In computer graphics, the Cyrus–Beck algorithm is a generalized algorithm for line clipping. It was designed to be more efficient than the Cohen–Sutherland algorithm, which uses repetitive clipping."Clipping" (presentation). Cyrus–Beck is a general algorithm and can be used with a convex polygon clipping window, unlike Cohen-Sutherland, which can be used only on a rectangular clipping area.
Here the parametric equation of a line in the view plane is
where .
Now to find the intersection point with the clipping window, we calculate the value of the dot product. Let be a point on the clipping plane .
Calculate :
if < 0, vector pointed towards interior; if = 0, vector pointed parallel to plane containing ; if > 0, vector pointed away from interior.
Here 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 is 0) and hence clip the line.
Notes
See also Algorithms used for the same purpose:
Cohen–Sutherland algorithm Liang–Barsky algorithm Nicholl–Lee–Nicholl algorithm 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 https://web.archive.org/web/20101203041134/http://cs1.bradley.edu/public/jcm/cs535CyrusBeck.html https://web.archive.org/web/20110725233122/http://softsurfer.com/Archive/algorithm_0111/algorithm_0111.htm