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# Line Clipping:

It is performed by using the line clipping algorithm. The line clipping algorithms are:

- Cohen Sutherland Line Clipping Algorithm
- Midpoint Subdivision Line Clipping Algorithm
- Liang-Barsky Line Clipping Algorithm

## Cohen Sutherland Line Clipping Algorithm:

In the algorithm, first of all, it is detected whether line lies inside the screen or it is outside the screen. All lines come under any one of the following categories:

- Visible
- Not Visible
- Clipping Case

**1. Visible:** If a line lies within the window, i.e., both endpoints of the line lies within the window. A line is visible and will be displayed as it is.

**2. Not Visible:** If a line lies outside the window it will be invisible and rejected. Such lines will not display. If any one of the following inequalities is satisfied, then the line is considered invisible. Let A (x_{1},y_{2}) and B (x_{2},y_{2}) are endpoints of line.

x_{min},x_{max} are coordinates of the window.

y_{min},y_{max} are also coordinates of the window.

x_{1}>x_{max}

x_{2}>x_{max}

y_{1}>y_{max}

y_{2}>y_{max}

x_{1}<x_{min}

x_{2}<x_{min}

y_{1}<y_{min}

y_{2}<y_{min}

**3. Clipping Case:** If the line is neither visible case nor invisible case. It is considered to be clipped case. First of all, the category of a line is found based on nine regions given below. All nine regions are assigned codes. Each code is of 4 bits. If both endpoints of the line have end bits zero, then the line is considered to be visible.

The center area is having the code, 0000, i.e., region 5 is considered a rectangle window.

**Following figure show lines of various types**

Line AB is the visible case

Line OP is an invisible case

Line PQ is an invisible line

Line IJ are clipping candidates

Line MN are clipping candidate

Line CD are clipping candidate

## Advantage of Cohen Sutherland Line Clipping:

- It calculates end-points very quickly and rejects and accepts lines quickly.
- It can clip pictures much large than screen size.

## Algorithm of Cohen Sutherland Line Clipping:

**Step1:**Calculate positions of both endpoints of the line

**Step2:**Perform OR operation on both of these end-points

**Step3:**If the OR operation gives 0000

Then

line is considered to be visible

else

Perform AND operation on both endpoints

If And ≠ 0000

then the line is invisible

else

And=0000

Line is considered the clipped case.

**Step4:**If a line is clipped case, find an intersection with boundaries of the window

m=(y_{2}-y_{1} )(x_{2}-x_{1})

**(a)** If bit 1 is “1” line intersects with left boundary of rectangle window

y_{3}=y_{1}+m(x-X_{1})

where X = X_{wmin}

where X_{wmin}is the minimum value of X co-ordinate of window

**(b)** If bit 2 is “1” line intersect with right boundary

y_{3}=y_{1}+m(X-X_{1})

where X = X_{wmax}

where X more is maximum value of X co-ordinate of the window

**(c)** If bit 3 is “1” line intersects with bottom boundary

X_{3}=X_{1}+(y-y_{1})/m

where y = y_{wmin}

y_{wmin} is the minimum value of Y co-ordinate of the window

**(d)** If bit 4 is “1” line intersects with the top boundary

X_{3=X}1+(y-y_{1})/m

where y = y_{wmax}

y_{wmax} is the maximum value of Y co-ordinate of the window

## Example of Cohen-Sutherland Line Clipping Algorithm:

Let R be the rectangular window whose lower left-hand corner is at L (-3, 1) and upper right-hand corner is at R (2, 6). Find the region codes for the endpoints in fig:

The region code for point (x, y) is set according to the scheme

Bit 1 = sign (y-y_{max})=sign (y-6) Bit 3 = sign (x-x_{max})= sign (x-2)

Bit 2 = sign (y_{min}-y)=sign(1-y) Bit 4 = sign (x_{min}-x)=sign(-3-x)

Here

So

A (-4, 2)→ 0001 F (1, 2)→ 0000

B (-1, 7) → 1000 G (1, -2) →0100

C (-1, 5)→ 0000 H (3, 3) → 0100

D (3, 8) → 1010 I (-4, 7) → 1001

E (-2, 3) → 0000 J (-2, 10) → 1000

We place the line segments in their appropriate categories by testing the region codes found in the problem.

**Category1 (visible):** EF since the region code for both endpoints is 0000.

**Category2 (not visible):** IJ since (1001) AND (1000) =1000 (which is not 0000).

**Category 3 (candidate for clipping):** AB since (0001) AND (1000) = 0000, CD since (0000) AND (1010) =0000, and GH. since (0100) AND (0010) =0000.

The candidates for clipping are AB, CD, and GH.

In clipping AB, the code for A is 0001. To push the 1 to 0, we clip against the boundary line x_{min}=-3. The resulting intersection point is I_{1} (-3,3). We clip (do not display) AI_{1} and I_{1} B. The code for I_{1}is 1001. The clipping category for I_{1} B is 3 since (0000) AND (1000) is (0000). Now B is outside the window (i.e., its code is 1000), so we push the 1 to a 0 by clipping against the line y_{max}=6. The resulting intersection is l_{2} (-1,6). Thus I_{2} B is clipped. The code for I_{2} is 0000. The remaining segment I_{1} I_{2} is displayed since both endpoints lie in the window (i.e., their codes are 0000).

For clipping CD, we start with D since it is outside the window. Its code is 1010. We push the first 1 to a 0 by clipping against the line y_{max}=6. The resulting intersection I_{3} is (,6),and its code is 0000. Thus I_{3} D is clipped and the remaining segment CI_{3} has both endpoints coded 0000 and so it is displayed.

For clipping GH, we can start with either G or H since both are outside the window. The code for G is 0100, and we push the 1 to a 0 by clipping against the line y_{min}=1.The resulting intersection point is I_{4} (2,1) and its code is 0010. We clip GI_{4} and work on I_{4} H. Segment I_{4} H is not displaying since (0010) AND (0010) =0010.

### Program to perform Line Clipping using Cohen Sutherland Algorithm:

**Output:**