Computer Graphics

Line Clipping• Cohen Sutherland Algorithm (Line)

(xmin , ymin )

(xmax , ymax )

x = xmin x = xmax

y = ymin

y = ymax

(x1, y1)

cliprectangle

maxmin

maxmin

yyyxxx

For a point For a point ((x,yx,y) ) to be inside the clip rectangleto be inside the clip rectangle::

Point Clipping

cliprectangle

(xa, ya)(xb , yb)

(xc, yc) (xd , yd)

(x0, y0)

(x1, y1)

(x , y )

cliprectangle

(xa, ya)(xb , yb)

(xc, yc) (xd , yd)

(x0, y0)

(x1, y1)

(x , y )

1 1 1 1

1 1 1 1

1: , 0, : ( ) ,

1: , 0, : ( ) ,

T L

B R

Top x x y y m Left y m x x y mm

Bottom x x y y m Right y m x x y mm

Line Clipping

0000

1000

0100

1001 1010

0001 0010

0101 0110clip

rectangle

Region outcodesRegion outcodes

min

max

yyyy

:1bit : 0bit

min

max

xxxx

:3bit : 2bit

Cohen-Sutherland Algorithm

The Cohen-Sutherland Line-Clipping Algorithm performs initial tests on a line to determine whether intersection calculations can be avoided.1. First, end-point pairs are checked for trivial

Acceptance.2. If the line cannot be trivially accepted, region

checks are done for Trivial Rejection.3. If the line segment can be neither trivially

accepted or rejected, it is divided into two segments at a clip edge, so that one segment can be trivially rejected.

These three steps are performed iteratively until what remains can be trivially accepted or

rejected.

Cohen-Sutherland Algorithm

Cohen-Sutherland Algorithm

Algorithm1-Compute the codes for the Two end points2-Enter in loop, check if both region codes are

zero(0000 and 0000) put line in display file for display and exit loop, return

3-If both region codes are not zero then take logical AND of both codes, check result for nonzero if so reject line exit loop, return

4-If result is zero then subdivide the line from intersection point of line and clipping boundary and repeat step 2,3,4.

5. Special Case when test 4 fails.

cliprectangle

AB

C

D

E

An ExampleAn Example

Cohen-Sutherland Algorithm

An ExampleAn Example

cliprectangle

B

C

D

E

Cohen-Sutherland Algorithm

An ExampleAn Example

cliprectangle

B

C

D

Cohen-Sutherland Algorithm

An ExampleAn Example

cliprectangle

B

C

Cohen-Sutherland Algorithm

Q1. Use Cohen Sutherland Algorithm to clip line p1(70,20) and P2 (100,10) against window lower left hand corner (50,10) and upper right hand corner (80,40).Q2. Given a clipping window A(20,20), B(60,20), C(60,40), D(20,40). Using sutherland cohen algorithm find the visible portion of line segment joining the points p(40,80),Q(120,30).

Thank You