Cyrus–Beck algorithm

The Cyrus–Beck algorithm is a line clipping algorithm. It was designed to be more efficient than the Sutherland–Cohen algorithm which uses repetitive clipping ^[1]. 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:

$\begin{align} p(t) &=& tp_1 + (1-t)p_0\\ &=& p_0 + t(p_1-p_0) \end{align}$

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.

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

Notes

1. ^ "Clipping" (presentation)

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://softsurfer.com/Archive/algorithm_0111/algorithm_0111.htm

See also

Algorithms used for the same purpose:

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