AM | Location : United States







Related Discussions:- Find the normalization transformation, Assignment Help, Ask Question on Find the normalization transformation, Get Answer, Expert's Help, Find the normalization transformation Discussions

Write discussion on Find the normalization transformation
Your posts are moderated
Related Questions
Explain the merits and demerits of Penetration techniques. The merits and demerits of the Penetration techniques are as follows:     It is an inexpensive method.     It h

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

Where the video controller is used?  A special purpose processor, which is used to control the operation of the display device, is called as display controller or video control

What do you mean by emissive and non-emissive displays? EMISSIVE: The emissive display changes electrical energy into light energy. The plasma panels, thin film ele

Interlaced GIF: The conventional which is non-interlaced GIF graphic downloads one line of pixels at one time from top to bottom and browsers display all lines of the image as it

Mathematical description of a Perspective Projection A perspective transformation is found by prescribing a center of projection and a viewing plane. Let here assume that P(x

Vanishing Point - Viewing Transformations This point is that point at those parallel lines shows to converge and vanish. A practical illustration is a long straight railroad

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

Problem: (a) List four components of ‘Multimedia'. (b) Write short notes on the following: (i) itunes (ii) ipods (c) Some Multimedia development teams can have an

General Perspective transformation w.r.t. an arbitrary center of projection Suppose here that the COP is at C(a,b,c), as demonstrated in Figure. By Figure, the vectors CP