Complete Guide to Two-Dimensional Viewing and Clipping in Computer Graphics

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.

Point clipping is essentially the evaluation of the following inequlities:

((x_min ≤ x ≤ x_max) (y_min ≤ y ≤ y_max))

where x_min, x_max, y_min and y_max define the clipping window. A point (x, y) is considered inside the window when the inequalities all evaluate to true.

Math:

Here the (x_min, y_min) = (1, 2) and (x_max, y_max) = (5, 4), the point coordinates are p1(2, 3), p2(3, 1)

For p1,

1 < 2 < 5

2 < 3 < 4

it satisfies the conditions

For p2,

1 < 3 < 5

2 < 1 < 4 (invalid condition)

it does not satisfy the condition for y, and it is clipped.

Line clipping:

Line clipping algorithm is used to remove the parts of lines that are outside the area viewport. Line clipping reduces the computation cost by enabling or disabling rendering operations within a defined region.

The Cohen-Sutherland Algorithm:

In this algorithm, divide the line clipping process into two phases: (1) identify those lines which intersect the clipping window and so need to be clipped and (2) perform the clipping.

 All lines fall into one of the following clipping categories:

•      Visible---- both endpoints of the line lie within the window.

•   Not visible--- the line definitely lies outside the window. This will occur if the line from (x₁,y₁) to (x₂,y₂) satisfies any one of the following four inequalities:

X₁ ,X₂ > X_max  and y₁, y₂ > y_max

X₁ ,X₂ < X_min  and y₁, y₂ < y_min

• Clipping candidate--- the line is in neither category 1 nor 2.

In Fig, line AB is in category 1 (visible); lines CD and EF are in category 2 (not visible); and lines GH, IJ, and KL are in category 3 (clipping candidate).