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Topic: Point in polygon

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  Wikinfo | Polygon
A polygon (from the Greek poly, for "many", and gwnos, for "angle") is a closed planar path composed of a finite number of straight line segments.
Polygons are named according to the number of sides, combining a Greek root with the suffix -gon, e.g.
A concyclic or cyclic polygon is a polygon whose vertices all lie on a single circle.
www.wikinfo.org /wiki.php?title=Polygon   (930 words)

 Point in Polygon Strategies
MacMartin (MacMartin 1992) pointed out that for polygons with a large number of edges there are generally runs of edges which have Y components with the same sign.
When a point is tested, the angle from the anchor edge is computed and a binary search is used to determine the wedge it is in, then the corresponding polygon edge is tested against it (Figure 4).
Points exactly on the unshared edge of a polygon will be classified as arbitrarily inside or outside the polygon by this method, however.
www.acm.org /pubs/tog/editors/erich/ptinpoly   (4418 words)

 Determining Whether A Point Is Inside A Complex Polygon
The solution is to compare each side of the polygon to the Y (vertical) coordinate of the test point, and compile a list of nodes, where each node is a point where one side crosses the Y threshold of the test point.
So, the test point is outside the polygon, as indicated by the even number of nodes (two and two) on either side of it.
Points which are exactly on the Y threshold must be considered to belong to one side of the threshold.
www.alienryderflex.com /polygon   (815 words)

 Point in polygon - Wikipedia, the free encyclopedia
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon.
One simple way of finding whether the point is inside or outside a simple polygon is to test how many times a ray starting from the point intersects the edges of the polygon.
This algorithm does not always produce the correct answer if P lies directly on the polygon's boundary; if implemented on a computer with floating point arithmetic, the results may also be wrong if the point lies very close to that boundary, because of rounding errors.
en.wikipedia.org /wiki/Point_in_polygon   (440 words)

If the distance between the first and last points of a polygon is less than half the spatial grid spacing, then the polygon is assumed to be closed, otherwise the polygon is assumed to be open.
Notice that the last point of the control polygon is the same as the first point of the polygon, thus creating a closed curve.
Run a straight line of IB points from the current point to the point (1,2), and tethers the first point with a spring whose resting length is zero and stiffness is 10000.
www.math.utah.edu /IBIS/man/node41.html   (1780 words)

 Classes: MeshDataEdit
Points and polygons may only be created or modified in the primary active layer, which is given by this layer number.
Enumerate the points or polygons in the specified layers.
The new point's vmap values are calculated as a weighted average of the vmaps of the points in the points array.
mywebpages.comcast.net /erniew/lwsdk/docs/classes/me.html   (2165 words)

 Figures and polygons
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.
A circle is the collection of points in a plane that are all the same distance from a fixed point.
www.mathleague.com /help/geometry/polygons.htm   (620 words)

 Determining if a point lies on the interior of a polygon
This also works for polygons with holes given the polygon is defined with a path made up of coincident edges into and out of the hole as is common practice in many CAD packages.
A point is on the interior of this polygons if it is always on the same side of all the line segments making up the path.
To determine whether a point is on the interior of a convex polygon in 3D one might be tempted to first determine whether the point is on the plane, then determine it's interior status.
astronomy.swin.edu.au /pbourke/geometry/insidepoly   (835 words)

 softWoRx Help: Edit Polygon
Polygons are "manually" created by defining polygon points with clicks of the left mouse button in the image window.
When you have created the last point of the polygon, it must then be "closed" by joining the last point with the first point.
By default, the point is snapped to the area of maximum intensity gradient in the specified box around the chosen point.
www.indiana.edu /~elegans/Deconv/EditPolygon.html   (1904 words)

 Polygon - Wikipedia, the free encyclopedia
If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary.
Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g.
The area of a polygon is the measurment of the 2-dimensional region enclosed by the polygon.
en.wikipedia.org /wiki/Polygon   (1077 words)

 A Point About Polygons | Linux Journal
In all cases, the polygon is specified as an array of X,Y coordinates of the corner points.
Imagine you could detect whether a point was in a polygon or not by placing a friendly trained snail at the point and telling him to head for the North Pole.
Points the routine says are inside the polygon it draws red, points outside are blue.
www.linuxjournal.com /article.php?sid=2029   (2173 words)

