Cyrus–Beck algorithm

The Cyrus–Beck algorithm is a generalized line clipping algorithm. It was designed to be more efficient than the Sutherland–Cohen algorithm which uses repetitive clipping. Cyrus–Beck is a general algorithm and can be used with a convex polygon clipping window unlike Sutherland-Cohen that can be used only on a rectangular clipping area.

Here the parametric equation of a line in the view plane is:

${\begin{aligned}p(t)&=&tp_{1}+(1-t)p_{0}\\&=&p_{0}+t(p_{1}-p_{0})\end{aligned}}$

where $0\leq t\leq 1$.

Now to find intersection point with the clipping window we calculate value of dot product. Let p_E be a point on the clipping plane E.

Calculate $n\cdot (p(t)-p_{E})$.

if > 0 vector pointed towards interior

if = 0 vector pointed parallel to plane containing p

if < 0 vector pointed away from interior

Here n stands for normal of the current clipping plane (pointed away from interior).

By this we select the point of intersection of line and clipping window where (dot product = 0 ) and hence clip the line.

Notes

1] Sutherland-Cohen can be used only on a rectangular clipping area.

2] Cyrus–Beck is a general algorithm and can be used with a convex polygon clipping window.

   p(t) = p0 + t(p1-p0)        /* it's parametric function */

3] if > 0 ; vector says p(t) is OUTSIDE && A < 90 degree.

   if < 0 ; vector says p(t) is INSIDE && a > 90 degree.

   if = 0 ; vector says p(t) is on edge E .. here outer normal edge is perpendicular to the E and p(t)-B

  .. we will writing here a function code for it as given below :

   /*
  
   if( DtProd (N,P(t)-B) > 0)
          {
             p(t) OUTER & A < 90 degree ;    /* P(t) is OUTSIDE ..
         
          }
   else if( DtProd (N,P(t)-B) < 0)
          {
             p(t) INNER & A > 90 degree ;    /* P(t) is INSIDE ..
         
          }
  else( DtProd (N,P(t)-B) = 0)
          {
             p(t) lies on to the edge E ;    /* where outer normal edge N would be perpendicular to both E and p(t)-B..
         
          }

 */

See also

Algorithms used for the same purpose:

• Cohen-Sutherland
• Liang-Barsky
• Nicholl–Lee–Nicholl
• Fast-clipping

References in other media:

• Tron: Uprising

References

• Mike Cyrus, Jay Beck. "Generalized two- and three-dimensional clipping". Computers & Graphics, 1978: 23-28.
• James D. Foley. Computer graphics: principles and practice. Addison-Wesley Professional, 1996. p. 117.

External links

• http://cs1.bradley.edu/public/jcm/cs535CyrusBeck.html
• http://web.archive.org/web/20110725233122/http://softsurfer.com/Archive/algorithm_0111/algorithm_0111.htm