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{{Expand German|Rasterung von Linien|fa=yes|topic=sci|date=December 2009}}
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A '''line drawing algorithm''' is a graphical [[algorithm]] for approximating a line segment on discrete graphical media. On discrete media, such as [[pixel]]-based [[computer display|display]]s and [[computer printer|printer]]s, line drawing requires such an approximation (in nontrivial cases).


On continuous media, by contrast, no algorithm is necessary to draw a line. For example, [[oscilloscope]]s use natural phenomena to draw lines and curves.
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The Cartesian slope-intercept equation for a straight line is
== ayvpGC Brazil 6s GEVLSf7r ==
Y= mx+b
With m representing the slope of the line and b as the y intercept. Given that the two endpoints of the line segment are specified at positions (x1,y1) and (x2,y2). we can determine values for the slope m and y intercept b with the following calculations,


m=(y2-y1)/(x2-x1)
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so, b=y1-m.x1
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==A na&iuml;ve line-drawing algorithm==
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<code>
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dx = x2 - x1
<ul>
dy = y2 - y1
 
'''for''' x '''from''' x1 '''to''' x2 {
  <li>[http://www.guanyuai.org/forum.php?mod=viewthread&tid=566962 http://www.guanyuai.org/forum.php?mod=viewthread&tid=566962]</li>
  y = y1 + dy * (x - x1) / dx
 
  plot(x, y)
  <li>[http://assy1.com/vb/showthread.php?p=64045#post64045 http://assy1.com/vb/showthread.php?p=64045#post64045]</li>
}</code>
 
It is assumed here that the points have already been ordered so that <math>x_2 > x_1</math>.
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This algorithm works just fine when <math>dx >= dy</math> (i.e., slope is less than or equal to 1), but if <math>dx < dy</math> (i.e., slope greater than 1), the line becomes quite sparse with lots of gaps, and in the limiting case of <math>dx = 0</math>, only a single point is plotted.
 
 
</ul>
The na&iuml;ve line drawing algorithm is inefficient and thus, slow on a digital computer. Its inefficiency stems from the number of operations and the use of floating-point calculations. Line drawing algorithms such as [[Bresenham's line algorithm|Bresenham]]'s or [[Xiaolin Wu's line algorithm|Wu]]'s are preferred instead.
 
==List of line drawing algorithms==
The following is a partial list of line drawing algorithms:
*[[Digital Differential Analyzer (graphics algorithm)]] &mdash; Similar to the naive line-drawing algorithm, with minor variations.
*[[Bresenham's line algorithm]] &mdash; optimized to use only additions (i.e. no divisions or multiplications); it also avoids floating-point computations.
*[[Xiaolin Wu's line algorithm]] &mdash; can perform [[spatial anti-aliasing]]
 
 
==References==
Fundamentals of Computer Graphics, 2nd Edition, A.K. Peters by Peter Shirley
 
{{DEFAULTSORT:Line Drawing Algorithm}}
[[Category:Computer graphics algorithms]]
 
{{Link FA|de}}

Latest revision as of 00:58, 2 December 2014

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