# Line Clipping

You’re sitting there doing nothing when you suddenly want to learn about computer graphics line clipping. Everyone’s been there. Graphics require line clipping to keep lines in the display window. There are several algorithms for this, but we’ll focus on the Cohen-Sutherland approach today.

This divide-and-conquer technique, developed in 1967 by Danny Cohen and Ivan Sutherland (who also designed the first computer graphics application), effectively clips lines to a rectangle window. This technique can decide the direction to clip a line and handle each scenario with a few comparisons and bitwise operations. This will make you a Cohen-Sutherland clipping expert ready to use the algorithm in your projects. So relax, get a drink, and let’s begin!

## Understanding Cohen-Sutherland Line Clipping

The Cohen-Sutherland line clipping algorithm quickly determines if a line segment is inside, outside, or contacts a window edge. Start by assigning 4-bit codes to each window side. 0001, 0010, 0100, and 1000 could signify left, bottom, right, and top. A line running across that side would have its bit set to 1. Next, establish the window edge codes for your line segment’s endpoints. If both endpoints share a code, the line is inside or outside the window. Not unless it intersects an edge.

Say your window is (0, 0) to (10, 10) and your line is (5, 15) to (15, 5). First point: 0101 (left/top), second: 1001 (right/top). Lines must intersect two edges due to different codes. Compare the slopes of your line and the window edges the endpoints are in to locate the intersection points. Intersection is where slopes are equal. Clip the line to the intersection points and continue with additional segments until it passes through the window or is totally clipped.

The Cohen-Sutherland algorithm efficiently clips lines to display windows. Clip lines and accelerate computer graphics with this approach and some clever code. Try it!

## How the Algorithm Works – Clipping Window and Region Codes

The Cohen-Sutherland line clipping algorithm requires knowledge of clipping windows and area codes.Like a “viewfinder” for an image, the clipping window displays the piece you want to show. Clip any line segments outside this window. Region codes let the algorithm determine if a line segment is inside or outside the window.

Region codes are a binary representation of where a point is in relation to the window. The Cohen-Sutherland algorithm uses 4 bits to represent 8 regions – 0000 is inside, and the other 7 codes indicate a point outside a side of the window.When you have the region codes for the start and end points of a line, you can logically AND them together. If the result is 0000, the entire line segment is inside the window – no clipping needed! If not, you need to clip.

Clipping is done by computing the intersection of the line and the window edge. New start and end points are calculated, region codes recomputed, and the process repeats until you have a series of line segments completely within the window.By using this logical approach, the Cohen-Sutherland algorithm efficiently clips lines to the viewing window. It’s a foundational algorithm used in computer graphics that you’ll often encounter in software and hardware for imaging, gaming, and CAD.Clipping windows, region codes, and how the Cohen-Sutherland algorithm displays only the windowed image are now clear. Clever technique, eh?

### Cohen-Sutherland Algorithm pseudocode

The Cohen-Sutherland line clipping algorithm quickly determines if a line segment is inside, outside, or crosses a rectangle. It divides 2D space into nine rectangle-based sections with 4-bit codes. It then analyzes each line endpoint to see which regions they are in and uses simple logic to determine the line-rectangle relationship.

Define a rectangle with minimal and maximum x and y coordinates (xmin, xmax, ymin, ymax) to implement this technique. Define area codes as:

• 0000 – Inside
• 0001 – Left
• 0010 – Right
• 0100 – Bottom
• 1000 – Top

For each endpoint of the line (x, y), determine its region code with this logic:

“`

code = 0

• if (x < xmin) code = code | 0001
• if (x > xmax) code = code | 0010
• if (y < ymin) code = code | 0100
• if (y > ymax) code = code | 1000

“`

Once you have the region codes for each endpoint, here is the logic to determine the relationship:

• If both endpoints have code 0000, the line is completely inside.
• If one endpoint has code 0000, check the other code. If it’s not 0000, the line crosses.
• If both codes are not 0000 but share no common bits (no region in common), the line is outside.
• Otherwise, the line crosses the rectangle.

This algorithm is efficient because it only checks each endpoint’s region once. Computer graphics still utilize it to clip lines and polygons. These instructions will get you cutting lines quickly!

The Cohen-Sutherland line clipping algorithm has some key advantages and disadvantages to consider.

One of the biggest pros of the Cohen-Sutherland algorithm is its speed and efficiency. It uses a fast rejection method to quickly determine if a line segment lies completely outside the clipping window. If so, the line can be rejected without any further calculations. This makes the algorithm very efficient for clipping lines.

Another advantage is that it handles line clipping for all types of lines – horizontal, vertical and diagonal. The algorithm classifies line segments based on the position of the endpoints relative to the clipping window. This allows it to handle clipping for any orientation of line.

Finally, the Cohen-Sutherland algorithm is conceptually quite simple. It uses a basic encoding scheme to determine in/out codes for the line endpoints and a series of logical tests to check if the line should be rejected, clipped or accepted. This makes the algorithm easy to understand and implement.

One disadvantage is that the Cohen-Sutherland algorithm cannot handle clipping for curved lines or splines. It is designed specifically for straight line segments. Curved lines would require a different approach. Another downside is that the algorithm may perform unnecessary clipping in some cases. It takes a very systematic approach to clipping lines which can result in clipping line segments that do not actually intersect the clipping window. This can impact the efficiency and performance of the algorithm.

The Cohen-Sutherland line clipping algorithm clips straight lines quickly and effectively. It’s simple but effective for many line trimming tasks, despite its limits. By analyzing the pros and cons, you can decide if this algorithm is ideal for your line cutting needs.

### Application and Examples of Cohen-Sutherland Algorithm

The Cohen-Sutherland line clipping algorithm has various graphics uses. Some examples:

### Window Clipping

In graphics systems, the Cohen-Sutherland technique is often used to clip lines to window or viewport borders. Drawing only visible lines increases efficiency.

### Polygon Clipping

Expand the algorithm to trim polygons to window limits. Polygon edges are trimmed individually. The clipped polygon is formed by reconnecting the clipped edges.

### Hidden Surface Removal

Hidden surface removal methods like Painter’s start with line clipping. Clipping lines to the window lets you rapidly reject lines outside the viewport. Hidden surface removal only considers lines inside the window.

### 3D Volume Viewing

In 3D computer graphics, the view volume is the scene’s visible area at a certain angle. The Cohen-Sutherland algorithm renders only visible geometry by clipping lines and polygons to the view volume. This boosts 3D graphics performance.

As shown, the Cohen-Sutherland line clipping algorithm and its extensions are useful in 2D and 3D computer graphics. It clips lines to windows, viewports, and view volumes quickly, rejecting invisible geometry early in the graphics pipeline. This optimises graphics systems by concentrating computing resources on visible material.

### Conclusion

A step-by-step explanation of the Cohen-Sutherland line cutting algorithm. The math may look difficult, but the notion is simple. This adaptable technique clips lines rapidly and efficiently to fit into a rectangle viewing window, enabling many computer graphics applications. Remember that methods like this enabled sophisticated images on your screen. Who knew so much went into even the simplest computer graphics? This should clarify some arithmetic and logic. Now you can clip to your heart’s content or learn how your gadgets handle it. Despite difficult geometry, the options are unlimited.