Cyrus Beck Algorithm - Line Clipping Algorithm
Cyrus Beck Line clipping algorithm is actually, a parametric line-clipping algorithm. The term parametric means that we require finding the value of the parameter t in the parametric representation of the line segment for the point at that the segment intersects the clipping edge. For good understanding, identify the Figure (a) as in above, here P Q is a line segment, that is intersecting at the two edges of the convex window.
Note: The algorithm is appropriate to the "convex polygonal window".
Figure: (a): Interaction of line PQ and Window
Here, just again call the parametric equation of line segment PQ that we have already studied.
This is simply P + t (Q - P) 0 ≤ t ≤ 1
Here, t → linear parameter incessantly changes value.
∴P + t (Q - P) ⇒ (x_{1}, y_{1}) + t (x_{2} - x_{1}, y_{2} - y_{1}) = (x, y) be any point on PQ. ------ (1)
For such equation (1) we have subsequent cases:
1) While t = 0 we obtain the point P.
2) While t = 1 we get the point Q.
3) While t varies then 0 ≤ t ≤ 1 then line in between point P and Q is traced.
For t = ½ we find the mid-point of PQ.
4) While t < 0 line on Left hand side of P is traced.
5) While t > 1 line on Right hand side of Q is traced.
Consequently, the variation in parameter t is actually generating line in point wise method. The range of the parameter values will discover the portion to be clipped through any of convex polygonal region consisting of n-vertices or lattice points to be identified through the user. There is one type of clipping situation is shown in Figure (a) of Interaction of line PQ and Window.