Geometrical examine Types of Line Clipping

Geometrical examine of the above kinds of clipping (it assists to get point of intersection of line PQ along with any edge).

Assume (x₁, y₁) and (x₂, y₂) be the coordinates of P and Q respectively.

1)   Top case/above

If y1 > yw_max then 1st bit of bit code = 1 (suggesting above) else bit code = 0

2)   Bottom case/below case

If y₁ < yw_min   then 2^nd   bit = 1 (that is below) else bit = 0

3)   Left case: if x₁ < xw_min then 3rd bit = 1 (that is left) else 0

4)   Right case: if x₁ > xw_max then 4th bit = 1 (that is right) else 0

Likewise, the bit codes of the point Q will also be allocated.

1)   Top/above case:

Equation of top edge is: y = yw_max. The equation of line PQ is y - y₁ = m (x - x₁);

Here, m = (y₂ - y₁)/ (x₂ - x₁). The coordinates of the point of intersection will be (x, yw_max) ∴equation of line among point P and intersection point is (yw_max - y₁) = m ( x - x₁) rearrange we find  x = x  +  1

 (yw_max  - y₁ ) = m (x - x₁)

 Now arrange then we find

x = x₁ + (1/m) (yw_max  - y₁ ) ------------------ (A)

Thus, we acquire coordinates (x, yw_max) that is coordinates of the intersection.

2)   Bottom/below edge begin along with y = yw_min and proceed as for above mentioned case.

∴equation of line among intersection point (x', yw_min) and point Q that is (x₂, y₂) Is (yw_min - y₂) = m (x′ - x₂) rearranging that we determine,

x′ = x₂   + (1/m)( yw_min - y₂)------------------------(B)

The coordinates of the point of intersection of PQ along with the bottom edge will be

x₂   + (1/m)( yw_min - y₂),yw_min)

3)   Left edge: the equation of left edge is x = xw_min.

Here, the point of intersection is (xw_min, y).

By using 2 point from the equation of the line we contain:

(y - y₁) = m (xw_min - x₁)

So now again arranging that, we find, y = y₁ + m (xw_min - x₁).                   -------------------- (C)

Consequently, we find value of xw_min and y both that are the coordinates of intersection point is identified via ( xw_min , y₁ + m( xw_min  - x₁ )) .

4)   Right edge: proceed as in left edge case although start along with x-xw_max.

Here point of intersection is (xw_max, y′).

By using 2 point form, the equation of the line is (y′ - y₂) = m (xw_max - x₂)

y' = y₂ + (m(xw_max - x₂))-------------------(D)

The coordinates of the intersection of PQ along with the right edge will be

( xw_max , y₂  + m( xw_max  - x₂ )).