# Midpoint Subdivision Algorithm For Line Clipping Pdf Download

## Midpoint Subdivision Algorithm for Line Clipping

Line clipping is the process of removing lines or portions of lines outside an area of interest. Typically, any line or part thereof which is outside of the viewing area is removed. Line clipping is an important operation in computer graphics, as it can improve the efficiency and quality of rendering by discarding invisible or irrelevant parts of the scene.

There are many algorithms for line clipping, each with its own advantages and disadvantages. One of the algorithms is the midpoint subdivision algorithm, which is based on the idea of recursively dividing the line segment into two halves and testing the midpoint of each half against the clipping window. The algorithm is simple, fast, and suitable for machines that do not support multiplication and division operations.

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## Algorithm Description

The midpoint subdivision algorithm works as follows:

Calculate the position of both endpoints of the line segment using a 4-bit code that indicates whether the point is above, below, left, or right of the clipping window. This code is also known as the outcode.

Perform a bitwise OR operation on both outcodes. If the result is zero, then the line segment is guaranteed to be visible and can be drawn. If the result is non-zero, then proceed to the next step.

Perform a bitwise AND operation on both outcodes. If the result is non-zero, then the line segment is guaranteed to be invisible and can be discarded. If the result is zero, then proceed to the next step.

For the line segment that is neither completely visible nor completely invisible, find the midpoint of the segment and calculate its outcode.

If the midpoint outcode is zero, then the line segment crosses the clipping window and needs to be clipped. To do this, divide the segment into two halves and repeat steps 2 to 5 for each half until a visible or invisible segment is obtained.

If the midpoint outcode is non-zero, then compare it with one of the endpoint outcodes. If they are different, then repeat steps 2 to 5 for the half that contains the different outcode. If they are same, then discard the whole segment as it lies outside the clipping window.

## Example

Consider a clipping window with coordinates (-3, 1) to (2, 6) and a line segment with endpoints A (-4, 2) and B (-1, 7). The following steps illustrate how the midpoint subdivision algorithm works:

The outcode for point A is 1000, indicating that it is left of the window. The outcode for point B is 0100, indicating that it is above the window. The OR operation gives 1100, which is non-zero, so we proceed to step 3.

The AND operation gives 0000, which means that the line segment may cross the window. We proceed to step 4.

We find the midpoint C (-2.5, 4.5) and calculate its outcode as 0000, which means that it lies inside the window. We proceed to step 5.

We divide the segment AB into AC and CB and repeat steps 2 to 5 for each half. For AC, we get OR = 1000 and AND = 0000, so we repeat step 4 and find D (-3.25, 3.25) with outcode = 1000. We compare it with A and see that they have same outcode, so we discard AC as it lies outside the window. For CB, we get OR = 0100 and AND = 0000, so we repeat step 4 and find E (-1.25, 5.75) with outcode = 0000. We compare it with B and see that they have different outcodes, so we repeat steps 2 to 5 for CE and EB.

For CE, we get OR = 0000 and AND = 0000, which means that it is visible and can be drawn. For EB, we get OR = 0100 and AND = 0100, which means that it is invisible and can be discarded.

The final result is that only CE is visible and needs to be drawn.

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