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
QUESTION (a) Give some ways you can change the magnification of a document? (b) Give three ways to display a panel? (c) Identify the differences between Selection tool an

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 red

Achieve a perspective projection on the z = 0 plane of the unit cube, demonstrated in Figure (l) from the cop at E (0, 0, 10) upon the z-axis. Figure: I 01:  currently c

What is  Raster Scan Display A raster scan display device using CRT on the other hand directs the electron beam across the screen, one row at a time from top to bottom. In a ra

Plasma Panel - Raster Graphics and Clipping This is an inherent memory device. Images can be written into the surface point by point and they keep stable, without flicked for

Area-Subdivision method This method is a type of an image-space method although uses object-space operations re-ordering or sorting of surfaces as per to depth. Area sub-div


difference between vecgen and breshnam algorithm

How many 128 x 8 RAM chips are needed to provide a memory capacity of 4096 16 bits?

Passive Computer Animations: That has no option for users to utilize computer graphics today is mostly interactive for example: movies. Frame animation is non-interactive anim