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Markov Chains || Step-By-Step || ~xRay Pixy

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Learn Markov Chains step-by-step using real-life examples. Video Chapters: Markov Chains 00:00 Introduction 00:19 Topics Covered 01:49 Markov Chains Applications 02:04 Markov Property 03:18 Example 1 03:54 States, State Space, Transition Probabilities 06:17 Transition Matrix 08:17 Example 02 09:17 Example 03 10:26 Example 04 12:25 Example 05 14:16 Example 06 16:49 Example 07 18:11 Example 08 24:56 Conclusion
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Nicholl - Lee Nicholl (NLN) Line Clipping in Computer Graphics

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 In the Cohen-Sutherland method, multiple intersections may be calculated along the path of a single line before an intersection on the clipping rectangle or line is completely rejected. 

In Nicholl - Lee Nicholl Line Clipping, Extra intersection calculations are eliminated. 

ADVANTAGE OF Nicholl - Lee Nicholl (NLN) Line Clipping

1.) The number of clipping points is reduced to one, compared to other algorithms that may require two or more clipping. 

2.) Nicholl - Lee Nicholl (NLN) Line Clipping is FAST. Clipping algorithms for Circle, Curved boundary clipping regions are SLOWER because intersections calculations involve nonlinear curve equations. 

3.)  Nicholl - Lee Nicholl (NLN) Line Clipping avoids multiple clipping of Line segments. 

4.) As Compare to Cohen Sutherland and Liang-Barsy Nicholl - Lee Nicholl Line Clipping performed fewer comparisons.  

How Nicholl - Lee Nicholl Line Clipping works? 

Nicholl - Lee Nicholl Line Clipping, uses symmetry to categorize endpoints into one of the three regions. straight line segments are drawn from the line end point, passing through the corners of the clipping window. 

What are the three regions used by Nicholl - Lee Nicholl Line Clipping for endpoints?

   1.) The point inside the Clip Window


   2.) A point in an Edge region.


   3.) A point in the Corner region.

NOTE: If Point lies in any one of the other 6 regions, we can use symmetry transformation to move it.

CASE 1. If the point (P1) is Inside the Clip Window and Point (P2) is outside. 

Then the intersection with the appropriate window boundary is carried out depending on which one of the four regions L(Left), R(Right), T(Top), and B(Bottom) contains P2.

For Example: Check this diagram given below - 

CASE 2. If P1 is in the region to the left of the window.

In this case, 4 regions used to determine a unique boundary for the line segment: L, LT, LR, and LB.

If Point P2 is in the region L, Clip the line at the left boundary and save the line segment from the intersection point to p2.  

If Point P2 is in the region LT, save the line segment from the left window boundary to Top boundary.

NOTE: If the point is not in any of the 4 regions, The Entire Line is Clipped. 





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