Computer Graphics:Module 4

Module 4: 2D Viewing and clipping

Que:Define Window , Viewport and Clipping.

•Window: World coordinate area selected for display is called window. Mostly rectangular shape window considered. 
•Viewport: An area from display device where area from window mapped.
In general we can say window means “what to see” and Viewport means “where to see”
•Clipping: Finding inside or outside region using algorithm or with any procedure with respect to window is called clipping.

Que:Derive Composite matrix for Window to Viewport Transformation.

Que:Explain Point Clipping and use of Point Clipping.

•Point with coordinate (x,y) can be clipped against the window with coordinates Xwmin, Ywmin,Xwmax,Ywmax using following inequalities:

    Xwmin ≤  x  ≤  Xwmax

    Ywmin ≤  x  ≤  Ywmax

•Point will be accepted if it satisfies both inequalities.

Que:Explain Cohen-Sutherland line clipping Algorithm.

Cohen Sutherland Line Clipping Algorithm

•It is oldest and most popular algorithm.

Step1) Accept line end points A(x1,y1) ,B(x2,y2) and window coordinates Xwmin,Ywmin,Xwmax,Ywmax as input.

Step2) Calculate Region codes for line endpoints i.e. B4B3B2B1. Let for (X,Y)point

            B1=Sign(Xwmin-X)  :Left

            B2=Sign(X-Xwmax)  :Right

            B3=Sign(Ywmin-Y)  :Bottom         

            B4=Sign(Y-Ywmax)  :Top

            such that Sign A=1 if A>0    Sign A=0 if A<0

Step3) - If region codes for both endpoint are 0000 then line is totally inside accept and stop.

           - If  AND of region codes is non zero value then line is totally outside, Discard the line and stop.

           - If AND of region codes is Zero, then line is clipping candidate.

Step4) Determine which boundary is intersecting based on 1 in region code.

            B1=1   then x’=Xwmin  :Left

            B2=1 then x’=Xwmax  :Right

            B3=1 then y’=Ywmin  :Bottom         
            B4=1 then y’=Ywmax  :Top

Step5)  Determine intersecting coordinates (x’,y’)using following equations.

                                        when y’=Ywmin  or y’=Ywmax      x'=x1+1/m(y'-y1)

                                        when x’=Xwmin or x’=Xwmax       y'=y1+m(x'-x1)

                                                                                                             

Step 6) Go to step (2) 

Que: Explain Liang-Barsky Line Clipping Algorithm.

Que: Explain Polygon clipping Algorithms.