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) ⇒ (x₁, y₁) + t (x₂ - x₁, y₂ - y₁) = (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.

Posted Date: 4/3/2013 3:17:29 AM | Location : United States

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