2016 Update

Task/Ray-casting-algorithm/00DESCRIPTION

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 {{Wikipedia|Point_in_polygon}}
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+<br>
 Given a point and a polygon, check if the point is inside or outside the polygon using the [[wp:Point in polygon#Ray casting algorithm|ray-casting algorithm]].
 
 A pseudocode can be simply:
@@ -27,6 +29,7 @@ So the problematic points are those inside the white area (the box delimited by
 
 [[Image:posslope.png|128px|thumb|right]]
 [[Image:negslope.png|128px|thumb|right]]
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 Let us take into account a segment AB (the point A having y coordinate always smaller than B's y coordinate, i.e. point A is always below point B) and a point P. Let us use the cumbersome notation PAX to denote the angle between segment AP and AX, where X is always a point on the horizontal line passing by A with x coordinate bigger than the maximum between the x coordinate of A and the x coordinate of B. As explained graphically by the figures on the right, if PAX is greater than the angle BAX, then the ray starting from P intersects the segment AB. (In the images, the ray starting from P<sub>A</sub> does not intersect the segment, while the ray starting from P<sub>B</sub> in the second picture, intersects the segment).
 
 Points on the boundary or "on" a vertex are someway special and through this approach we do not obtain ''coherent'' results. They could be treated apart, but it is not necessary to do so.
@@ -68,4 +71,5 @@ An algorithm for the previous speech could be (if P is a point, Px is its x coor
     '''end''' '''if'''
   '''end''' '''if'''
 
-(To avoid the "ray on vertex" problem, the point is moved upward of a small quantity &epsilon;)
+(To avoid the "ray on vertex" problem, the point is moved upward of a small quantity &nbsp; <big>&epsilon;</big>.)
+<br><br>