A 3D inclusion test on large dataset

This paper proposes a 3D inclusion test which enables processing very large datasets in a limited amount of time. Each point in the dataset is provided with a label according to its location relative to a polyhedron. These 3D objects can be modeled in a number of ways, related to its purpose or application in which it is used. The two representation types considered in this paper are the Boundary Representation (B-Rep) and the Constructive Solid Geometry (CSG). In order to be able to process a large amount of points in a relative limited amount of time, a preprocessing phase is essential prior to performing a sequence of operations. In this initial step, the space is subdivided into a 3D array of voxels. The voxelization procedure deviates slightly between the two representation types, but the general principle remains the same. This subdivision allows fast retrieval of the status (inside/outside) of a very large amount of points in space.

[1]  Tian-Yuan Shih,et al.  On the complexity of point-in-polygon algorithms , 1997 .

[2]  Robert J. Walker,et al.  Practical Point-in-Polygon Tests Using CSG Representations of Polygons , 1999, ALENEX.

[3]  G. Taylor,et al.  POINT IN POLYGON TEST , 1994 .

[4]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[5]  Sébastien Thon,et al.  A Low Cost Antialiased Space Filled Voxelization Of Polygonal Objects , 2004 .

[6]  Eric Haines,et al.  Point in Polygon Strategies , 1994, Graphics Gems.

[7]  Kai Hormann,et al.  The point in polygon problem for arbitrary polygons , 2001, Comput. Geom..

[8]  Francisco R. Feito-Higueruela,et al.  Orientation, simplicity, and inclusion test for planar polygons , 1995, Comput. Graph..

[9]  Rafael Jesús Segura,et al.  Point in solid strategies , 2005, Comput. Graph..

[10]  Michael N. DeMers,et al.  Fundamentals of Geographic Information Systems , 1996 .

[11]  Wencheng Wang,et al.  Point-in-polygon tests by convex decomposition , 2007, Comput. Graph..

[12]  Ivana Kolingerová,et al.  A cell-based point-in-polygon algorithm suitable for large sets of points , 2001 .

[13]  Wencheng Wang,et al.  2D point-in-polygon test by classifying edges into layers , 2005, Comput. Graph..

[14]  Francisco R. Feito-Higueruela,et al.  Inclusion test for general polyhedra , 1997, Comput. Graph..

[15]  Paul S. Heckbert,et al.  Graphics gems IV , 1994 .

[16]  Borut Zalik,et al.  Point-in-polygon tests for geometric buffers , 2005, Comput. Geosci..

[17]  Hongsheng Chen,et al.  Hardware accelerated voxelization , 2000, Comput. Graph..