 Polygon Triangulation
In computer graphics, polygon triangulation algorithms are widely used for tessellating curved geometries, as are described by splines [Kumar and Manocha 1994].
These polygons are computed from the trapezoidal decomposition by checking whether the two vertices of the original polygon lie on the same side.
A monotone polygon can be triangulated in linear time by using a simple greedy algorithm which repeatedly cuts off the convex corners of the polygon [Fournier and Montuno 1984].
www.cs.unc.edu /~dm/CODE/GEM/chapter.html   (837 words)

 [Exaflop.org] Simple Point In Polygon (convex) Tests
I was quite disappointed when I looked at the c.g.a faq and found that the recomended technique was to find the point of intersection of the ray in the polygons plane and then do a separate test to see if that point lay inside the polygon.
I have included the 2d test as it may be useful for such applications as selecting a polygon in a point and click environment etc.
If we build our normals so they point outwards from the center of the polygon then a positive value will mean that the test point lies outside of that edge and cant possibly be inside the polygon (test over).
www.exaflop.org /docs/naifgfx/naifpip.html   (430 words)

 VIMAGE -- Collect Image Point/Polygon Statistics
Polygons may be expressed as simple closed polygons, polygons with multiple rings, or polygons stored as a topology.
POINT: Only computes a value for point vectors (one vertex), and the value will be the value of the image pixel in which this point falls.
The statistics for polygons are based on all pixels for which the center of the pixel falls within, or on the boundary of the pixel.
www.pcigeomatics.com /cgi-bin/pcihlp/VIMAGE   (1492 words)

 Polygons ( POLYGON )
A polygon is called simple if all nodes of the graph induced by its segments have degree two and it is called weakly simple, if its segments are disjoint except for common endpoints and if the chain does not cross itself.
When a weakly simple polygon P is traversed either the bounded region is consistently to the left of P or the unbounded region is consistently to the left of P.
P is initialized to a rational approximation of the (floating point) polygon Q of coordinates with denominator at most prec.
www.cs.cmu.edu /~smonti/html/leda/POLYGON.html   (791 words)

 Convex Hull of a 2D Point Set or Polygon
This algorithm also applies to a polygon, or just a set of segments, whose hull is the same as the hull of its vertex point set.
In this case, the boundary of a compact set is bounded by a polygon in 2D, and a polyhedron in 3D.
Note that for each point of S there is one push and at most one pop operation, giving a maximum of 2n stack operations for the whole algorithm.
geometryalgorithms.com /Archive/algorithm_0109/algorithm_0109.htm   (2504 words)

 point-to-polygon   (Site not responding. Last check: 2007-10-16)
find a point for an area polygon which is definitely inside the polygon.
If that point is found to be outside the polygon, it locates the closest line segment to the "centroid".
From there, a sequence of points are tested along the perpendicular to that line segment, until an inside point is found.
grass.itc.it /pipermail/grass5/1992-June/000301.html   (152 words)

 Point in a poly
For non intersecting polygons if the winding number is non-zero then the test point is inside the polygon.
A figure 8 will give a negitive winding number for a test point in one of the loops and a positive winding number for the other loop, with all points outside having a winding number of 0.
The basic idea is to total the angle changes for a wiper arm with its origin at the point and whos end follows the polygon points.
www.whisqu.se /per/docs/math26.htm   (288 words)

 PNPOLY - Point Inclusion in Polygon Test - WR Franklin (WRF)
Points that are on the boundary are classified as either inside or outside.
The polygon may contain multiple separate components, and/or holes, provided that you separate the components and holes with a (0,0) vertex, as follows.
If the polygons form a planar graph with each edge labelled with its two polygon neighbors, then one simple way is to run a semi-infinite ray up from the point until it hits its first edge.
www.ecse.rpi.edu /Homepages/wrf/Research/Short_Notes/pnpoly.html   (1911 words)

The polygon is outlined by using the current pen and filled by using the current brush and polygon fill mode.
[in] Pointer to an array of POINT structures that specify the vertices of the polygon, in logical coordinates.
The polygon is closed automatically by drawing a line from the last vertex to the first.
msdn.microsoft.com /library/en-us/gdi/fillshap_0u26.asp?frame=true   (307 words)

 Polygon (Java 2 Platform SE v1.4.2)
Internally, a polygon comprises of a list of (x, y) coordinate pairs, where each pair defines a vertex of the polygon, and two successive pairs are the endpoints of a line that is a side of the polygon.
The first and final pairs of (x, y) points are joined by a line segment that closes the polygon.
The coordinate arrays and the data in them are left untouched but the number of points is reset to zero to mark the old vertex data as invalid and to start accumulating new vertex data at the beginning.
java.sun.com /j2se/1.4.2/docs/api/java/awt/Polygon.html   (951 words)

