COHEN-SUTHERLAND LINE CLIPPING

                                             This is one amongst the oldest and most well liked line-clipping procedures. Generally, the tactic hastens the processing of line segments by performing initial tests that reduce the amount of intersections that has got to he calculated.
Every line end-point in a very picture is assigned a four-digit code, called a locality code that identifies the placement of the purpose relative to the boundaries of the clipping rectangle. Regions are founded in relevance the boundaries. Each bit position within the region code is employed to point one amongst the four relative coordinate positions of the purpose with relevancy the clip window: to the left, right, top, or bottom. By numbering the bit positions within the region code as 1 through 4 from right to left, the coordinate regions are often correlated with the bit positions as

bit 1: left
bit 2: right
bit 3: below
bit 4: above

A value of 1 in any bit position indicates that the purpose is in this relative position; otherwise, the bit position is about to 0. If some extent is within the clipping rectangle, the region code is 0000. some extent that's below and to the left of the rectangle incorporates a region code of 0101.
Bit values within the region code are determined by comparing endpoint coordinate values (x, y) to the clip boundaries. Bit 1 is about to 1 if x < xwmin. the opposite three bit values are often determined using similar comparisons. For languages within which bit manipulation is feasible, region-code bit values are often determined with the subsequent two steps: 

1) Calculate differences between endpoint coordinates and clipping boundaries.
2) Use the resultant sign little bit of each difference calculation to line the corresponding value within the region code. Bit 1 is that the sign {bit of|little {bit of|little {bit of|little little bit of}}} x – xwmin; bit 2 is that the sign bit of xwmax - x; bit 3 is that the sign bit of y - ywmin; and bit 4 is that the sign bit of ywmax - y.

Once we've established region codes for all line endpoints, we will quickly determine which lines are completely inside the clip window and which are clearly outside. Any lines that are completely contained within the window boundaries have a locality code of 0000 for both endpoints, and that we trivially accept these lines. Any lines that have a 1 within the same bit position within the region codes for every endpoint are completely outside the clipping rectangle, and that we trivially reject these lines. we might discard the road that incorporates a region code of 1001 for one endpoint and a code of 0101 for the opposite endpoint. Both endpoints of this line are left of the clipping rectangle, as indicated by the 1 within the first bit position of every region code. a way that may be accustomed test lines for total clipping is to perform the logical and operation with both region codes. If the result's not 0000, the road is totally outside the clipping region. Lines that can't be identified as completely inside or completely outside a clip window by these tests are checked for intersection with the window boundaries. we start the clipping process for a line by comparing an out of doors endpoint to a clipping boundary to work out what proportion of the road are often discarded. Then the remaining a part of the road is checked against the opposite boundaries, and that we continue until either the road is completely discarded or a bit is found inside the window. We founded our algorithm to test line endpoints against clipping boundaries within the order left, right, bottom, top. as an example the precise steps in clipping lines against rectangular boundaries using the Cohen-Sutherland algorithm, may be processed. Starting with the underside endpoint of the road from P1, to P2, we check P, against the left, right, and bottom boundaries successively and find that now is below the clipping rectangle.

We then find the intersection P’1 with the underside boundary and discard the road section from P1 to P’1. the road now has been reduced to the section from P’1 to P2. Since P2, is outside the clip window, we check this endpoint against the boundaries and find that it's to the left of the window. intersection P’2 is calculated, but now is above the window. therefore the final intersection calculation yields p"2, and also the line from P’1 to P"2 is saved. This completes processing for this line, so we save this part and persist to the subsequent line. Point P3 within the next line is to the left of the clipping rectangle, so we determine the intersection P’3, and eliminate the road section from P3 to P'3 By checking region codes for the road section from P’3 to P4, we discover that the rest of the road is below the clip window and may be discarded also. Intersection points with a clipping boundary are often calculated using the slope-intercept sort of the road equation. For a line with endpoint coordinates (x1, y1) and (x2, y2), they coordinate of the intersection with a vertical boundary are often obtained with the calculation

                                                                Y = y1 + m(x - x1)

Where the x value is about either to xwmin, or to xwmax, and also the slope of the road is calculated as m = (y2 – y1)/(x2, - x1). Similarly, if we are searching for the intersection with a horizontal boundary, the x coordinate are often calculated as

                                                              X = x1 + (y – y1)
                                                                                 m

with y set either to xwmin, or to xwmax.