Mapping of a fraction -windowing transformations, Computer Graphics

Mapping of a Fraction -Windowing Transformations

The mapping of a fraction of a world coordinate scene to device coordinates is considered to as Viewing Transformation. In common 2Dimentional viewing transformations are considered to as window to windowing transformation or viewport transformation.

1736_Mapping of a Fraction -Windowing Transformations 1.png

Figure: Windowing Transformation

We can see in above figure, here all parts of the picture which lie outside the window are clipped and the contents that lie within the widow are transferred to device coordinates. Secondly, we can also observe that while window chooses a part of the scene, viewport displays the chosen part at the desired location on the display region. While window is changed we see a dissimilar part of the scene at similar portion as viewport on display. If we modify the viewport only, we notice identical part of the scene drawn at a diverse scale or at a diverse place on the display. By successively decreasing or raising the size of the window around a part of the scene the viewport kept fixed, we can determine the effect of zoom out or in respectively on the displayed part. By mathematically, viewing transformation can be represented as V=W.N

Here,

  • V refers Viewing transformation that maps a part of world coordinate scene to device coordinates;
  • W refers to workstation transformation that maps normalized device coordinates to physical device coordinates;
  • N refers to Normalization transformation utilized to map world coordinates to normalized device coordinates.

 

Window to Viewpoint Coordinates transformation:

159_Mapping of a Fraction -Windowing Transformations 2.png

Figure: Window to Viewport Transformation

Figure as shown in above, demonstrates window-viewpoint mapping. Now, it is depicted here a point at position (Xw, Yw) in window is mapped on position (Xv, Yv) in the connected viewpoint.

Consequently, as to keep the same relative placement in the viewpoint like in the window we need:

   (xv - xvmin)/( xvmax  - xvmin)        =(xw - xwmin)/(xwmax  - xwmin)..............1(a)

   (yv - yvmin)/ (yvmax  - yvmin)       = (yw - ywmin)/(ywmax  - ywmin)................1(b)

Again arranging equation (a) and (b) of (1) we denote viewpoint position (xv, yv) which is:

{ xv = xvmin + (xw - xwmin) Sx

yv = yvmin + (yw - ywmin) Sy }..........................(2)

Here,

Sx scaling factor along x axis = (xvmax  - xvmin)/(xwmax  - xwmin)

Sy scaling factor along y axis = (yvmax  - yvmin)/(ywmax  - ywmin).........................................(3)

Note: if Sx = Sy then the relative proportions of objects are preserved else the world object will be contracted or stretched in either x or y direction while displayed on output device.

Posted Date: 4/3/2013 3:57:05 AM | Location : United States







Related Discussions:- Mapping of a fraction -windowing transformations, Assignment Help, Ask Question on Mapping of a fraction -windowing transformations, Get Answer, Expert's Help, Mapping of a fraction -windowing transformations Discussions

Write discussion on Mapping of a fraction -windowing transformations
Your posts are moderated
Related Questions
what is physx?

Low Level Techniques or Motion Specific These techniques are utilized to control the motion of any graphic element in any animation scene completely. These techniques are also

Cases for Digital Differential Analyzer Algorithm 1)  If in case 1, we plot the line another way round that is, moving in y direction via 1 unit every time and after that hunt

Illustrate the Advantages of using virtual reality - it's safer (As techniques can be tried out in advance without the dangers of real operation for example maintaining a nucle

Categories of Parallel Projection Parallel projection can be categorized as per to the angle which the direction of projection makes along with the projection plane. For illu

How to implement z-buffer algorithm using C programming

Program of PERT in c language

Figure uses three dashed arcs and one small circle. Dashed line or arc is a style attribute that can be attached with a line or a curve. In OpenGL you can use the line stipple func

State the technology used in LCD Some passive matrix (Pixels are illuminated in scanline order like a raster display but  the lack of phospherescence causes flicker) LCDs have

Question 1 What is Packet-switching network? Discuss its basic operation Question 2 Briefly describe Jackson's theorem Question 3 List and explain the two popular