Liang b arsky line clipping algorithm, Computer Graphics

Write the Liang B arsky line clipping algorithm. Why is Liang Barsky algorithm more efficient than the Cohen Sutherland algorithm? 

Liang Barsky Line Clipping: Faster line clippers have been developed that are based an analysis of the parametric equation of a line segment, Which we can write in the form: where using these parametric equation Cyrus and Beck developed an alga that is generally more efficient than the Cohen Sutherland alga. Later Liang and Barsky independently devised an even faster parametric line clipping alga. In this first write the paint clipping conditions in the parametric form: each of these four inequalities can be expressed as: where parameters p and q are defined.  Any line that is parallel to one of the clipping boundaries has pk­ = 0 for the value of k corresponding to that boundaries ( k = 1, 2, 3, and 4 correspond to the left, right, bottom and top boundaries ) If for the value of k we also find qk < 0, then line is completely outside the boundary and can be eliminated from further consideration. If qk > 0, the infinite extension of the line processed from the outside to the inside of the infinite extension of this particular clipping boundary. If pk > 0 the line proceeds from the inside to the outside. For a nonzero value of p k, we can calculate the value of u that corresponds to the point where the infinitely extended line intersects the extension of boundary k.  For each line, we can calculate values for parameters u­1 and u2 that define that part of the line that lies within the clip rectangle. The value of r is determined by looking at the rectangle edges for which the line proceeds from the outside to the inside . For these edges we calculate. The value of as taken as the largest of the set consisting of 0 and the various values of r. Conversely the value of is determined by examining the boundaries for which the line proceeds from inside to outside. A value of r is calculated for each of these boundaries, and the value of is the minimum of the set consisting of 1 and the calculated r values. If u1 > u2 the line is completely outside the clip window and of can be rejected. Otherwise the endpoints of the clipped line are calculated from the two values of parameter u.  This algorithm is presented in the following procedure, Line intersection parameters are initialized to the values u1 = 0 and u2 = 1. For each clipping boundary the appropriate values for p and q are calculated and rsed by the function clip test to determine whether the line can be rejected of whether the intersection parameters are to be adjusted. When p > 0, the parameter r is used to update  u1; when p > 0 parameter r is used to update u. If updating u­1 or u2 results in u1 > u2 we reject the line. Otherwise we update the appropriate u parameter only if the new value results in a shortening of the line. When p = 0 and q < 0 we can discard the line since it is parallel to and outside of this boundary If the line has not been rejected after all four values of p and q have been tested, the endpoints of the clipped line are determined from values of u1 and u­­2.

Efficiency of Liang Algorithm than Cohen Sutherland algorithm: The Liang-Barky  algorithm is more efficient than the Cohen Sutherland algorithm, since intersection calculations are reduced. Each update of parameters u and u requires only one division; and window intersections of the line are computed only once, when the final values of u and u have been computed. In contrast, the Cohen Sutherland algorithm can repeatedly calculate intersections along a line path, even though the line may be completely outside the clip window. And each intersection calculation requires both a division and a multiplication. Both the Cohen Sutherland and the Liang Barky algorithms can be extended to three dimensional clipping. 

Posted Date: 7/1/2012 6:35:42 AM | Location : United States

Related Discussions:- Liang b arsky line clipping algorithm, Assignment Help, Ask Question on Liang b arsky line clipping algorithm, Get Answer, Expert's Help, Liang b arsky line clipping algorithm Discussions

Write discussion on Liang b arsky line clipping algorithm
Your posts are moderated
Related Questions
Can you tell which main components (hardware and software) are needed for computer graphics? Besides the computer, some special devices and software may be needed especially fo

What do you mean by Perspective projection?  Perspective projection is one in which the lines of projection are not parallel. Instead, they all converge at a single point known

Important Points About the Diffuse Reflection An extremely rough surface appears uniformly bright from each viewing direction Q the intensity of reflected light is identical i

Normal 0 false false false EN-US X-NONE X-NONE

DV Encoder Types: While DV is captured in a computer this is stored in an AVI file, that is Microsoft's standard file format used for video files. Video support in Windows is prov

Write a C program to create a window of specified size and position and draw the following objects with dimensions of your choice, to fit within the window.   (a) A point  (b) A

Removing Polygons Hidden through a Surrounding Polygon: The key to capable visibility calculation lies actually a polygon is not visible whether it is in back of a surrounding

Geometric tables - Polygon Tables 1) Vertex table: Keep vertices' coordinates values in the object. 2) Edge table: Keep pointers back in to the vertex table for identif

Boundary Fill Algorithm Boundary fill algorithm is suitable when the boundary has single color while flood fill algorithm is more suitable for filling regions which are defined

De Casteljau Algorithm For computation of Bézier curves an iterative algorithm known as de Casteljau algorithm is used.  The algorithm uses repeated linear interpolation.