geometrical examine types of line

Question

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 )).