Haines, E.: Point in polygon strategies. In Heckbert, P., ed.: Graphics Gems IV, Academic Press (1994) 24--46  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tries to eliminate their disadvantages. Our basic idea is based on the used ray polygon intersection test. This is the last test in each collision detection that determines the intersected polygon and calculates the accurate intersection point P . Some of the fastest algorithms (see [Bad90] and [Hai94] use barycentric coordinates # and #: # V 0 P = # # V 0 V 1 # # V 0 V 2 (1) of a triangle V 0 , V 1 , V 2 for the calculation (see Figure 5) 0 2 V V V Figure 5: The illustration above shows the barycentric coordinates. In the beginning, these algorithms calculate the ....

E. Haines. Point in Polygon Strategies. In Graphics Gems IV, pages 24--46, Pittsburgh, 1994.

....of n points P 0 ,P 1 , P n 1 ,P n P 0 , determine whether R is inside or outside the polygon P . While the definition of the interior of standard geometric primitives such as circles and rectangles is clear, the interior of self intersecting closed polygons is less obvious. In literature [1,4,5,7,8,10,13,14], two main definitions can be found. The first one is the even odd or parity rule, in which a line is drawn from R to some other point S that is guaranteed to lie outside the polygon. If this line RS crosses the edges e i P i P i 1 of the polygon an odd number of times, the point is inside P ....

....odd number of times, the point is inside P , otherwise it is outside (see Fig. 1(a) This rule can easily be turned into an algorithm that loops over the edges of P , decides for each edge whether it crosses the line or not, and counts the crossings. Various implementations of this strategy exist [2 4,6,8,10 12] which differ in the way how to compute the intersection between the line and an edge and how this rather costly procedure can be avoided for edges that can be guaranteed not to cross the line. We discuss these issues in detail in Section 3. Corresponding author. E mail addresses: ....

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E. Haines, Point in polygon strategies, in: P. Heckbert (Ed.), Graphic Gems IV, Academic Press, Boston, MA, 1994, pp. 24--46.

....The test should decide whether q is inside, outside, or on the boundary of P . An approach first published by Shimrat [9] with a bug fix by Hacker [5] is to count whether moving q to infinity crosses an even or odd number of edges of P . Haines surveys this and other point in polygon tests [6]. We can represent points as homogeneous column vectors, e.g. p i = p i .x, p i .y, 1) T in three dimensions and p i = p i .x, p i .y, p i .z, 1) T in four. We can represent the 2D point at infinity along the x axis as # = 1, 0, 0) T . For mathematical details, see Stolfi s work on ....

Eric Haines. Point in polygon strategies. In Paul Heckbert, editor, Graphics Gems IV, pages 24--46. Academic Press, Boston, MA, 1994.

....of the point in the polygon is studied. For that, both the polygon and the point are projected to 2D (generally, rejecting one of the three coordinates will be sufficient) then, the inclusion of the point on the projected polygon is studied. Any test of inclusion such as the crossing count one [Haines94] or Feitos [Feito95] can be used. In the case that the point is inside the polygon, then the ray intersects the polygon. The problem of the previous process mainly lies on that the whole process is threatened by problems of integrity and precision. Besides, it is necessary to calculate the point ....

Haines, E.: Point in Polygon strategies. Ed. Glassner, A. Graphics Gems IV, Academic Press, 1994.

....distances from # # i to # # ; # # i are the projections of # # i onto # # ;and# # # # are the projections of # # i onto #,whichis the line of intersection. Otherwise, we must test if # # is totally contained in # # or vice versa. This can be done by performing a point in triangle test [Haines94] for one vertex of # # against # # and vice versa. 2.1 Optimizations Since the intervals can be translated without altering the result of the interval overlap test, equation (3) can be simplified into: # # # # # # # # # i # # # ## ## ## (5) Therefore # does not need to be computed. Also, ....

Eric Haines, "Point in Polygon Strategies," in Graphics Gems IV, edited by Paul S. Heckbert, Academic Press Professional, Cambridge, MA, pp. 24--46, 1994.

....method utilizing preprocessing via a constructive solid geometry (CSG) tree representation of polygons. This method permutes sibling nodes within the tree and prunes unnecessary edge tests to make testing the remaining edges as fast as possible. 1 1. 1 Existing Point in Polygon Algorithms Haines [10] gives a thorough comparative treatment of existing point in polygon algorithms. Haines assumed that all test points would first be clipped against the polygons bounding boxes; in his test implementation, he approximated bounding boxes by generating the polygon vertices within the unit square. ....

....box area to polygon area is high, in which case the exterior edges algorithm is fastest. Haines results indicate that the grid method [1] is the fastest algorithm when preprocessing and extra storage are available in abundance. Details of these algorithms, test timings, and code are available in [10]. 1.2 CSG Representation of Polygons In a polygon, each bounding edge defines the boundary of two half planes; orienting the edges counterclockwise about the polygon, we have that the half plane to the left of the edge is considered to be inside the polygon, and the one to the right outside. The ....

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Eric Haines. Point in polygon strategies. In Paul S. Heckbert, editor, Graphics Gems IV, chapter 1.4, pages 24--46. Academic Press, Boston, MA, USA, 1994.