 Using point-in-polygon test   (Site not responding. Last check: 2007-10-16)
Points on the polyline or coincident with vertices are assumed to be inside of the polygon.
A data point gets the number of the first of given polygons it is in, or NA otherwise.
You can parse the output with tools you have at the hand (grep, awk, Perl...) and select points you are interested in.
www.frw.ruu.nl /gstat/manual/node42.html   (94 words)

 UNIT 33 - SIMPLE ALGORITHMS II - POLYGONS   (Site not responding. Last check: 2007-10-16)
Discuss the results of using the polygon area and point in polygon algorithms when the polygon is not correctly structured (e.g.
Modify the point in polygon algorithm to determine correctly if the point lies on the boundary of the polygon, in addition to inside or outside.
Modify the polygon area algorithm to test for and accommodate negative y coordinates.
www.geog.ubc.ca /courses/klink/gis.notes/ncgia/u33.html   (1356 words)

 Point-in-Polygon algorythm
The point-in-polygon algorythm allows you to programmatically check if a particular point is inside a polygon or outside of it.
A common way to tackle the problem is to count how many times a line drawn from the point (in any direction) intersects with the polygon boundary.
You can easily check multiple points at once, as shown in the example that follows the class code.
www.assemblysys.com /dataServices/php_pointinpolygon.php   (288 words)

 Point Inside Polygon
The code is based on an algorithm which takes the dot and cross product of vectors from the point itself to neighbouring points in the polygon.
If we write the expressions for the dot and cross product, we see that by dividing the two we get the tangent of the angle between two vectors extending from the point to two neighbouring points in the polygon.
This method is more robust than the Inside method, Since you can check a vector or points, and you can find out if each point is inside, is outside, is on the line, or is a vertex point all at once.
www.dfanning.com /tips/point_in_polygon.html   (445 words)

 Ray Tracing News, Volume 5, Number 3
From the vector components (dx, dy) from a test point to a polygon vertex, get an angle using arctan (or the fast approximation, in which case do not scale to radians or degrees; use the angle value in the range 0 to 8).
The case of a test point coincident with a polygon vertex must be explicitly checked, as the arctangent for a zero-length vector is undefined.
If your polygon is convex, (more generally, your polygon is star-shaped,) you can pre-process the polygon into triangle strips by connecting any point in the kernel of the polygon with each vertex of the polygon.
www.acm.org /tog/resources/RTNews/html/rtnv5n3.html   (3923 words)

 Test Whether A Point Is Inside A Complex Polygon With Spline Curves
Now imagine that this is a piece of "string art" from the 1970s, and all the points along the first fl line [Sx,Sy to a,b] are connected with blue strings to all the points along the second fl line [a,b to Ex,Ey].
Each of these two values must be independently tested against our test point — but first each of the two F values must be checked to see if it lies in the range 0 to 1 — if not, it must be ignored, since it is off the end of the spline.
This C code sample is designed around the assumption that the entire polygon resides inside the square that spans from -1 to +1 on each axis.
alienryderflex.com /polyspline   (1430 words)

If an arc between polygons A and B intersects, record an intersection with the boundary of both A and B, irrespective of which side of the arc A and B lie on.
When an arc is found to intersect a vertical line, record the y value of the intersection and the polygon lying below the intersection (right polygon if the arc runs from W to E, left polygon otherwise)
Now have just two values to store for each point - will still need to check every arc against every point, unless some sorting is done first.
www.geo.wvu.edu /~elmes/Geog651/PIPHANDOUT.htm   (479 words)

 determine_if_a_point_is_in_region [TV3DWiki]
Ive come across the need to determine if a point is inside of a region or not.
For non-.Net folk, the variable type Drawing.PointF is merely a structure that holds a floating point coordinate.
If odd, it is inside '--Since each point connects with the next point in the array to form a line, '--and the polygon is closed, we can check to see if we "go through" it.
wiki.truevision3d.com /determine_if_a_point_is_in_region   (267 words)

 Polygon Edit Tools
The polygon that contains the start point of the selection line is merged with the one containing the end point.
The attributes of the second polygon are kept.
All the adjacent polygons with the same value in the selected dissolve fields are merged to the selected polygon.
www.ian-ko.com /et/ETUserGuide/polygon_edit_tools.htm   (546 words)

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