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2014-01-23T17:44:19Z

106.188.106.195:

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.<ref>[http://www.slideshare.net/johanna20/clipping-presentation "Clipping" (presentation)]</ref> 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:

<math>
\begin{align}
p(t) &=& tp_1 + (1-t)p_0\\
&=& p_0 + t(p_1-p_0)
\end{align}
</math>

where <math>0 \leq t \leq 1 </math>.

Now to find intersection point with the clipping window we calculate value of dot product. Let ''p''<sub>''E''</sub> be a point on the clipping plane ''E''.

Calculate <math>n\cdot (p(t)-p_E)</math>.
:: 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==
{{Reflist}}

==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. ''[http://books.google.com/books/about/Computer_graphics.html?id=-4ngT05gmAQC 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{{dead link|date=May 2013}}

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[[Category:Clipping (computer graphics)]]
[[Category:Articles created via the Article Wizard]]

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Normalized Google distance