....each shell of R (except its outer shell and the construction shell) check if an arbitrary vertex of the shell is in R 0 . If so, move the shell to R 0 . The problem of point in region testing can be solved using techniques similar to those used in the two dimensional version of the problem [21]. It is possible to use an algorithm that counts the number of intersections of a ray, starting at point p, against the faces of region R 0 (care should be taken in treating the difficulties introduced when the ray crosses an edge or a vertex on the boundary of R 0 ) Another possibility is an ....

Eric Haines. Point in polygon strategies. In Paul Heckbert, editor, Graphics Gems IV, pages 24--46. Academic Press, Boston, 1994.

....the table in a natural way. We concentrate on the I E Vis column, distinguishing internal (I) from external (E) visibility edges. It is natural to hypothesize that ZP information suffices to make this distinction, due to the connection to the well known ray crossings point in polygon algorithm [Hai94] [O R98, Sec. 7.4] which depends only on parity. 2 ZP Counterexample A counterexample to this hypothesis is shown in Fig. 2. 1 Let [x; y] be the chain counterclockwise from x to y. The two n = 12 vertex polygons differ in the subchains [1; 7] and [1 0 ; 7 0 ] the former lies below the ....

E. Haines. Point in polygon strategies. In Paul Heckbert, editor, Graphics Gems IV, pages 24--46. Academic Press, Boston, MA, 1994.

....geometry (CSG) tree representation of polygons. This method prunes unnecessary edge comparisons during the test, as described in Section 2. By permuting sibling nodes within the tree, as described in Section 3, we can attempt to optimize the pruning. 1. 1 Existing Point in Polygon Tests Haines [9] gives a thorough comparative treatment of existing point in polygon algorithms. Haines tested different types of polygons: regular polygons, and random, possibly self intersecting, polygons. His results indicate that the fastest oneshot method is the crossings test of Shimrat [11] as corrected by ....

....first be clipped against the polygons bounding boxes; in his test implementation, he approximated bounding boxes by generating the polygon vertices within the unit square. His tests were conducted on one particular architecture. Details of these algorithms, test timings, and code are available in [9]. 1.2 CSG Representation of Polygons In a polygon, each bounding edge defines the boundary of two half planes; orienting the edges counterclockwise about the polygon, we have that the halfplane to the left of the edge is considered to be inside the polygon, and the one to the right outside. The ....

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Eric Haines. Point in polygon strategies. In Paul S. Heckbert, editor, Graphics Gems IV, chapter 1.4, pages 24--46. Academic Press, Boston, MA, USA, 1994.

....DOUBLE, etc. 4 SET MEMBERSHIP CLASSIFICATIONS ON THE EVM 4.1 Point in Polyhedra. The chosen method is an adaptation from the wellknown crossings test [Shimr62] also known as the parity, or even odd test [Prepa85, M nty88] This test leads to the fastest algorithm without any preprocessing [Haine94]. The adaptation consists in considering a semi line parallel to the A axis (B axis for the 2D case) starting from and ending at the test point. Then a sweep plane(line) like process is performed, which starts with an OUT condition and updates it whenever the OPP boundary is crossed (or just ....

....with the proposed one. The experimental results show that the average EVM performance is quite better than other methods, and not too far from the optimum (the W k case study) The above methods use the vertex list as their only data structure. Faster O(log n) methods have been developed elsewhere [Haine94], but they need to do a preprocess to generate an alternate polyhedron representation and or additional efficiency structures. Similarly in [Aguil98a] other OPP representation and data structure are proposed, that allows us to do most of the set membership classifications in time O(log n) 7 ....

Haines,E: Point in Polygon Strategies. In Heckbert,P, editor, Graphics Gems IV. pp.2446. Academic Press, Boston, 1994.

....far less memory intensive than the grid method and faster than basic methods. Keywords: Geometric Modeling, Rendering Algorithms Using CSG Representations of Polygons for Practical Point in Polygon Tests (Extended Abstract) There have been many point in polygon test algorithms presented; Haines [1] gives a thorough comparative treatment of existing point in polygon algorithms, and the terminology that we use is based upon that work. The best of the current methods utilizing a preprocessing phase (the grid method [1] requires a lot of extra storage in addition to the basic polygon ....

....There have been many point in polygon test algorithms presented; Haines [1] gives a thorough comparative treatment of existing point in polygon algorithms, and the terminology that we use is based upon that work. The best of the current methods utilizing a preprocessing phase (the grid method [1]) requires a lot of extra storage in addition to the basic polygon information. We present a method based on constructive solid geometry (CSG) representations of polygons [2] requiring only two integers and three reals per edge plus an integer and two pointers per polygon (the original ....

[Article contains additional citation context not shown here]

Eric Haines. Point in polygon strategies. In Paul S. Heckbert, editor, Graphics Gems IV, chapter 1.4, pages 24--46. Academic Press, Boston, MA, 1994.

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Haines, E.: Point in polygon strategies. In Heckbert, P., ed.: Graphics Gems IV, Academic Press (1994) 24--46

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Haines, E.: Point in polygon strategies. In Heckbert, P., ed.: Graphics Gems IV, Academic Press (1994) 24--46

No context found.

E. Haines. Point in polygon strategies. In P.S. Heckbert, editor, Graphics Gems IV, pages 24--46. Academic Press, 1994.

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Haines, E. Point in Polygon Strategies. Graphics Gems IV. Academic Press, 1994.

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