In the algorithm, first of all, it is detected whether line lies inside the screen or it is outside the screen. All lines come under any one of the following categories:. Visible: If a line lies within the window, i. A line is visible and will be displayed as it is.
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All Processing code for this article, along with images, can be found on Github. For a copy-pasteable version of the algorithm, click here. Tri-color plot by Paul Rickards.
Detail of section showing clipped parallel lines. Naturally I sat around noodling away on a Saturday trying to recreate it! I should point out that I do not know if this is the exact technique used by Paul in his plots; rather it is simply my interpretation of how I would go about generating something similar. Here are some of the results of my approach. Tiles with random angles and uniform line spacing. Tiles with random angles and random line spacing. Tiles with noise-based angles and random line spacing.
Tiles with random angles and Y-axis-based spacing. Tiles with random angles and image-based line spacing. Detail of image-based portrait. The basic idea is to i draw a single line at an arbitrary angle, ii create parallel copies of it spaced by some user-specified distance, and finally ii clip them off to fall within a specified square. So how do we actually perform these steps? In particular, how do we manage the third step, where we clip lines to fall within a given square?
The solution is a general class of algorithms designed for computer graphics called clipping algorithms. The idea is to be able to clip a shape to only the parts of it that fall within a window. Enter the Cohen-Sutherland line clipping algorithm! The Cohen-Sutherland algorithm is a fast algorithm for clipping a line to the part of it that lies within a specified rectangular window. To perform these steps, we need only consider the endpoints of our line.
If both endpoints lie inside the clip window, then the entire line lies inside the window. Similarly, if both endpoints of a line lie within the same side of the clip window, the line must lie outside it entirely, Below are illustrated the four cases. Also note that you can have an endpoint belonging to multiple regions, such as the top and left region as is the case for the left endpoint of the topmost line in the figure below.
Finally, we get to the case where either both the endpoints lie on different sides of the clip window or one of them does with the other within the window itself. Illustrated below are the three cases that are possible.
Importantly, note that we can still have the case that the line falls outside the clip window, as illustrated by the leftmost line above. The first thing we need to do is to somehow be able to encode the location of an endpoint in terms of the four regions shown above. The Cohen-Sutherland algorithm does this through a simple integer-based bitmap for each endpoint. The first image below shows how the algorithm uses four bits to represent regions. The image further below shows the resulting encoding for each region.
So far so good! We now have a way to encode the location of an endpoint in terms of the outer regions of the clip window. Inside the loop above, the first if condition checks if both the endpoints have a zero code recall that this pertains to the clip window itself.
In this case, we just want to draw the entire line as is; we just set accept to true and break out of the loop. The second condition checks if the bitwise AND of the two endcodes is non-zero. If the two endpoints share a region, their corresponding bits would be set to 1, and when we apply the bitwise AND, we would get a 1. We simply leave accept as it is initialized to false and break out. Now we come to the final case, where we know the line has some endpoint outside the clip window and we want to clip its end off.
Now we want to clip off the line from this end up to the window edge. Basically we want to calculate a new X and Y coordinate to replace the endpoint. Since we have four edges, we need to deal with each case separately:. Above, we use bit manipulations in the if statement conditions to determine which side of the clip window the endpoint lies on, and calculate some new coordinates to clip it to. After this, we replace the old coordinates with the new one. It takes a little bit of maths to figure it out: we find the equation of the line, and find its intersection at the edge of the window.
So the code we get is the following:. Putting it all together, here is our final function for Cohen-Sutherland line clipping in one nice copy-pasteable snippet:. Absolutely beautiful! Leave accept as 'false' and exit loop. Subscribe for updates!
Line Clipping | Set 1 (Cohen–Sutherland Algorithm)
Cohen Sutherland Algorithm is a line clipping algorithm that cuts lines to portions which are within a rectangular area. It eliminates the lines from a given set of lines and rectangle area of interest view port which belongs outside the area of interest and clip those lines which are partially inside the area of interest. The algorithm divides a two-dimensional space into 9 regions eight outside regions and one inside region and then efficiently determines the lines and portions of lines that are visible in the central region of interest the viewport. The more efficient Cohen-Sutherland Algorithm performs initial tests on a line to determine whether intersection calculations can be avoided. What is the limitation of Cohen Sutherland algorithm?
Viewing & Clipping
The Cohen—Sutherland algorithm is a computer-graphics algorithm used for line clipping. The algorithm divides a two-dimensional space into 9 regions and then efficiently determines the lines and portions of lines that are visible in the central region of interest the viewport. The algorithm was developed in during flight-simulator work by Danny Cohen and Ivan Sutherland. The numbers in the figure below are called outcodes. An outcode is computed for each of the two points in the line. The outcode will have 4 bits for two-dimensional clipping, or 6 bits in the three-dimensional case.
The Cohen-Sutherland Line Clipping Algorithm
Given a set of lines and a rectangular area of interest, the task is to remove lines which are outside the area of interest and clip the lines which are partially inside the area. Cohen-Sutherland algorithm divides a two-dimensional space into 9 regions and then efficiently determines the lines and portions of lines that are inside the given rectangular area. The Cohen—Sutherland algorithm can be used only on a rectangular clip window. For other convex polygon clipping windows, Cyrus—Beck algorithm is used.