Question

Consider the clipping of a line segment in two dimensions against a rectangular clipping window. Show that you require only the endpoints of the line segment to determine whether the line segment is not clipped, is partially visible, or is clipped out completely.

Answer 1

Answer / Explanation:

Assuming we define the end points as ( x₁ , y₁) and (x₂ , y₂) and the rectangular window edge as ( Xmin ,Ymin and Xmax , Ymax)

The illustration of the above assumption is represented in the diagram below.

Now, suppose the line segment is between the points P₁ = ( x₁ , y₁) , and

P₂ = (x₂ , y₂).

We can then create a line recalling and using parametric form,

P(t) = ( 1 - t) P₁ + tP₂ , t ∈ {0 , 1 },

So, for the X axis, we have,

tₓ = P₁ₓ - x ÷ P₁ₓ - P₂ₓ

We need to note that at this point we need to know the minimum and maximum unclipped  values for parameter t from each dimension.

Therefore,

- ( tmin , tmax ) = ( 0,1) means unclipped line

-tmin > tmax means completely clipped out line

– Some other range means partially clipped out line.