Point Clipping Algorithm in Computer Graphics

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In the previous chapter, we presented an overview of several clipping algorithms. From this chapter, we will explain these clipping algorithms in detail for a better understanding of these concepts. In this chapter, we will cover point clipping in detail. This is the most fundamental and easiest algorithm to clip a point inside a viewport.

What is Clipping?

We have covered the concept of Windowing and Viewing in the previous chapter. These are useful when putting something inside a fixed window. And to reduce computation, we ignore all the things outside the window.

Formally, clipping means the procedure used to identify parts of a picture that are either inside or outside a specified region. This region is called the clip window. Clippings are used in these fields and some other fields as well.

• Extracting specific parts of a scene for viewing
• Determining visible surfaces in 3D views
• Handling drawing and painting operations
• Supporting multi-window environments

The clip window can either be a simple polygon or have more complex boundaries like curves, depending on the application.

What is Point Clipping?

Point clipping is a type of clipping algorithm that focuses specifically on determining whether a point lies within the clip window or not. This method checks if a point is within the bounds of the rectangular region defined by the clip window.

Here the point (x, y) is inside the window in the left figure so it is not clipped. But in the right hand side image, the window is shifted to the right and the point in outside the window, so it will be clipped (removed from the window) its calculation is not needed anymore.

How Point Clipping Works?

Assume we have a point P = (x, y) and a rectangular clip window defined by the following boundaries:

• xw_min − The minimum x-coordinate of the clip window
• xw_max − The maximum x-coordinate of the clip window
• yw_min − The minimum y-coordinate of the clip window
• yw_max − The maximum y-coordinate of the clip window

To determine whether the point P lies within the clip window, we check the following inequalities:

• xw_min < x < xw_max
• yw_min < y < yw_max

If the point P satisfies all these conditions, it is saved for display. However, if P does not satisfy any of these inequalities, it is considered outside the clip window and is clipped, meaning it will not be displayed.

Here the (xw_min, yw_min) = (1, 2) and (xw_max, yw_max) = (5, 4), the point coordinate is (2, 3)

For the first case, it satisfies the conditions:

• 1 < 2 < 5
• 2 < 3 < 4

For the second case, the point is at (3, 1) so it does not satisfies the condition for y, and it is clipped.

• 1 < 3 < 5
• 2 < 1 < 4 (invalid condition)

Applications of Point Clipping

While point clipping is not as commonly used as other types of clipping (such as line or polygon clipping), there are specific cases where point clipping is essential. For example −

• In particle systems, where points represent individual particles in scenes like explosions or sea foam, point clipping ensures that only particles within the visible region are displayed.
• In large datasets, where millions of points need to be visualized, point clipping helps in managing and displaying only the relevant data points within the clip window.

Point clipping provides a simple and efficient method to manage such cases, ensuring that only necessary data is shown on the screen.

Conclusion

In this chapter, we covered the basics of clipping and the different types of clipping algorithms. We then focused on point clipping, explaining how it works by checking whether a point lies inside or outside a rectangular clip window. We also discussed the importance of point clipping in specific applications, such as particle systems and large datasets.