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
Sketch Line Segment That Joining By Using Bresenham Line Algorithm Example: Sketch line segment that joining (20, 10) and (25, 14) by using Bresenham line generation algorit

Panning and zooming Components (such as your Polybounce or Animation) is simply a matter of reFrameing the world window. To pan right or left horizontally, one shifts it in the pos

PCs or Personal Computers Really - Hardware for Animation  these are really versatile machines that have been around for years. PCs are the favorite of many computer users, due

Implement the Scan line polygon fill algorithm for any arbitrary polygon in C-language and then use your code to fill each of the following type of polygon. i)  Convex polygon

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

Area subdivision Method - Visible Surface Detection What are the circumstances to be fulfilled, in Area-subdivision method, thus a surface not to be divided in addition? S

Card or Page Based Tools : In these authoring systems, components are organized as pages of a book or a stack of cards. Thousands of pages or cards may be obtainable in the stack

Program of PERT in c language

QUESTION 1 Assume you work as Producer for the national TV channel in Mauritius. As such, you have been requested by the Director of Production to submit a proposal in the for

Draw a long line segment using (i) DDA line drawing algorithm (ii) Bresenham line drawing algorithm (iii) OpenGL function using GL_LINES.  Observe if DDA line segment deflects from