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Liang-Barsky Clipping Algorithm Guide

The document describes the Liang-Barsky line clipping algorithm. It uses the parametric equation of a line and inequalities of the clipping window boundaries to determine intersections and clip lines. It then provides an example of applying the algorithm to clip a line with endpoints P1(-1, -2) and P2(2,4) within a viewport window of boundaries XL=0, XR=1, YB=0, YT=1.

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53 views3 pages

Liang-Barsky Clipping Algorithm Guide

The document describes the Liang-Barsky line clipping algorithm. It uses the parametric equation of a line and inequalities of the clipping window boundaries to determine intersections and clip lines. It then provides an example of applying the algorithm to clip a line with endpoints P1(-1, -2) and P2(2,4) within a viewport window of boundaries XL=0, XR=1, YB=0, YT=1.

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BAC

UNIT: Computer Graphics Design (BAC 3206)

LEC: MR. DAVID OPONDO ORIEDI

Assignment 1(group work)

Group members

1.20/03829-Ondima Yobes

2.21/05311 Hashim Jibril

3.20/02882 Ryan Mugo

4.20/03734 Moses Thuo

5.20/03697 Joy Wanjiku

1. Describe Liang Barsky clipping algorithm


The Liang-Barsky clipping algorithm is an efficient line clipping algorithm used in computer

graphics. It utilizes the parametric equation of a line and inequalities that describe the range

of the clipping window to determine the intersections between the line and the clip window.

Here’s a high-level description of the algorithm:

1. Parametric Line Equation: The algorithm starts with the parametric form of

a line segment between two points ( P_1(x1, y1) ) and ( P2(x2, y2) ): [ X = x1

+ t(x2 - x1) ] [ Y = y1 + t(y2 - y1) ] where ( t ) is a parameter that ranges from

0 to 1.

2. Defining Boundaries: The clipping window is defined by its boundaries

( xwmin, xwmax, ywmin, ywmax ). The algorithm checks the line against

these boundaries to find the intersections.

3. Calculating Intersections: For each boundary, the algorithm calculates two

values, ( pk ) and ( qk ), which are derived from the line’s direction and the

clipping window’s boundaries. These values are used to find the parameter ( t )

at which the line intersects the clipping boundary.


4. Determining Visibility: The algorithm determines the values of ( t ) for which

the line segment is inside the clipping window. If ( t1 ) and ( t2 ) are the

entering and exiting values of ( t ), the line is visible when ( t1 < t2 ).

5. Clipping the Line: If the line is found to be partially or completely within the

clipping window, the algorithm calculates the new endpoints of the clipped

line segment using the visible ( t ) values.

6. Drawing the Line: Finally, the clipped line segment is drawn within the

clipping window.

2. Let P1(-1, -2) and P2(2,4) be end points of a line to be clipped using Liang

Barsky technique. Let the boundaries of viewport window be as follows:

Left boundary (XL) = 0, Right boundary (XR) = 1, Bottom boundary

(YB) = 0 and Top boundary (YT) = 1. Clip the line. Show computations.

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